Method and system for robust positioning using ranging signals

Abstract

A method for position calculation of an antenna is provided. The method comprises calculating ranges between the antenna and the at least three transponders. The calculation includes range measurements between an antenna and at least three transponders. Respective positions of the at least three transponders are known. The method further comprises providing a first coordinate of three coordinates. The three coordinates indicate a position of the antenna. The method further comprises calculating second and third coordinates of the three coordinates based on the calculated ranges between the antenna and the at least three transponders. The method further comprises predicting ranges between the antenna and the at least three transponders based on the provided first coordinate and the calculated two coordinates. The method further comprises performing an optimization process based on the calculated ranges and the predicted ranges to infer an optimized position of the antenna. Further, a system for position calculation and an air vehicle comprising the system are provided.

Claims

1. A method for position calculation of an antenna, the method comprising: calculating, by range measurements between an antenna on a first vehicle and at least three transponders on a second vehicle, ranges between the antenna and the at least three transponders, wherein respective positions of the at least three transponders are known; providing a first antenna coordinate of three antenna coordinates indicating a position of the antenna, wherein the first antenna coordinate is assumed for or known before predicting the ranges between the antenna and the at least three transponders; calculating second and third antenna coordinates of the three antenna coordinates based on the calculated ranges between the antenna and the at least three transponders; predicting ranges between the antenna and the at least three transponders based on the assumed or known first antenna coordinate and the calculated two antenna coordinates; performing an optimization process based on the calculated ranges and the predicted ranges to infer an optimized position of the antenna; and steering the first vehicle for landing on the second vehicle based on the optimized position of the antenna.

2. The method of claim 1, wherein the transponders are mounted on a moving vehicle.

3. The method of claim 1, wherein the transponders have a fixed position with respect to each other.

4. The method of claim 1, wherein the first antenna coordinate may be a z-coordinate for a vertical direction in a respective coordinate system, and wherein the second and third antenna coordinates are x and y coordinates for horizontal directions in the respective coordinate system.

5. The method of claim 1, wherein the second and third antenna coordinates are calculated using a linear least squares method, when the first antenna coordinate is provided and the respective positions of the at least three transponders are known.

6. The method of claim 1, wherein the step of performing the optimization process comprises subtracting the predicted ranges from the calculated ranges, wherein result of this subtraction is squared and summed yielding to a figure of merit associated with the first antenna coordinate.

7. The method of claim 1, wherein, during the optimization process, at least one other first antenna coordinate is provided, wherein the ranges between the antenna and the at least three transponders are predicted based on each of the at least one other first antenna coordinate and the calculated two antenna coordinates, and wherein the optimization process is performed based on the calculated ranges and the predicted ranges to infer the optimized position of the antenna based on a figure of merit to be minimized.

8. The method of claim 1, wherein the second and third antenna coordinates are calculated under use of a linear least squares' method.

9. The method of claim 1, wherein the first vehicle is moving.

10. The method of claim 1, wherein the second vehicle is moving.

11. The method of claim 1, wherein the first and second vehicles are moving.

12. A non-transitory computer-readable data carrier having stored a computer program product, the computer program product comprising instructions which, when the computer program product is executed by a computer, cause the computer to carry out a method for position calculation of an antenna, the method comprising: calculating, by range measurements between an antenna on a first vehicle and at least three transponders on a second vehicle, ranges between the antenna and the at least three transponders, wherein respective positions of the at least three transponders are known; providing a first antenna coordinate of three antenna coordinates indicating a position of the antenna, wherein the first antenna coordinate is assumed for or known before predicting the ranges between the antenna and the at least three transponders; calculating second and third antenna coordinates of the three antenna coordinates based on the calculated ranges between the antenna and the at least three transponders; predicting ranges between the antenna and the at least three transponders based on the assumed or known first antenna coordinate and the calculated two antenna coordinates; performing an optimization process based on the calculated ranges and the predicted ranges to infer an optimized position of the antenna; and steering the first vehicle for landing on the second vehicle based on the optimized position of the antenna.

13. A system for position calculation of an antenna, the system comprising: an antenna on a first vehicle adapted to transmit and receive electromagnetic waves; a processor adapted to calculate, by range measurements between the antenna and at least three transponders on a second vehicle, ranges between the antenna and the at least three transponders, wherein respective positions of the at least three transponders are known, provide a first antenna coordinate of three antenna coordinates indicating a position of the antenna, wherein the first antenna coordinate is assumed for or known before predicting the ranges between the antenna and the at least three transponders, calculate second and third antenna coordinates of the three antenna coordinates based on the calculated ranges between the antenna and the at least three transponders; predict ranges between the antenna and the at least three transponders based on the assumed or known first antenna coordinate and the calculated two antenna coordinates; perform an optimization process based on the calculated ranges and the predicted ranges to infer an optimized position of the antenna; and steer the first vehicle for landing on the second vehicle based on the optimized position of the antenna.

14. The system of claim 13, wherein the position calculation is performed in a vertical take-off maneuver from a moving platform or a landing maneuver onto a moving platform, wherein the moving platform comprises the transponders.

15. An air vehicle comprising the system of claim 13.

Description

(1) Other objects, features, advantages and applications will become apparent from the following description of non-limiting embodiments regarding the accompanying drawings. In the drawings, all described and/or illustrated features, alone or in any combination form the subject matter disclosed therein, irrespective of their grouping in the claims or their relations/references. The dimensions and proportions of components or parts shown in the figures are not necessarily to scale; these dimensions and proportions may differ from illustrations in the figures and implemented embodiments.

(2) FIG. 1 schematically illustrates a system for position calculation of an antenna and an air vehicle mounting at least part of the system;

(3) FIG. 2 schematically illustrates a method for position calculation of an antenna;

(4) FIG. 3 schematically illustrates a figure of merit versus altitude, true height is 50 m;

(5) FIG. 4 schematically illustrates a number of solver failures out of 100 position calculation attempts as a function of the VTOL aircraft antenna position according to nonlinear least squares method; and

(6) FIG. 5 schematically illustrates a number of solver failures out of 100 position calculation attempts as a function of the VTOL aircraft antenna position according to the method disclosed herein.

(7) The system, the method and the air vehicle will now be described with respect to the embodiments.

(8) In the following, without being restricted thereto, specific details are set forth to provide a thorough understanding of the present disclosure. However, it is dear to the skilled person that the present disclosure may be used in other embodiments, which may differ from the details set out below.

(9) It will be understood that when an element is referred to as being connected or coupled to another element, the elements may be directly connected or coupled or via one or more intervening elements. If two elements A and B are combined using an or, this is to be understood to disclose all possible combinations, i.e. only A, only B as well as A and B. An alternative wording for the same combinations is at least one of A and B. The same applies for combinations of more than 2 elements.

(10) FIG. 1 schematically illustrates a system (100) for position calculation of an antenna (120) and an air vehicle (110) mounting at least part of the system (100).

(11) The system (100) comprises an antenna (120) and a processing unit (not explicitly shown but may be part of the box as shown as the antenna (120)). The antenna (120) is adapted to transmit and receive electromagnetic waves. The processing unit is adapted to calculate, by range measurements between the antenna (120) and at least three transponders (T1, T2, T3), ranges between the antenna (120) and the at least three transponders (T1,T2, T3). Respective positions of the at least three transponders (T1, T2, T3) are known. The processing unit is further adapted to provide a first coordinate of three coordinates indicating a position of the antenna (120). The processing unit is further adapted to calculate second and third coordinates of the three coordinates based on the calculated ranges between the antenna (120) and the at least three transponders (T1, T2, T3). The processing unit is further adapted to predict ranges between the antenna (120) and the at least three transponders (T1, T2, T3) based on the provided coordinate and the calculated two coordinates. The processing unit is further adapted to perform an optimization process based on the calculated ranges and the predicted ranges to infer an optimized position of the antenna (120).

(12) The position calculation may be performed in a vertical take-off manoeuvre from a moving platform or a landing manoeuvre onto a moving platform, wherein the moving platform comprises the transponders (T1, T2, T3), Further, the processing unit may be connected to the antenna (120).

(13) The air vehicle (110) is for example a helicopter, an aircraft or an unmanned vehicle, UAV, comprising the system (100), The system (100) may be mounted on the air vehicle (110), Further, the system (100) may also be just partly connected or mounted to the air vehicle (110). The transponders (T1, T2, T3) may also be considered as part of the system. However, these transponders (T1, T2, T3) may be separated entities in communication with each other and not directly connected but separated from the air vehicle (110).

(14) More details and aspects are mentioned in connection with the embodiments described above or below. The embodiment shown in FIG. 1 may comprise one or more optional additional features corresponding to one or more aspects mentioned in connection with the proposed concept or one or more embodiments described below (e.g. FIGS. 2-5).

(15) FIG. 2 schematically illustrates a method for position calculation of an antenna. The method comprises calculating (S210) ranges between the antenna and the at least three transponders. The calculation includes range measurements between an antenna and at least three transponders. The at least three transponders may be separated to each other. Further, each of the at least three transponders may be separated to the antenna when performing the calculation, Respective positions of the at least three transponders are known. This knowledge may be a priori. Further, this knowledge may be gathered by a further communication channel over air. The method further comprises providing (S220) a first coordinate of three coordinates. The three coordinates indicate a position of the antenna. The method further comprises calculating (S230) second and third coordinates of the three coordinates of the antenna based on the calculated ranges between the antenna and the at least three transponders. The method further comprises predicting (S240) ranges between the antenna and the at least three transponders based on the provided first coordinate and the calculated two coordinates. The method further comprises performing (S250) an optimization process based on the calculated ranges and the predicted ranges to infer an optimized position of the antenna.

(16) Accordingly, a more robust position may be calculated. The antenna may be part of a moving vehicle. The moving vehicle may be an air vehicle, such as an aircraft, an unmanned vehicle or a helicopter. In particular, the method may be for landing the moving vehicle on another moving vehicle. The other moving vehicle may be a vessel, the helicopter should be landing or landed on. The other moving vehicle may comprise the at least three transponders. The at least three transponders may be arranged on the other moving vehicle such that they have static distances to each other while the steps of the method are performed.

(17) The first coordinate may be a single one coordinate of the three coordinates of the antenna position. The origin of the cartesian coordinate system in which the antenna position is mechanized may be in a plane of the at least three transponders. Further, the origin may also be one of the at least three transponders.

(18) The second and third coordinates may respectively differ from the first coordinate, such that only the first coordinate is provided. The term provided may mean that in a first step of the optimization method, the first coordinate may be assumed or already known. The a priori knowledge may be due to a priori data or a simple guess.

(19) The antenna may be a single antenna arranged on the moving vehicle, which allows calculating the position of the antenna. Thus, when equipping the moving with multiples of these antennas, additionally the attitude of the moving vehicle can be calculated. Consequently, the moving vehicle can be steered such that it can land on the other moving vehicle based on this information.

(20) The transponders may be passive or active transceivers to retransmit or reflect corresponding electromagnetic waves to the antenna in order to perform range measurements.

(21) The term range may also be understood as the term distance. Thus, the range measurement may also be called distance measurement.

(22) The optimization process may be a minimization problem solving algorithm.

(23) The optimized position may be the result of the optimization process. The optimized position may be the same or different from the position associated with the provided first coordinate and the calculated second and third coordinates.

(24) The first coordinate may be assumed for predicting the respective ranges between the antenna and the at least three transponders.

(25) A good assumption may lead to a fast solving of the optimization process.

(26) The first coordinate may be known before predicting the respective ranges between the antenna and the at least three transponders.

(27) The transponders may be mounted on the moving vehicle, like a vessel. The transponders may have a fixed position with respect to each other. The first coordinate may be a z-coordinate for a vertical direction in a respective coordinate system. The second and third coordinates may be x and y coordinates for a horizontal direction in the respective coordinate system.

(28) The second and third coordinates may be calculated using a linear least squares method, when the first coordinate is provided and the respective positions of the at least three transponders are known.

(29) The step of performing the optimization process may comprise subtracting the predicted ranges from the calculated ranges. The result of this subtraction may be squared. Further, this result may be summed. The squared result and/or the summed squared result may yield to a figure of merit. The figure of merit may be associated with the provided first coordinate.

(30) During the optimization process, at least one other first coordinate may be provided. The ranges between the antenna and the at least three transponders may be predicted based on each of the at least one other first coordinate and the calculated two coordinates. The optimization process may be performed based on the calculated ranges and the predicted ranges to infer the optimized position of the antenna based on the figure of merit to be minimized.

(31) The second and third coordinates may be calculated under use of a linear least squares' method.

(32) More details and aspects are mentioned in connection with the embodiments described above or below. The embodiment shown in FIG. 2 may comprise one or more optional additional features corresponding to one or more aspects mentioned in connection with the proposed concept or one or more embodiments described above (e.g. FIG. 1) or below (e.g. FIGS. 3-5).

(33) In the following (with regards to FIG. 3-5), an exemplary algorithm for calculating a VTOL aircraft antenna position from range measurements to three or more transponders at known positions is derived. The algorithm may be part of the method as described with respect to FIG. 2 and may also be part of the implementation of the system according to FIG. 1 and in particular in the implementation of the processing unit described with respect thereto.

(34) A squared range measurement to the first transponder can be modelled as follows:

(35) $?_{1}^{2} = {(x - x_{1})}^{2} + {(y - y_{1})}^{2} + {(z - z_{1})}^{2} .$

(36) Hereby, the coordinates x,y,z denote the position of the VTOL aircraft antenna, and x.sub.1,y.sub.1,z.sub.1 are the position coordinates of the first transponder.

(37) Expanding yields

(38) $?_{1}^{2} = x^{2} - 2 x_{1} x + x_{1}^{2} + y^{2} - 2 y_{1} y + y_{1}^{2} + z^{2} - 2 z_{1} z + z_{1}^{2} .$

(39) Introducing a second transponder with index j, one can write

(40) $?_{2}^{2} = x^{2} - 2 x_{2} x + x_{2}^{2} + y^{2} - 2 y_{2} y + y_{2}^{2} + z^{2} - 2 z_{2} z + z_{2}^{2} .$

(41) Squaring the relationship

(42) $?_{1} = ?_{1} - ?_{2} + ?_{2}$

(43) yields

(44) $?_{1}^{2} = {(?_{1} - ?_{2})}^{2} + 2 (?_{1} - ?_{2}) ?_{2} + ?_{2}^{2} .$

(45) Inserting in the squared range equation of the first transponder yields

(46) $?_{1}^{2} = {(?_{1} - ?_{2})}^{2} + 2 (?_{1} - ?_{2}) ?_{2} + ?_{2}^{2} = x^{2} - 2 x_{1} x + x_{1}^{2} + y^{2} - 2 y_{1} y + y_{1}^{2} + z^{2} - 2 z_{1} z + z_{1}^{2} .$

(47) Subtracting the squared range equation of he second transponder yields

(48) $?_{1}^{2} - ?_{2}^{2} = {(?_{1} - ?_{2})}^{2} + 2 (?_{1} - ?_{2}) ?_{2} + ?_{2}^{2} - ?_{2}^{2} = x^{2} - 2 x_{1} x + x_{1}^{2} + y^{2} - 2 y_{1} y + y_{1}^{2} + z^{2} - 2 z_{1} z + z_{1}^{2} - x^{2} + 2 x_{2} x - x_{2}^{2} - y^{2} + 2 y_{2} y - y_{2}^{2} - z^{2} + 2 z_{2} z - {z_{2}^{2} (?_{1} - ?_{2})}^{2} + 2 (?_{1} - ?_{2}) ?_{2} = - 2 (x_{1} - x_{2}) x + x_{1}^{2} - x_{2}^{2} - 2 (y_{1} - y_{2}) y + y_{1}^{2} - y_{2}^{2} - 2 (z_{1} - z_{2}) z + z_{1}^{2} - z_{2}^{2} .$

(49) Moving all known quantities to the left, one gets

(50) ${(?_{1} - ?_{2})}^{2} + 2 (?_{1} - ?_{2}) ?_{2} - (x_{1}^{2} + y_{1}^{2} + z_{1}^{2}) + (x_{2}^{2} + y_{2}^{2} + z_{2}^{2}) = - 2 (x_{1} - x_{2}) x - 2 (y_{1} - y_{2}) y - 2 (z_{1} - z_{2}) z .$

(51) With d.sub.1.sup.2=(x.sub.1.sup.2+x.sub.1.sup.2+x.sub.1.sup.2) and d.sub.2.sup.2=(x.sub.2.sup.2+x.sub.2.sup.2+x.sub.2.sup.2), this can be expressed as follows:

(52) ${(?_{1} - ?_{2})}^{2} + 2 (?_{1} - ?_{2}) ?_{2} - d_{1}^{2} + d_{2}^{2} = (- 2 (x_{1} - x_{2}) - 2 (y_{1} - y_{2}) - 2 (z_{1} - z_{2})) (\begin{matrix} x \\ y \\ z \end{matrix}) .$

(53) The VTOL aircraft antenna position now depends linearly on a non-linear combination of measurements and transponder positions.

(54) An attempt could now be made to solve for the VTOL aircraft antenna position directly, Writing now this equation for all transponder measurements in matrix-vector notation yields

(55) 0 $(\begin{matrix} {(?_{1} - ?_{2})}^{2} + 2 (?_{1} - ?_{2}) ?_{2} - d_{1}^{2} + d_{2}^{2} \\ {(?_{1} - ?_{3})}^{2} + 2 (?_{1} - ?_{3}) ?_{3} - d_{1}^{2} + d_{3}^{2} \\ {(?_{1} - ?_{4})}^{2} + 2 (?_{1} - ?_{4}) ?_{4} - d_{1}^{2} + d_{4}^{2} \\ .Math. \end{matrix}) = (\begin{matrix} - 2 (x_{1} - x_{2}) & - 2 (y_{1} - y_{2}) & - 2 (z_{1} - z_{2}) \\ - 2 (x_{1} - x_{3}) & - 2 (y_{1} - y_{3}) & - 2 (z_{1} - z_{3}) \\ - 2 (x_{1} - x_{4}) & - 2 (y_{1} - y_{4}) & - 2 (z_{1} - z_{4}) \\ .Math. & .Math. & .Math. \end{matrix}) (\begin{matrix} x \\ y \\ z \end{matrix}) .$

(56) This set of equations is of the form

(57) $y = H x,$

(58) the least squares solution for x is given by

(59) $x = {(H^{T} H)}^{- 1} H^{T} y,$

(60) also a weighted least squares could be considered. However, if all transponders lie in the same plane, H does not have full column rank, and consequently the inverse) (H.sup.7H).sup.?1 cannot be computed: With all transponders in the same plane, mirroring the true VTOL aircraft antenna position at this plane leads another position, for which the same range measurements would be obtained.

(61) A solution to this problem can be found by assuming the altitude z would be known. In that case the equation derived previously,

(62) ${(?_{1} - ?_{2})}^{2} + 2 (?_{1} - ?_{2}) ?_{2} - d_{1}^{2} + d_{2}^{2} = (- 2 (x_{1} - x_{2}) - 2 (y_{1} - y_{2}) - 2 (z_{1} - z_{2})) (\begin{matrix} x \\ y \\ z \end{matrix}),$

(63) can be rearranged, yielding

(64) ${(?_{1} - ?_{2})}^{2} + 2 (?_{1} - ?_{2}) ?_{2} - d_{1}^{2} + d_{2}^{2} + 2 (z_{1} - z_{2}) z = (- 2 (x_{1} - x_{2}) - 2 (y_{1} - y_{2})) (\begin{matrix} x \\ y \end{matrix}) .$

(65) Writing now again all this equation for transponder measurements in matrix vector notation yields

(66) $(\begin{matrix} {(?_{1} - ?_{2})}^{2} + 2 (?_{1} - ?_{2}) ?_{2} - d_{1}^{2} + d_{2}^{2} + 2 (z_{1} - z_{2}) z \\ {(?_{1} - ?_{3})}^{2} + 2 (?_{1} - ?_{3}) ?_{3} - d_{1}^{2} + d_{3}^{2} + 2 (z_{1} - z_{3}) z \\ {(?_{1} - ?_{4})}^{2} + 2 (?_{1} - ?_{4}) ?_{4} - d_{1}^{2} + d_{4}^{2} + 2 (z_{1} - z_{4}) z \\ .Math. \end{matrix}) = (\begin{matrix} - 2 (x_{1} - x_{2}) & - 2 (y_{1} - y_{2}) \\ - 2 (x_{1} - x_{3}) & - 2 (y_{1} - y_{3}) \\ - 2 (x_{1} - x_{4}) & - 2 (y_{1} - y_{4}) \\ .Math. & .Math. \end{matrix}) (\begin{matrix} x \\ y \end{matrix}) .$

(67) This set of equations can be solved straight using linear least squares or other means, if the altitude z is known. In case the altitude is known, this set of equations is solved for the horizontal VTOL aircraft antenna position coordinates x,y, no further steps are needed.

(68) However, in general the altitude is not known. Therefore, a candidate altitude z is assumed, and a horizontal VTOL aircraft antenna position coordinates x,y is calculated using linear least squares, or any other means. Then, based on the candidate altitude z and the resulting VTOL aircraft antenna position coordinates x,y, the ranges to the transponders are calculated. These predicted ranges are subtracted from the actual range measurements, and the resulting differences are squared and summed. This yields a figure of merit for the candidate altitude z. Now an optimization process is implemented, which searches for the minimum figure of merit as a function of the candidate altitude z. The candidate altitude z and horizontal VTOL aircraft antenna position coordinates x,y that lead to the minimum figure of merit represent the result provided by the method.

(69) An illustrative example for the figure of merit as function of the altitude is shown in FIG. 3.

(70) It has to be noted that the proposed method can be used either to provide epoch per epoch independent position estimates of the VTOL aircraft antenna, or to provide a position estimate for initialization of a Kalman filter or another sensor fusion algorithm, which might then employ additional sensors like accelerometers and gyroscopes.

(71) It has to be noted that the approach described above is not restricted to VTOL aircrafts, vessels and transponders. It applies to any situation where an unknown position is calculated from range measurements, whereby the positions to which the range measurements are made must be known.

(72) A standard approach for solving the problem addressed herein would be to use non-linear least squares, non-linear weighted least squares, Levenberg-Marquardt or related algorithms.

(73) The method described herein may have two main advantages over these standard solutions: No initial guess for the VTOL aircraft antenna horizontal position required; for the standard solutions, the choice of the initial guess can make the difference between convergence and divergence, The described method is more robust than the standard approaches.

(74) The increased robustness achieved with the described method is illustrated by the results of Monte-Carlo simulation runs. For these Monte-Carlo runs, four transponders were assumed at following positions: [?2;?2;0], [2;?2;0], [2;2;0], [?2;2;0]. The range measurements to these transponders were corrupted with zero mean Gaussian noise with a standard deviation of 0.1 meters.

(75) For a non-linear least squares approach, the number of solver failures out of 100 position calculation attempts as a function of the VTOL aircraft antenna position is shown in FIG. 4. As an initial guess for the altitude, the mean of the four range measurements was used. The x- and y-coordinates of the initial position guess were zero. Obviously, in close proximity to the transponders, no solver failures occur, i.e. the non-linear least squares always converged. In greater distances from the transponders, several solver failures can be observed, i.e, the probability for divergence increases.

(76) For the same scenario, the results obtained with the method as described above are shown in FIG. 5. No solver failures are observed.

(77) More details and aspects are mentioned in connection with the embodiments described above or below. The embodiment shown in FIGS. 3-5 may comprise one or more optional additional features corresponding to one or more aspects mentioned in connection with the proposed concept or one or more embodiments described above (e.g. FIGS. 1-2) or below.

(78) According to one or more aspect, the problem of calculating the VTOL aircraft antenna position from range measurements to three or more transponders at known positions may be solved.

(79) The calculation of the position of a source on a two-dimensional plane may be performed under use of time difference of arrival measurements (TDOA) at several antennas of a VTOL aircraft. For example, a two-step approach is used: First, the two coordinates of the source are expressed as a function of the unknown time of flight of the signal from the source to one of the antennas. Then, inserting this relationship in the equation that relates time of flight to the distance between antenna and source eliminates the source position from the equation, yielding a quadratic equation for the time of flight, Solving for the time of flight, and inserting in the relationship derived in the first step yields the source position. A drawback of this approach is that it solves a two-dimensional problem only, while for supporting VTOL aircraft landings, a three dimensional position information may be required.

(80) The aspects and features mentioned and described together with one or more of the previously detailed examples and figures, may as well be combined with one or more of the other examples in order to replace a like feature of the other example or in order to additionally introduce the feature to the other example.

(81) Furthermore, the following claims are hereby incorporated into the detailed description, where each claim may stand on its own as a separate example. While each claim may stand on its own as a separate example, it is to be noted thatalthough a dependent claim may refer in the claims to a specific combination with one or more other claimsother examples may also include a combination of the dependent claim with the subject matter of each other dependent or independent claim. Such combinations are explicitly proposed herein unless it is stated that a specific combination is not intended. Furthermore, it is intended to include also features of a claim to any other independent claim even if this claim is not directly made dependent to the independent claim.

Method and system for robust positioning using ranging signals

Assignee

Inventors

Cpc classification

Classification Explorer

G05D1/101

PHYSICS

Classification Explorer

B64U2101/20

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

G01S5/02

PHYSICS

Classification Explorer

G01S19/38

PHYSICS

Classification Explorer

G05D1/0022

PHYSICS

Classification Explorer

B64C39/024

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

G01S19/06

PHYSICS

Classification Explorer

G05D1/226

PHYSICS

Classification Explorer

G01S11/02

PHYSICS

Classification Explorer

G01S19/42

PHYSICS

International classification

Classification Explorer

B64C39/02

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

G05D1/00

PHYSICS

Abstract

Claims

Description