RADIO LOCATION FINDING

Abstract

A method (1) for passively locating a radio emission source (2a, 2b) is described. The method includes including receiving radio signal datasets (D) corresponding to each of three of more sensors (3). Each sensor (3) includes at least one radio receiver (4). The method also includes receiving or retrieving a physical location corresponding to each sensor (3). The physical locations define a convex hull (5). The method also includes determining whether an emitter signal (8) within a target frequency range is present in any of the radio signal datasets (D), and assigning any radio signal dataset which comprises the emitter signal as a detection dataset. The method also includes, in response to determining three or more detection datasets, calculating a signal location (r) based on arrival times of the emitter signal and the respective physical locations. The method also includes generating a locus of possible positions based on calculating two or more alternative signal locations. Each alternative signal location is calculated by adding synthetic noise to one or more of the detection datasets and repeating the calculations used to calculate the signal location. When the signal location is inside the convex hull, cluster filtering based on circles or spheres is applied. When the signal location is outside the convex hull, cluster filtering is based on ellipses or ellipsoids and on the locus of possible positions. The method also includes outputting one or more estimated radio emission source locations. Each estimated radio emission source location is determined based on a respective cluster of signal locations.

Claims

1. A method of passively locating a radio emission source, comprising: receiving radio signal datasets corresponding to each of three of more sensors, each sensor comprising at least one radio receiver; receiving or retrieving a physical location corresponding to each sensor, wherein the physical locations define a convex hull; determining whether an emitter signal within a target frequency range is present in any of the radio signal datasets, and assigning any radio signal dataset which comprises the emitter signal as a detection dataset; in response to determining three or more detection datasets: calculating a signal location based on arrival times of the emitter signal and the respective physical locations; generating a locus of possible positions based on calculating two or more alternative signal locations, each alternative signal location calculated by adding synthetic noise to one or more of the detection datasets and repeating the calculations used to calculate the signal location; in response to the signal location is within the convex hull, applying a first cluster filter to the signal location and previously calculated signal locations within a preceding time period, wherein the first cluster filter applies circular or spherical boundaries having a fixed radius for each of the signal location and the previously calculated signal locations; in response to the signal location is outside the convex hull, applying a second cluster filter to the signal location and the previously calculated signal locations within the preceding time period, wherein the second cluster filter applies elliptical or ellipsoidal boundaries for each of the signal location and the previously calculated signal locations, each elliptical or ellipsoidal boundary having a long axis and a short axis with length equal to the fixed radius, wherein a ratio of the long and short axes is equal to a ratio of maximum and minimum distances spanning the respective locus of possible locations, and the long axis is aligned parallel to the maximum distance; outputting one or more estimated radio emission source locations, each estimated radio emission source location determined based on a respective cluster of signal locations.

2. A method according to claim 1, wherein determining whether the emitter signal within the target frequency range is present in any of radio signal datasets comprises performing a correlation analysis of each radio signal dataset against each other radio signal dataset.

3. The method according to claim 1, wherein in response to determining three detection datasets, the signal location is calculated in two dimensions; or wherein in response to determining four or more detection datasets, the signal location is calculated in three dimensions.

4. (canceled)

5. The method according to claim 1, wherein the signal location is only calculated in response to determining four or more detection datasets, and wherein the signal location is calculated in three dimensions.

6. The method according to claim 1, wherein the signal location and/or any previously calculated signal locations are projected onto a two-dimensional surface prior to application of the first and second cluster filters.

7. The method according to claim 1, wherein adding synthetic noise to a detection dataset comprises applying a temporal offset to that detection dataset.

8. The method according to claim 1, wherein adding synthetic noise to a detection dataset comprises generating a noise signal and adding it to that detection dataset.

9. The method according to claim 1, wherein the locus of possible positions is generated by fitting a curve or surface to the alternative locations.

10. The method according to claim 1, wherein an estimated radio emission source location is determined and output to correspond to each cluster of signal locations which includes more than a threshold number.

11. The method according to claim 1, wherein each estimated radio emission source location is determined as an average of a respective cluster of signal locations.

12. The method according to claim 1, wherein each estimated radio emission source location is determined by: fitting a linear regression line to the respective cluster of signal locations; extrapolating the linear regression line to the output time.

13. The method according to claim 1, further comprising tracking clusters of signal locations across the preceding time period, wherein: in response to a cluster is stationary, determining the estimated radio emission source location as an average of the signal locations belonging to that cluster; in response to a cluster is moving, fitting a linear regression line to the signal locations belonging to that cluster and extrapolating the linear regression line to an output time.

14. The method according to claim 1, further comprising causing one or more optical telescopes and/or hardware drone countermeasures to be directed towards a corresponding estimated radio emission source location.

15. The method according to claim 1, further comprising: based on the signal location and the previously calculated signal locations within the preceding time period, determining a bearing angle which maximises a number of signal locations within an angular threshold of the bearing angle.

16. A method according to claim 15, further comprising receiving or calculating an outer perimeter such that, when viewed from any position on the outer perimeter, the convex hull subtends a fixed angle; wherein application of the first cluster filter is further conditional upon the signal location is within the outer perimeter; wherein application of the second cluster filter is further conditional upon the signal location is within the outer perimeter.

17. A method of calculating a bearing to a radio emission source, comprising: receiving radio signal datasets corresponding to each of three of more sensors, each sensor comprising at least one radio receiver; receiving or retrieving a physical location corresponding to each sensor, wherein the physical locations define a convex hull; determining whether an emitter signal within a target frequency range is present in any of the radio signal datasets, and assigning any radio signal dataset which comprises the emitter signal as a detection dataset; in response to determining three or more detection datasets: calculating a signal location based on arrival times of the emitter signal and the respective physical locations; based on the signal location and previously calculated signal locations within a preceding time period, determining a bearing angle which maximises a number of signal locations within an angular threshold of the bearing angle; outputting the bearing angle.

18. Apparatus for passively locating a radio emission source, comprising: a communications interface configured to receive radio signal datasets corresponding to each of three of more sensors, each sensor comprising at least one radio receiver; wherein the communications interface is further configured to receive a physical location corresponding to each sensor, or the apparatus stores the physical locations and is configured to retrieve the physical locations, wherein the physical locations define a convex hull; the apparatus configured: to receive radio signal datasets corresponding to each of three of more sensors, each sensor comprising at least one radio receiver; to receive or retrieve a physical location corresponding to each sensor, wherein the physical locations define a convex hull; to determine whether an emitter signal within a target frequency range is present in any of the radio signal datasets, and to assign any radio signal dataset which comprises the emitter signal as a detection dataset; in response to determining three or more detection datasets: to calculate a signal location based on arrival times of the emitter signal and the respective physical locations; to generate a locus of possible positions based on calculating two or more alternative signal locations, each alternative signal location calculated by adding synthetic noise to one or more of the detection datasets and repeating the calculations used to calculate the signal location; in response to the signal location is within the convex hull, to apply a first cluster filter to the signal location and previously calculated signal locations within a preceding time period, wherein the first cluster filter applies circular or spherical boundaries having a fixed radius for each of the signal location and the previously calculated signal locations; in response to the signal location is outside the convex hull, to apply a second cluster filter to the signal location and the previously calculated signal locations within the preceding time period, wherein the second cluster filter applies elliptical or ellipsoidal boundaries for each of the signal location and the previously calculated signal locations, each elliptical or ellipsoidal boundary having a long axis and a short axis with length equal to the fixed radius, wherein a ratio of the long and short axes is equal to a ratio of maximum and minimum distances spanning the respective locus of possible locations, and the long axis is aligned parallel to the maximum distance; to output one or more estimated radio emission source locations, each estimated radio emission source location determined based on a respective cluster of signal locations.

19. A system comprising: three or more sensors, each sensor comprising at least one radio receiver, wherein physical locations of the sensors define a convex hull; the apparatus according to claim 18, configured to receive respective radio signal datasets from the three or more sensors.

20. The system according to claim 19, wherein each sensor is configured to transmit the corresponding radio signal dataset continuously.

21. The system according to claim 19, wherein each sensor is configured to locally cache the respective radio signal dataset and to transmit the cached radio signal dataset to the apparatus in batches.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Certain embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:

[0048] FIG. 1 is a schematic plan view of a system for radio location finding;

[0049] FIG. 2 is a schematic block diagram of the system shown in FIG. 1;

[0050] FIG. 3 is a process flow diagram of a method of radio location finding;

[0051] FIG. 4 is a schematic block diagram of a sensor for use in the system shown in FIG. 1;

[0052] FIG. 5 schematically illustrates the same signal being received at different times by sensors at different physical locations;

[0053] FIGS. 6A to 6D schematically illustrate a sliding window correlation analysis between a pair of signals;

[0054] FIG. 7 schematically illustrates applying synthetic noise to a set of correlated signals to estimate the sensitivity of a calculated signal location to noise;

[0055] FIG. 8 schematically illustrates determining a locus of possible positions representing the sensitivity of a calculated signal location to noise;

[0056] FIG. 9 schematically illustrates variability in sequentially calculated signal locations;

[0057] FIG. 10 schematically illustrates application of a first cluster filter;

[0058] FIG. 11 schematically illustrates application of a second cluster filter;

[0059] FIG. 12 schematically illustrates angular bins for determining a bearing angle;

[0060] FIG. 13 is a histogram corresponding to FIG. 12;

[0061] FIG. 14 schematically illustrates the definition of an outer perimeter for an arrangement of sensors; and

[0062] FIG. 15 schematically illustrates the definition of an outer perimeter for a different arrangement of sensors to that shown in FIG. 14.

DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS

[0063] In the following, like parts are denoted by like reference numerals.

[0064] The present specification concerns improvements in time-of-arrival based methods for determining a location of and/or bearing to a radio emission source. In particular, the present specification concerns improvements in estimating radio emission source locations which are outside a convex hull defined by the locations of sensors (radio receivers).

[0065] The methods described herein may be applied to wide-band radio receivers, removing the need to know a transmission frequency of a radio emission source in advance.

[0066] Although often described herein in relation to detection of unauthorised radio emission sources such as drones, the methods of the present specification are equally applicable to any application concerning passive location of one or more radio emission sources.

[0067] Referring to FIG. 1, a system 1 for passively locating a radio emission source 2 is shown.

[0068] Referring also to FIG. 2, a block diagram of the system 1 is shown.

[0069] The system 1 includes three or more sensors 3. Each sensor 3 includes (or takes the form of) at least one radio receiver 4 (FIG. 4). The sensors 3 are spread across a region, for example around and/or within the perimeter of an airport. The physical locations of each sensor 3, for example coordinates (x, y) in a local coordinate system or a latitude and longitude, are either known in advance or included in data sent from that sensor 3. The physical locations of the sensors 3 define a convex hull 5. As explained herein, the processing to estimate a location of a radio emission source 2 differs between radio emission sources 2a estimated to lie within the convex hull 5 and radio emission sources 2b estimated to lie outside the convex hull 5. There may be any number N of sensors 3 in the system 1, although the minimum number is three, i.e. N≥3.

[0070] The system 1 includes an apparatus 6 for passively locating one or more radio emission sources 2. The apparatus includes a communications interface (not shown) configured to receive radio signal datasets D (FIG. 4) corresponding to each of the sensors 3 via wired and/or wireless links 7. In some examples, the apparatus 6 may receive radio signal datasets D from the sensors 3 via a mixture of wired or wireless links 7. For example, some sensors 3 may be connected to the apparatus 6 by wired links 7, whilst other sensors 3 are connected to the apparatus 6 by wireless links 7.

[0071] If the physical locations of one or more of the sensors 3 are not stored in advance within the apparatus 6, the communications interface (not shown) of the apparatus 6 may be further configured to receive a physical location corresponding to each sensor 3. In some implementations, one or more of the sensors 3 may be mobile/moveable, and may include location sensors such as, for example, an inertial compass, a global position system (GPS) receiver and so forth. Such mobile sensors 3 may update the apparatus 6 of their present location periodically, continuously, in response to a request from the apparatus 6, by including the current physical location in the corresponding radio signal dataset D, and so forth.

[0072] The system 1 is a passive location-finding system, in the sense that it relies upon detecting radio frequency signals 8 emitted by a radio emission source 2 in order to estimate a location for that radio emission source 2. This is in contrast to an active location-finding system such as radar.

[0073] In some implementations, each sensor 3 may transmit a corresponding radio signal dataset D continuously. In other words, each sensor may transmit its radio signal dataset D live or in “real time” with monitoring the spectrum or spectra corresponding to that sensor's radio receiver(s) 4 (FIG. 4). In practice, the terms “live” and/or “real time” mean transmitting with as little delay as possible, i.e. as soon as the radio signal dataset is available with no imposed delay. Such a configuration may be applicable to a use in which there is no concern about the sensors 3 being located by another party, for example, when detecting unauthorised drones being flown into/near restricted airspace.

[0074] In other implementations, each sensor 3 may be configured to locally cache its respective radio signal dataset D, and to transmit the cached radio signal dataset to the apparatus 6 in batches. For example, according to a predetermined schedule, or in response to receiving a signal from the apparatus 6. Radio signal datasets D may be transmitted regularly, for example several times per second, or every few seconds or minutes. Alternatively, radio signal datasets D may be transmitted sporadically, for example every ten minutes, every hour, or at longer intervals.

[0075] Longer caching periods may be particularly useful when live information is not important. For example, a municipal authority may wish to determine how many drones are being flown, for how long, and over which locations, as part of routine planning. A number of battery powered sensors 3 may be distributed around a region to record radio signal datasets. The radio signal datasets may be retrieved by an operator visiting the sensors 3 with the apparatus 6 or a suitable portable device, and connecting to the sensor 3 using a wired cable, a short range wireless communication protocol such as Bluetooth® and so forth.

[0076] Another approach which uses locally cached radio signal datasets is to deploy battery powered, portable sensors 3 around an area for a duration, followed by retrieving the sensors 3 and returning to a central location for data retrieval.

[0077] Battery powered sensors 3 may be used in any example of the system 1 for which a mains connection may be difficult or impractical, whether transmission of radio signal datasets D is continuous, periodic or on demand. Battery powered sensors 3 may be rechargeable using energy harvesting devices such as solar panels, wind turbines etc.

[0078] Referring also to FIG. 3, a process flow diagram of a method of passively locating a radio emission source 2 is shown.

[0079] The method is computer implemented, for example executed by one or more digital electronic processors of the apparatus 6. The apparatus 6 may take the form of a dedicated device, for example an application specific integrated circuit (ASIC). Alternatively, the apparatus 2 may take the form of a suitable programmed microcontroller, general purpose computer, and so forth.

[0080] Radio frequency datasets D corresponding to each of N≥3 sensors 3 are received (step S1). For convenience of reference in the following discussions, let the radio signal dataset D received from the n.sup.th of N sensors 3 be denoted D.sub.n. The radio signal datasets D.sub.1, . . . , D.sub.n, . . . , D.sub.N may take any suitable format, for example, in-phase and quadrature, I(t), Q(t) radio signal data corresponding to each radio receiver 4 (FIG. 4) of the respective sensor 3. Additionally or alternatively, radio signal datasets D.sub.n may include, or take the form of, more processed data such as power spectra corresponding to each radio receiver 4 (FIG. 4) of the respective sensor 3. In some examples, a radio signal dataset D.sub.n received in the form of raw IQ data may be augmented during this step by the apparatus 6 calculating the corresponding power spectra.

[0081] Referring also to FIG. 4, a block diagram of an exemplary sensor 3 is shown.

[0082] The sensor 3 includes at least one antenna 9, one or more radio receivers 4 and a controller 10 for managing and/or implementing the functions of the sensor 3. The antenna 9 may be a single antenna, or an array of antennae such as a phased array. The antenna 9 (or antennae 9) may take the form of one or more omnidirectional antennae, one or more directional antennae, or a mixture of omnidirectional antennae and directional antennae.

[0083] Whilst only a single radio receiver 4.sub.1 is required, in general the sensor 3 may include any number M≥1 of radio receivers 4.sub.1, 4.sub.2, . . . , 4.sub.m, . . . , 4.sub.M. Each radio receiver 4.sub.m may include, or be connected to the antenna(e) 9 via, a respective passband filter 11.sub.1, . . . , 11.sub.M. In this way, each radio receiver 4.sub.m may receive a different frequency range from each other receiver 4.sub.k≠m. The frequency ranges of passband filters 11.sub.m may partially overlap with the frequency range(s) of one or more other passband filters 11.sub.k≠m. Alternatively, in some implementations the frequency ranges of the passband filters 11.sub.1, . . . , 11.sub.M may be mutually exclusive.

[0084] Radio frequency signals 8 received by the antenna(e) 9 are filtered by the one or more passband filters 11.sub.1, . . . , 11.sub.M and corresponding passband signals 12.sub.1, . . . , 12.sub.M are passed to the respective radio receivers 4.sub.1, . . . , 4.sub.M. Each radio receiver 4.sub.m measures IQ data 13.sub.m and passes this to the controller 10 of the sensor 3. The controller 10 compiles the radio signal dataset D for the sensor 3, and transmits it (wired or wirelessly) to the apparatus 6.

[0085] In general, each radio receiver 4 (or the combination of radio receiver 4 and passband filter 11) may take the form of a wide-band receiver, for example having a bandwidth of 20 MHz or more, 40 MHz or more, or 100 MHz or more. Wide-band receivers may be particularly useful when the frequencies of signals 8 from radio emissions sources 2 are not known in advance. In other implementations, for example when the bandwidth of signals 8 from radio emissions sources 2 is known or predictable in advance, some or all of the radio receivers 4 may take the form of narrow-band receivers, for example each corresponding to bandwidths of 10 MHz or less, 5 MHz or less, or 1 MHz or less.

[0086] The sensor 3 shown in FIG. 4 is only one example of a suitable sensor 3 configuration. In general the system 1 may use any sensor 3 capable of detecting and recording radio signals 8.

[0087] Referring again to FIG. 3 in particular, the physical locations corresponding to each sensor 3 are received or retrieved (step S2). For example, each of N≥3 sensors 3 may correspond to a location expressed in a local coordinate system (x, y), or in terms of latitude and longitude. The physical locations of sensors 3 may also include an altitude/height of the sensor.

[0088] The method includes determining whether an emitter signal 8 within a target frequency range f.sub.low≤f≤f.sub.high is present in any of the radio signal datasets D.sub.1, . . . , D.sub.N, and any radio signal dataset D.sub.n which includes the emitter signal 8 is assigned as a detection dataset DET (step S3). The determination may be made by performing a correlation analysis amongst the radio signal datasets D.sub.1, . . . , D.sub.N. The correlation analysis may be useful because detecting a correlation between a pair of radio signal datasets D.sub.n, D.sub.k≠n may allow determining the presence of an emitter signal 8 at a lower signal-to-noise ratio than would be required if, for example, an amplitude threshold was used to trigger the process. In other applications, where signal strength is of less concern, it may be possible to use a detection based on exceeding a threshold to trigger a correlation analysis. In general, a number 0≤J≤N of the radio signal datasets D.sub.1, . . . , D.sub.N may include an emitter signal 8 within the target frequency range {f.sub.low; f.sub.high}. Hereinafter let the j.sup.th of J detection datasets be denoted as DET.sub.j.

[0089] The target frequency range {f.sub.low; f.sub.high} may be set and/or adjusted based on user input and/or automatic analysis of power spectra corresponding to radio signal datasets D.sub.n. For example, the method may include displaying power spectra corresponding to one or more of the radio signal datasets D.sub.1, . . . , D.sub.N to a user via a graphical user interface (GUI). In some implementations a power spectrum displayed to a user may be summed or otherwise aggregated across all of the radio signal datasets D.sub.1, . . . , D.sub.N. The GUI may allow a user to browse the power spectrum (or spectra) in frequency and/or time, for example by allowing a user to define a frequency range and/or time period to display. The user may then set the target frequency range {f.sub.low; f.sub.high} in response to spotting a signal within that frequency range. In some implementations, two or more different target frequency ranges {f.sub.low; f.sub.high} may be set to permit independently estimating locations for two or more radio emission sources 2 operating in different frequency bands.

[0090] Additionally or alternatively, the target frequency range(s) {f.sub.low; f.sub.high} may be set automatically based on analysis of received or calculated power spectra corresponding to the radio signal datasets D.sub.1, . . . , D.sub.N (as explained herein, power spectra may be part of each radio signal dataset D.sub.n or may be calculated by the apparatus 6). For example,

[0091] the target frequency range {f.sub.low; f.sub.high} may be set based on determining a peak in the power spectra and setting the target frequency range {f.sub.low; f.sub.high} with a pre-set bandwidth and centred on that peak. Automated determination may be restricted to particular frequency bands and/or may exclude certain frequency bands. For example, if the apparatus 6 is to be used for detecting drones approaching and/or encroaching on the airspace of an airport, then automated setting of the target frequency range {f.sub.low; f.sub.high} may be restricted to frequency bands typically used by commercially available drones, and/or the frequency bands used by the airport infrastructure may be excluded from automated determination of the target frequency range {f.sub.low; f.sub.high}.

[0092] In some implementations, an initial target frequency range {f.sub.low; f.sub.high} may be automatically determined and presented to a user via the GUI, and the user may then either accept or adjust the target frequency range {f.sub.low; f.sub.high} in terms of central frequency, bandwidth width and so forth.

[0093] Referring also to FIGS. 5 to 6D, the determination of which radio signal datasets D.sub.n are detection datasets DET.sub.j is further discussed.

[0094] FIG. 5 shows signals (for example I or Q data) as a function of time for a number N=4 of sensors 3, with the amplitudes offset relative to one another on the amplitude axis for visual clarity. The signals shown in FIG. 5 are for illustrative purposes only, and are synthetic (not measured signal data).

[0095] In this illustrative example, all four sensors 3 have captured the same signal 8, although the specific detected signal pulses 14.sub.1, 14.sub.2, 14.sub.3, 14.sub.4 differ in that they include noise. Moreover, the signal 8 reaches each sensor 3 at a slightly different time due to varying distances between the radio emission source 2 and each sensor 3.

[0096] The radio signal 8 is detected by comparing the radio signal datasets D.sub.n against each other, for example using correlation analysis as explained hereinafter. If a strong correlation is found between any pair of signals, 14.sub.1, . . . , 14.sub.4, then a signal has been detected and the corresponding signals are assigned as detection datasets DET. A radio signal 8 detected in this way from correlation analysis may then be cross-correlated with all the remaining signals to determine whether any others beyond the initial pair captured the same radio signal 8.

[0097] Alternatively, the radio signal 8 may be detected when a pulse in one of the radio signal datasets D.sub.n exceeds a threshold, for example five times a calibrated standard error for the corresponding sensor 3. This option may be useful for strong signals by allowing the length of signals which require correlation to be reduced. However, applying a detection threshold in this way may reduce the sensitivity of detection, because correlation analysis may detect a radio signal 8 has been captured in a pair of radio signal datasets D.sub.n, D.sub.k≠n at a lower signal-to-noise ratio, compared to applying an amplitude threshold.

[0098] In order to determine whether the same emitter signal 8 within the target frequency range {f.sub.low; f.sub.high} is commonly detected in two or more radio signal datasets D.sub.1, . . . , D.sub.N, a correlation analysis is performed to compare each radio signal dataset D.sub.n against each other radio signal dataset D.sub.k≠n. Generally, the entire duration of each radio signal dataset D.sub.n may be used, since it is not necessarily known in advance which if any of the radio signal datasets Dn may have captured a radio signal 8, or at what time. Alternatively, in applications were a threshold amplitude is used to obtain a positive detection, a portion of each radio signal dataset D.sub.n corresponding to a shorter window of time may be used. The first detected signal 8, whether found from correlation or from a threshold detection, is not necessarily the closest to the radio emission source 2 (for example a further sensor 3 may have a clearer line-of-sight), and consequently the apparatus 6 may also need to retrieve (also referred to as “backhauling”) data from each other radio signal dataset D.sub.n for at least a period of time extending before and after the first detection.

[0099] The correlation analysis preferably takes the form of a sliding-window correlation analysis, although any other technique known for signal correlations may be used instead. The correlation analysis may be performed based on amplitude data, complex IQ data, and so forth.

[0100] For example, a correlation analysis between a pair of radio signal datasets D.sub.n, D.sub.k≠n may be calculated as:

CORR.sub.n,k(Δt)=∫.sub.−∞.sup.∞A.sub.n(τ+Δt)A.sub.k(τ)dτ  (1)

[0101] In which A.sub.n(t) is the amplitude of a signal belonging to the n.sup.th radio signal dataset D.sub.n, A.sub.k(t) is the amplitude of the corresponding signal belonging to the k.sup.th radio signal dataset (k≠n), Δt is the offset in time applied to the signal A.sub.n(t), and τ is a dummy variable for the integration. The signals A.sub.n(t) and A.sub.k(t) may be normalised prior to calculating the value of the correlation integral CORR.sub.n,k(Δt). The signals A.sub.n(t) and A.sub.k(t) have finite duration and will be evaluated using numerical integration of Equation (1). An identical length segment is selected from each signal A.sub.n(t) and A.sub.k(t). Either or both signals A.sub.n(t) and A.sub.k(t) may be truncated or padded using zero-insertion prior to numerical evaluation of Equation (1).

[0102] Referring in particular to FIG. 6A, the signals 14.sub.3 (dashed line) and 14.sub.4 (solid line) shown in FIG. 5 are shown on the same axes without offsetting along the amplitude axis and for a time offset of zero (Δt=0).

[0103] Referring in particular to FIGS. 6B and 6C, the same signal signals 14.sub.3 (dashed line) and 14.sub.4 (solid line) are shown when the signal 14.sub.3 for the third sensor 3 are offset by different amounts towards correspondence with the signal 14.sub.4 for the fourth sensor 3. It may be observed that the contribution towards a net value of the correlation integral CORR.sub.n,m(Δt) will increase when the signals 14.sub.3, 14.sub.4 are offset so as to correspond with one another.

[0104] Referring in particular to FIG. 6D, the correlation integral CORR.sub.n,k(Δt) is evaluated for a range of time offsets Δt corresponding to the width of the sliding window. A peak in the value of the correlation integral CORR.sub.n,k(Δt) represents a likely correlation. A minimum threshold value of the correlation integral CORR.sub.n,k(Δt) may be applied to prevent false positives. In some examples, the correlation integral CORR.sub.n,k(Δt) may exhibit multiple peaks, in which case the largest peak is taken to represent the best offset Δt value. A signal may be detected as correlated to a first detected signal even if that signal has relatively worse signal-to-noise ratio.

[0105] In addition to determining whether two or more radio signal datasets D.sub.1, . . . , D.sub.N include detection of the same signal 8 and may be assigned as detection datasets DET.sub.j, the correlation analysis also determines the offsets Δt between arrival times of that signal 8 at each sensor 3. These offsets Δt are used later in the method for estimating the location of the radio emission source 2.

[0106] Referring again in particular to FIG. 3 if fewer than three detection datasets DET.sub.j are determined, i.e. J<3 (step S4|No), then no estimate of radio emission source 2 location is made, and the method proceeds to receiving subsequent radio signal datasets D.sub.1, . . . , D.sub.N (step S1).

[0107] However, if three or more detection datasets DET.sub.j are determined, i.e. J≥3 (step S4|Yes), then the method proceeds to calculation of a signal location r for the radio emission source 2 based on arrival times of the emitter signal 8 and the respective physical locations of the detecting sensors 3 (step S5). For example, the previously calculated offsets Δt may be used. Estimating the signal location r of an emission source 2 based on time-of-arrival data may be carried out using any known method.

[0108] The signal location r calculated at this stage should be differentiated from an estimated radio emission source location R which is subsequently calculated (step S10) based on calculated signal locations r spanning a time period T.

[0109] If there are only J=3 detection datasets DET.sub.j, then there is no choice and all three must be used to calculated a signal location r in two dimensions 9 (i.e. in a local coordinate system x-y or latitude-longitude). However, if there are J≥4 detection datasets DET.sub.j, then the signal location r may be estimated in three dimensions to add an estimation of altitude/height. Whether the signal location r is calculated in two or three dimensions (using three or four detection datasets DET.sub.j), if there are more detection datasets DET.sub.j then the minimum required, then a subset of the J detection datasets DET.sub.j may be used to estimate the signal location r. A subset may be chosen based on any suitable criteria including, but not limited to:

[0110] Using the subset (three or four) of detection datasets DET.sub.j corresponding to the strongest signals;

[0111] Using the subset of detection datasets DET.sub.j which correspond to the longest baseline;

[0112] Using the subset of detection datasets DET.sub.j which correspond to the largest area. The area corresponding to a group of three of more detection datasets DET.sub.j may correspond to a second convex hull defined by the respective physical locations of that group of detection datasets DET.sub.j;

[0113] Using a weighted combination of the preceding factors to determine the subset to use.

[0114] Alternatively, all of the detection dataset DET.sub.1, . . . , DET.sub.J may be used to produce a refined estimate of the signal location r corresponding to an emission source 2.

[0115] The calculation of the signal location r in two or three dimensions may be made conditional upon the number J of detection datasets DET.sub.j, for example in two dimensions when J=3, and in three dimensions when J≥4. Alternatively, the signal location r may always be calculated in two or three dimensions (three dimensions would require the minimum value of J to be set to J=4)

[0116] A locus of possible positions 15 (FIG. 8) is generated based on calculating two or more alternative signal locations p (step S6). Each alternative signal location p is calculated by adding synthetic noise to one or more of the detection datasets DET.sub.j, followed by repeating the signal location calculations using the modified data.

[0117] Referring also to FIGS. 7 and 8, generation of the locus of possible positions 15 is discussed.

[0118] Referring in particular to FIG. 7, normalised correlation integral values are illustrated for a case in which there are J=5 detection datasets DET.sub.j. The correlation integral values shown in FIG. 7 are synthetic for illustrative purposes.

[0119] One detection dataset DET.sub.j, for the sake of illustration the fifth DET.sub.5, is taken as a reference, and the time offsets Δt are calculated relative to this reference. Offset Δt.sub.1 is the time delay between the first DET.sub.1 and fifth DET.sub.5 detection datasets, offset Δt.sub.2 is the time delay between the second DET.sub.2 and fifth DET.sub.5 detection datasets, and so forth.

[0120] In one example, adding synthetic noise to a detection dataset DET.sub.j may take the form of applying a temporal offset δt to a time difference Δt corresponding to that detection dataset DET.sub.j. For example, to calculate an alternative signal location p, at least one of the detection datasets DET.sub.j may have an offset δt added or subtracted, whilst each other detection dataset DET.sub.k≠j may be unchanged, may have the offset δt added, or may have the offset δt subtracted. The process of calculating the signal location r is then repeated using the modified time differences Δt to calculate an alternative position location p. For the example shown in FIG. 7, the modified time differences would correspond to {Δt.sub.1±δt, Δt.sub.2±δt, Δt.sub.3±δt, Δt.sub.4±δt}. Each temporal offset δt may take the form of the same fixed time interval. Alternatively, in some examples each temporal offset δt may take the form of a (pseudo) randomly interval generated using a probability density function (i.e. every temporal offset δt value used is generated as a new, different value).

[0121] When the temporal offset δt takes the form of a fixed interval, one option for generating the alternative signal locations p is to take each detection dataset DET.sub.j in turn, then shift the time difference Δt for that detection dataset DET.sub.j forwards by the fixed temporal offset δt and calculate a first alternative signal location p, followed by shifting the time difference Δt for that detection dataset DET.sub.j backwards by the fixed temporal offset δt and calculating a second alternative signal location p. Once repeated for each detection dataset DET.sub.j, this will generate a number of 2.J alternative signal locations p.

[0122] Alternatively, the locus of possible locations 15 may be generated by calculating an alternative signal location p corresponding to every possible permutation (excluding doing nothing at all) of adding the fixed interval δt, subtracting the fixed interval δt, and doing nothing. When every possible permutation is calculated, the number of alternative signal locations p will be 3.J-1 (the minus one corresponds to the fact that doing nothing to the time differences Δt for all detection datasets simply corresponds to the signal location r).

[0123] In a further implementation, each alterative signal location p may be generated by applying a different pseudo-random temporal offset δt to each time difference Δt, with the temporal offsets δt generated in accordance with a probability density function centred at zero offset. A set of alternative signal locations p may be built up by repeating this process a predetermined number of times, for example 10 or more, 20 or more, 50 or more, or 100 or more times.

[0124] An advantage of the preceding methods is that the temporal offset(s) δt are applied directly to the time differences Δt already known from the correlation analysis of step S3. In this way, a measure of the sensitivity of the signal location r calculation to noise may be obtained without the need to repeat the correlation analysis in full. Such approaches may be less computationally intensive, reducing latency and/or power consumption.

[0125] In other examples, temporal offsets δt may be generated in any way described hereinbefore, then instead applied to the raw data of the detection datasets DET.sub.j, for example offsetting amplitude data and/or IQ data, followed by repetition of the correlation analysis.

[0126] Alternatively, adding synthetic noise to a detection dataset DET.sub.j may take the form of generating a noise signal (using a probability density function) and adding the generated noise signal to that detection dataset DET.sub.j, for example to the amplitude data and/or IQ data. The correlation analysis may then be repeated to determine time differences Δt for the modified datasets, and a corresponding alternative signal location calculated. This process may be repeated a number of times to build up a set of alternative signal locations p, for example 10 or more, 20 or more, 50 or more, or 100 or more times.

[0127] Once a set of at least two alternative signal locations p has been generated, the locus of possible locations 15 may be determined using the alternative signal locations p, and optionally also the calculated signal location r.

[0128] In one example, the locus of possible locations 15 may simply be assigned as the set of all the alternative signal locations p generated, optionally plus the calculated signal location r.

[0129] Another approach is to generate the locus of possible locations by fitting a curve (in two dimensions) or a surface (in three dimensions) to the alternative signal locations p (optionally plus the calculated signal location r).

[0130] For example, the locus of possible locations 15 may take the form of a curve (or surface) positioned, sized and orientated to enclose every alternative signal location p (and optionally the calculated signal location r) whilst minimising the area (or volume) within that curve (or surface). Referring in particular to FIG. 8, the rectangle 15a (dashed line) having side lengths w.sub.1 and w.sub.2 may be assigned as the locus of possible locations 15. The rectangle 15a may be fitted by varying the centroid, angle, and lengths w.sub.1, w.sub.2, to find the minimum area w.sub.1, w.sub.2 which encloses all of the alternative signal locations p.

[0131] A rectangle need not be used, and any other regular or irregular shape may be used instead. Alternatively, instead of fitting a particular shape, the locus of possible locations 15 may be generated by fitting a piecewise continuous curve or surface, or a further convex hull determined based on the alternative signal locations p.

[0132] Instead of enclosing all of the alternative signal locations p, the locus of possible locations 15 may instead be calculated as a curve (or surface) which corresponds to a particular confidence level, for example, between 50% and 95%. The curve (or surface) may be further constrained to have a particular shape, for example an ellipse (ellipsoid or oblate/prolate spheroid). Referring in particular to FIG. 8, the ellipse 15b (chained line) represents a locus of possible positions 15 in the form of a confidence boundary ellipse.

[0133] A still further alternative is to determine the locus of possible locations 15 as a curve (or surface) which encloses a threshold fraction of the alternative signal locations p, for example a fraction selected to be between 0.5 and 0.99. The curve (or surface) may be further constrained to have a particular shape, for example an ellipse (ellipsoid or oblate/prolate spheroid).

[0134] Referring again in particular to FIG. 3, following generation of the locus of possible positions 15 (step S6), it is determined whether the calculated signal location r lies inside or outside the convex hull 5 corresponding to the physical locations of the sensors (step S7). Alternatively, this determination (step S7) may be made based on whether any (or all) of the calculated signal location r and all previously calculated signal locations r within a preceding time period T are inside or outside the convex hull 5.

[0135] If the calculated signal location r is within the convex hull 5 (step S7|Yes) a first cluster filter is applied to the calculated signal location r and previously calculated signal locations within a preceding time period T (step S8). The first cluster filter applies circular (or spherical) boundaries having a predetermined radius w.sub.0 (FIG. 10).

[0136] If the calculated signal location r is outside the convex hull (step S7|No), a second cluster filter is applied to the calculated signal location r and the previously calculated signal locations within the preceding time period T (step S9). The second cluster filter applies elliptical (ellipsoidal or oblate/prolate spheroidal) boundaries having a short axis equal to the radius w.sub.0 used for the first cluster filter, and a ratio of long and short axes which is equal to a ratio of maximum and minimum distances spanning the locus of possible positions 15. For example, the ratio would be w.sub.2/w.sub.1 with w.sub.1=w.sub.0 using the rectangular locus 15a shown in FIG. 8, or the ratio of semi-major and semi-minor axes of the elliptical locus 15b shown in FIG. 8. The long axis of each elliptical (ellipsoidal or oblate/prolate spheroidal) boundary is aligned parallel to a direction which corresponds to the maximum distance spanning the locus of possible positions 15.

[0137] The second cluster filter (step S9) may apply ellipsoidal boundaries in the form of tri-axial ellipsoids, in which case there may be a further, intermediate axis in addition to the long and short axes. When the second cluster filter (step S9) applies ellipsoidal boundaries in the form of spheroids, the long axis or the short axis may correspond to a pair of axes having equal length (oblate has a pair of equal long axes and prolate a pair of short axes).

[0138] The first and second cluster filters (steps S8, S9) preferably take the form of nearest neighbour cluster analysis methods. The first and second cluster filters (steps S8, S9) may be applied in two or three dimensions in dependence on whether the signal locations r are calculated in two or three dimensions. For simplifying calculations, or when there is a mixture of two and three dimensional calculated signal locations r, the signal location r and/or any previously calculated signal locations r may be projected onto a two-dimensional surface prior to application of the first and second cluster filters (steps S8, S9). Where the extent of coverage for the system 1 is relatively small, the two-dimensional surface for projections into two dimensions may take the form of a plane. However, when the extent of coverage of the system 1 is larger, such that the shape of the Earth cannot be neglected, the two-dimensional surface for projections into two dimensions may instead take the form of a portion of a spherical surface (e.g. corresponding to altitude at the system 1 location, sea level etc). If the information is available for the location surrounding the system 1, the two-dimensional surface for projections into two dimensions may correspond to the ground (i.e. the surface of the earth/local topographic relief), in the form of land, water or a combination.

[0139] Referring also to FIGS. 9 to 11, the cluster filtering processes (steps S8, S9) are further explained.

[0140] FIG. 9 shows a series of calculated locations r corresponding to a preceding time period.

[0141] Every time a signal location r is calculated, it is added to a buffer (or similar/equivalent data structure) which stores the present location r and all the previously calculated locations r within a given time period T Whilst signal locations r need not be calculated at regular intervals, this is expected to be common in practice. For the sake of the following explanation it will be assumed that the method of FIG. 3 is carried out at intervals of duration α, where the time period T corresponds to a number H of intervals a, i.e. T=H.Math.α. Let the location calculated corresponding to time t−h.Math.α be denoted as r.sub.h with h an integer 0≤h≤H (such that r.sub.0 is the most recently calculated signal location). The calculated signal location r and the previously calculated signal locations within the preceding time period T would then correspond to the set {r.sub.0, r.sub.1, . . . , r.sub.h, . . . , r.sub.H}, for example stored in a buffer for use by the cluster filtering steps (S8 or S9) of the method.

[0142] In the example shown in FIG. 9, H=15. The nature of time-of-arrival location finding calculations results in the influence of noise causing calculated locations r.sub.1, . . . , r.sub.H to become elongated approximately along a line 16 passing through the centroid of the set of sensors 3 used for the calculation. Although there may be little or no elongation within the convex hull 5, the further outside the convex hull 5 the true location of an emission source 2 is, the more pronounced that elongation becomes.

[0143] The example shown in FIG. 9 corresponds schematically to a set {r.sub.0, r.sub.1, . . . , r.sub.h, . . . , r.sub.H} which might be observed for an emission source 2 lying outside the convex hull 5, for example emission source 2b shown in FIG. 1. The dashed ellipses shown in FIG. 9 correspond to the loci 15 of possible positions calculated for the corresponding signal locations r.sub.h, in the form of confidence ellipses. The loci of possible positions 15 may be aligned along different directions for each calculated location r.sub.h, for example because subset of sensors 3 used (and hence the corresponding centroid) may be different between calculations of signal location r.

[0144] In order to provide the most accurate estimation of the location R of an emission source 2, it is desirable to combine multiple calculated signal locations belonging to the set {r.sub.0, r.sub.1, . . . , r.sub.h, . . . , r.sub.H}. Cluster filtering is applied to screen out outliers (see for example r.sub.4 and r.sub.9 in FIG. 9). Within the convex hull 5, the hereinbefore described elongation along the line 16 is relatively minor (or non-existent), and cluster filtering using circular (in 2D) or spherical (in 3D) bounding surfaces may be applied. However, outside the convex hull, the inventors have observed from simulations and field trials that the elongation of calculated signal locations resulting from the combination of noise with the nature of time-of-arrival location finding (multilateration) calculations, renders conventional cluster filtering techniques less effective. Whilst the bounding surfaces for cluster filtering may be elongated to an ellipse (in 2D) or an ellipsoid (in 3D, for example a prolate spheroid), the question remains of what aspect ratio to use. The inventors have observed from simulations and field trials that using a fixed aspect ratio is not appreciably more effective than simply using a larger circle (or sphere). Instead, the inventors have determined from simulations and field trials that the accuracy of cluster filtering and locating an emission source 2 outside the convex hull 5 defined by the sensors may be improved based on the outputs of generating a locus of possible positions 15 (step S6). In particular, the second cluster filter (step S9) uses bounding surfaces having an aspect ratio which is independently set for each location r.sub.h of the set {r.sub.0, r.sub.1, . . . , r.sub.h, . . . , r.sub.H} to be equal to the aspect ratio of the corresponding locus r.sub.h of possible positions 15.

[0145] Referring in particular to FIG. 10, a schematic example of applying the first cluster filter (step S8) is shown.

[0146] In FIG. 10, the set {r.sub.0, r.sub.1, . . . , r.sub.h, . . . , r.sub.H} of the calculated signal location r.sub.0 and the previously calculated signal locations r.sub.1, . . . , r.sub.h, . . . , r.sub.H within the preceding time period T corresponds to H=8. The relative locations shown are schematic and intended for illustrative purposes. The dashed circles illustrate circular bounding curves 17 of fixed radius w.sub.0, and for visual clarity a bounding curve 17 is not drawn for the most recently calculated signal location r.sub.0.

[0147] There are two main approaches to the cluster filtering. In the first approach, for a pair of locations r.sub.h, r.sub.k≠h to be clustered the bounding circle 17 of one location r.sub.h, must encompass or intersect the location of the other r.sub.k≠h (the reverse is true by default for the first cluster filter). In the second approach, the requirement is relaxed such that a pair of locations r.sub.h, r.sub.k≠h are clustered if their respective bounding circles 17 overlap. In either case, more than one cluster may be determined, and locations r.sub.h, r.sub.k≠h which are not clustered when considered independently may become clustered via further locations.

[0148] Applying the first approach to the example shown in FIG. 10, r.sub.0 is within the bounding circles 17 of each of r.sub.2, r.sub.5 and r.sub.6 so these form a cluster. Moreover, r.sub.3 is within the bounding circle 17 of r.sub.6, and so is added to the overall cluster which is the set {r.sub.0, r.sub.2, r.sub.3, r.sub.5, r.sub.6}. Each of r.sub.1, r.sub.4 and r.sub.7 as illustrated is too far from any other location r.sub.h to form even a cluster of two.

[0149] In both the first and second cluster filters (steps S8, S9), clusters of between two and a minimum threshold number of locations r.sub.h (e.g. 5, 10 etc) may be ignored.

[0150] Applying the second approach, locations r.sub.4 and r.sub.7 remain outside the cluster, since the respective bounding circles 17 do not intersect those of any other locations r.sub.h. However, the bounding circle 17 of the location r.sub.1 intersects at least the bounding circle 17 of the location r.sub.5, so that r.sub.1 is also added to the cluster {r.sub.0, r.sub.1, r.sub.2, r.sub.3, r.sub.5, r.sub.6}.

[0151] Although in some examples clustering may be implemented such that a cluster may only grow from the most recently calculated signal location r.sub.0, it is preferred that clustering be permitted to grow from any location r.sub.h. This may result is determining two or more distinct clusters. If two or more clusters both exceed a minimum threshold number of locations r.sub.h, this may be indicative of two distinct radio emission sources 2.

[0152] The radius w.sub.0 used for a given system 1 will depend on a variety of factors including the specifics of the sensors 3, their physical locations, the local electromagnetic noise environment, and type of emission sources 2 it is desired to detect (e.g. drones, mobile telephones etc), and so forth. The radius w.sub.0 may be calibrated for a specific installation using simulations and/or field trials with emission sources 2 having known locations. For example, if it is desired to use a system 1 to detect drones, one or more types of drone including location sensors (e.g. GPS, inertial compass etc) may be moved around the area of the system 1 whilst the system logs calculated locations r.sub.h. The desired radius w.sub.0 may then be calibrated based on a desired metric, for example, so that a false positive rate of detections does not exceed a maximum tolerance. The minimum threshold number of locations r.sub.h for a cluster to be counted may also be a variable in such a calibration.

[0153] Referring in particular to FIG. 11, a schematic example of applying the second cluster filter (step S9) is shown.

[0154] In FIG. 11, the set {r.sub.0, r.sub.1, . . . , r.sub.h, . . . , r.sub.H} of the calculated signal location r.sub.0 and the previously calculated signal locations r.sub.1, . . . , r.sub.h, . . . , r.sub.H within the preceding time period T corresponds to H=7. The relative locations shown are schematic and intended for illustrative purposes. The dashed ellipses illustrate elliptical bounding curves 18. Unlike for the bounding circles 17 of the first cluster filter (step S8), each elliptical bounding curve 18 is different in dependence on the locus of possible positions 15 generated for the corresponding calculated signal location r.sub.h. Each elliptical bounding curve 18 has a fixed semi-minor axis of length w.sub.0, equal to the radii w.sub.0 of the bounding circles 17 of the first cluster filter. Each elliptical bounding curve 18 has a semi-major axis aligned parallel to a direction corresponding to the maximum dimension of the locus of possible locations 15 for the corresponding calculated signal location r.sub.h. For example, if the locus 15 is a rectangle 15a, the semi-major axis of the elliptical bounding curve 18 will be parallel to the long side w.sub.2, whereas if the locus 15 is an ellipse 15b, the semi-major axis of the elliptical bounding curve 18 will be parallel to the semi-major axis of the elliptical locus 15b. However, the length of the semi-major axis of each elliptical bounding curve 18 is set so that the elliptical bounding curve 18 will have an aspect ratio (of semi-major to semi-minor axes) which is equal to a ratio of maximum and minimum distances spanning the locus of possible locations 15 of the corresponding calculated signal location r.sub.h.

[0155] For the 3D case, the long axis (or axes) of a spheroid are similarly aligned with the respective axis (or axes) of the locus of possible positions. If bounding surfaces take the form of tri-axial ellipsoids, then the ratio of the intermediate axis to the short axis may also be set based on a dimension of the locus 15 along a corresponding direction.

[0156] The first and second approaches to clustering (as explained in relation to the first cluster filter (step S8)) also apply to the second cluster filter (step S9). It is preferable that both first and second cluster filters (steps S8, S9) apply the same approach. It should be noted that for the second cluster filter (step S9) applying the first approach, if the bounding ellipse 18 of one location r.sub.h encompasses or intersects the location of the other r.sub.k≠h, the reverse is not necessarily true, but a single overlap may be sufficient for clustering. Alternatively, a third approach may apply condition of mutual overlap for clustering, i.e. such that clustering is found only if the bounding ellipse 18 of location r.sub.h encompasses or intersects the location r.sub.k≠h whilst the bounding ellipse 18 of location r.sub.k≠h also encompasses or intersects the location r.sub.h.

[0157] Applying the first approach to the example shown in FIG. 11, a first cluster is formed by the set {r.sub.0, r.sub.1, r.sub.3, r.sub.5} and a second cluster is formed by the set {r.sub.2, r.sub.6}. It may be noted that although the bounding ellipse 18 corresponding to location r.sub.3 does not encompass the location r.sub.0, the location is added to the first cluster {r.sub.0, r.sub.1, r.sub.3, r.sub.5} because the bounding ellipse 18 corresponding to location r.sub.0 does encompass the location r.sub.3. Depending on whether a minimum number threshold is applied, the second cluster {r.sub.2, r.sub.6} may be ignored. For example, if the minimum threshold was three, the first cluster would be used and the second ignored, and so forth.

[0158] Applying the second approach to the example shown in FIG. 11, the first cluster would additionally include the location r.sub.4, since the corresponding bounding ellipse 18 intersects the bounding ellipses 18 of locations r.sub.1 and r.sub.5 (though only one is needed)

[0159] Simulations and/or experiments described hereinbefore in relation to calibrating the radius w.sub.0 should preferably also include simulations/measurements where the emission source 2 having known location is both inside and outside the convex hull 5, in order to calibrate the performance of both first and second cluster filters (steps S8, S9) for a particular system 1, its environment, and intended application.

[0160] Referring again in particular to FIG. 3, one or more radio emission source location estimates R are calculated (step S10). Each radio emission source location estimate R corresponds to a different cluster determined by the first or second cluster filter (steps S8, S9). Consequently, there may be zero, one, two or more radio emission source location estimates R. For example, if a minimum threshold number of locations r.sub.h is applied to screen out small clusters, then there may be no clusters which meet or exceed that minimum threshold.

[0161] Each estimated radio emission source location R may be simply determined as an average of a respective cluster of signal locations r.sub.h. For example, a first estimated radio emission source location R.sub.1 may be the average of a first cluster of signal locations r.sub.h and a second estimated radio emission source location R.sub.2 may be the average of a second cluster of signal locations r.sub.h. The average may be of any suitable type, for example a mean or a weighted mean. For example, each signal location r.sub.h in a cluster may be weighted inversely to an area or volume of the respective locus of possible locations 15 (so that those less sensitive to noise are weighted preferentially). However, a mean average need not be used, and other measures such as a median may be used (e.g. combining a median latitude with a median longitude).

[0162] An averaging process does not take into account that an emission source 2 may well be moving during the course of the preceding period T used for clustering. An alternative approach to calculation of the estimated radio emission source location R for each cluster is to fit a linear regression line to the respective cluster of signal locations r.sub.h (using time as the independent variable), followed by extrapolating the calculated linear regression line to the output time t.

[0163] In other implementations, a hybrid of the two approaches (average and regression line) may be applied. For example, each cluster of signal locations r.sub.h may be tracked across the preceding time period T This may also help to further screen out any errors, since a cluster which is not persistent may be erroneous. When a given cluster is stationary, the corresponding estimated radio emission source location R is calculated as an average. However, when a given cluster is moving, the corresponding estimated radio emission source location R is calculated using the regression line approach.

[0164] Each new, distinct cluster which is tracked may be initialised as stationary. A new cluster may be one having no corresponding cluster during an immediately previous iteration of the method. A minimum persistence may be imposed before outputting an estimated radio emission source location R corresponding to each new cluster. A stationary cluster may be changed to a moving cluster in response to a speed of the respective estimated radio emission source location R exceeding a motion threshold. Similarly, a moving cluster may be changed to a stationary cluster in response to a speed of the respective estimated radio emission source location R being below a static threshold. The motion threshold may be equal to the static threshold, but does not need to be equal. In some implementations, it may be possible for determination of whether a cluster is moving or stationary may be based at least on part on Doppler frequency shifts between the radio signal datasets. This latter option will only be viable for some combinations of sensor 3 frequency resolution of emission source 2 velocities. In particular, sole reliance on Doppler may be inadvisable as it may miss moving emissions sources 2 moving tangentially to a radial line originating at/within the system 1.

[0165] In some examples, every signal location r.sub.n belonging to a cluster of signal locations r.sub.n may be output as a separate estimated radio emission source location R. This may be in addition to an averaged or extrapolated location R, or instead of an averaged or extrapolated location R.

[0166] Once calculated, the one or more estimated radio emission source locations R are output (step S11). For example, when the system 1 is operating live (in real time), the one or more estimated radio emission source locations R may be output to a display being monitored by a user, via a message sent to a user over a network connection, via SMS, via e-mail, by causing a speaker to output an alarm signal, and so forth. When the system 1 is not operating live, the one or more estimated radio emission source locations R may be stored to a computer readable medium (e.g. a log file) for subsequent analyses.

[0167] In addition to alerting a user, one or more hardware systems connected to the system 1 may also be activated and/or controlled in dependence on outputting at least one estimated radio emission source location R. For example, in the application of detecting drones trespassing in restricted airspace, the output step S11 may include causing one or more optical telescopes (not shown) and/or hardware drone countermeasures (not shown) to be directed towards one or more estimated radio emission source locations R. This may help to improve reaction times for positively verifying that a drone is trespassing and removing a potential threat. Drone countermeasures may include one or more known systems including without limitation lasers, radio frequency jammers, global positioning system (GPS) spoofers, high power microwave devices, net launchers, interception drones and so forth.

[0168] The method has been explained as including the generation of the locus of possible positions 15 (step S6) unconditionally, since the locus 15 provides a useful measure of sensitivity of any given calculated location r.sub.h is useful information in and of itself. However, since this information is only required for the second cluster filter (step S9), in some implementations computational overheads may be reduced by instead making the generation of the locus of possible positions 15 (step S6) conditional on the calculated signal location r (r.sub.0) being outside the convex hull 5 (step S7|No).

Bearing Calculation

[0169] In addition to, or instead of, calculating zero of more estimates of radio emission source location R, the apparatus 6 may calculate a bearing angle θ.sub.B to an emission source 2.

[0170] For example, the calculation of a bearing angle θ.sub.B may be included at any point in the method of FIG. 3 (see step S13) following the calculation of the signal location r (step S5). In an alternative method (not specifically illustrated but including steps S1 through S5) the calculation of a bearing angle θ.sub.B may be performed in isolation of calculating estimates of radio emission source location(s) R.

[0171] Referring also to FIGS. 12 and 13, calculation of a bearing angle θ.sub.B is further described.

[0172] The calculation is performed based on the signal location r and the previously calculated signal locations r within the preceding time period T, i.e. the same set of signal locations r used for the cluster analyses (step S8 or S9). For the sake of explanations, again assume that the signal locations r are calculated at regular intervals so that this set is {r.sub.0, r.sub.1, . . . , r.sub.h, . . . , r.sub.H} as defined hereinbefore.

[0173] The bearing angle θ.sub.B is determined as the angle θ which maximises a number of signal locations r.sub.h within an angular threshold δθ of the bearing angle θ.sub.B.

[0174] Referring in particular to FIG. 12, a number H=18 of signal locations r are illustrated, with dashed lines delineating fixed angular intervals of δθ=10.sup.0 fanning out from an origin point 19.

[0175] Referring in particular to FIG. 13, determining the bearing angle θ.sub.B may include calculating an angular histogram having a bin width equal to the angular threshold δθ. The bearing angle θ.sub.B is then determined as a central angle of an angular histogram bin containing the greatest number of signal locations r.sub.h. In the example shown in FIGS. 12 and 13, the bearing angle is θ.sub.B=25° from the y-axis as illustrated, because the angular bin between 20° and 30° contains the largest number (eight) of signal locations r.sub.h. A minimum threshold may be applied to the number of locations r.sub.h within the angular bin before a peak is counted and used for determining a corresponding bearing angle θ.sub.B. If there are additional, distinct peaks in the angular histogram, each distinct peak may be assigned a corresponding bearing angle θ.sub.B. This may occur when there are two or more emission sources 2 active at the same time.

[0176] Alternatively, the angle θ may be swept through an arc (up to 2π/360°) in angular increments smaller than a desired angular threshold δθ (e.g. increments of δθ/10), counting the number of signal locations r.sub.h in the range θ-δθ<θ≤θ+δθ, until one or more peaks is found and assigned as the bearing angle θ. As with the angular histogram method, a minimum threshold number of locations r.sub.h may be imposed, and in some cases multiple peaks may exceed the minimum threshold and consequently be treated as separate bearing angles θ.sub.B.

[0177] If calculated, one or more bearing angles θ.sub.B may be output along with (or instead of) the estimated radio emission source location(s) R (step S11), in any way described hereinbefore.

[0178] Calculation of a bearing angle θ.sub.B requires definition of an origin point 19. In general, the bearing angle θ.sub.B may be calculated to originate from an origin point 19 corresponding to a centroid of the sensors 3 of the system 1.

[0179] Alternatively, the origin point 19 may be set and/or modified to correspond to a user defined location within the convex hull 5. In some implementations, the bearing angles θ.sub.B may be calculated from an origin point 19 corresponding to one of the sensors 3, or to an optical telescope (not shown) or a hardware drone countermeasure (not shown). Such an optical telescope and/or drone countermeasure may also be caused to point along the output bearing angle θ.sub.B.

[0180] An extension of the method of calculating a bearing angle θ.sub.B may be implemented. In a first step, a peak in an angular histogram or angular sweep may be determined as hereinbefore described from an arbitrary origin (e.g. the centroid of the sensors 3). In a second step, a linear regression may be applied to the locations r.sub.h corresponding to that (or each) peak, to obtain a unique bearing angle. An origination point may be set to any position along the unique bearing angle, and may be chosen for convenience in a given application. For example, the location of an optical telescope or drone countermeasure when the system is used to detect unauthorised drones in an airspace.

Outer Perimeter

[0181] The determination of one or more bearing angles θ.sub.B (step S13) may maintain reliability out to a larger distance from the convex hull 5 than the determination of one or more estimated radio emission source locations R (steps S6 through S10).

[0182] Consequently, in an implementation of the method of FIG. 3 which includes the optional step of determining a bearing angle θ.sub.B (step S13), computational overheads may be reduced and false positives also reduced by omitting the determination of estimated radio emission source location(s) R (steps S6 through S10) if the calculated signal location r is far enough from the system 1.

[0183] For example, the method may bypass the determination of one or more estimated radio emission source location R (steps S6 through S10) in response to the calculated signal location r is outside an outer perimeter 20 (FIG. 14) (step S14|No). The outer perimeter 20 is an outer perimeter in the sense that for a signal location r calculated as being outside this perimeter 20, estimates of radio emission source location(s) R are not made.

[0184] Referring also to FIG. 14, an outer perimeter 20 is illustrated corresponding to an exemplary system 1 including four sensors 3.

[0185] The outer perimeter 20 corresponds to the locus of positions on which the sensors 3 (and corresponding convex hull 5) subtend a constant angle β. In the example shown in FIG. 14, the illustrated outer perimeter 20 corresponds to an angle of β=30°, which in simulations and field trials the inventors have found to be a suitable angle in many real applications. Three points P.sub.1, P.sub.2, P.sub.3 are highlighted around the outer perimeter 20 to illustrate that the angle β subtended by the sensors 3 from any point is fixed.

[0186] Referring also to FIG. 15, another outer perimeter 20 is illustrated corresponding to an exemplary system 1 including eight sensors 3, corresponding to a fixed angle of β=30°.

[0187] Although the examples of outer perimeter 20 correspond to the same fixed angle of β=30°, the angle β may be varied. For example, for a system 1 intended to detect objects such as drones in and around a protected airspace, the outer perimeter 20 used may correspond to an angle β of between (and including) 20° and 40°. Equally, alternative methods of defining the outer perimeter 20 may be used, for example, the outer perimeter 20 may be defined as a locus of points a fixed distance from the convex hull 5.

[0188] In this way, bearing angles θ.sub.B may be determined regardless of range (step S13), the first cluster filter may be applied (step S8) in response to the calculated signal location r is within the convex hull 5 (step S7|Yes) and within the outer perimeter 20 (step S14|Yes) (the latter condition being always true if the former is true), and the second cluster filter may be applied (step S9) in response to the calculated signal location r is outside the convex hull 5 (step S7|No) and within the outer perimeter 20 (step S14|Yes).

[0189] In this way, a bearing angle may θ.sub.B always be calculated to provide at least a direction to a radio emission source 2. As the radio emission source 2 moves closer and crosses the outer perimeter 20, cluster filtering to calculate and output an estimated radio emission source location R will be carried out using the second cluster filter (step S9), in addition to the bearing angle θ.sub.B. As the radio emission source 2 moves closer still and crosses inside the convex hull 5, the first cluster filter (step S8) will be applied to determining an estimated radio emission source location R Although it is possible to continue calculating the bearing angle θ.sub.B for radio emission sources 2 within the convex hull 5, the availability of a more accurate estimated radio emission source location R at such ranges means that calculation of the bearing angle θ.sub.B may be of reduced value, and may be omitted for radio emission sources 2 within the convex hull 5.

MODIFICATIONS

[0190] It will be appreciated that various modifications may be made to the embodiments hereinbefore described. Such modifications may involve equivalent and other features which are already known in the design and use of methods and apparatuses for radio location finding based on times-of-arrival, and which may be used instead of or in addition to features already described herein. Features of one embodiment may be replaced or supplemented by features of another embodiment.

[0191] Although three particular approaches to cluster filtering have been described, any approaches using the same bounding curves (or surfaces) may be used.

[0192] Although claims have been formulated in this application to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel features or any novel combination of features disclosed herein either explicitly or implicitly or any generalization thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention. The applicants hereby give notice that new claims may be formulated to such features and/or combinations of such features during the prosecution of the present application or of any further application derived therefrom.