FASTENING DEVICE FOR A SYSTEM FOR LOCATING DEVICES IN TUBULAR LINERS

Abstract

A system is disclosed for locating a device (15) in a ducting system comprising a conduit (100) and a shaft (140) arranged next to or above the conduit (100), the system comprising a base station (12) of a radar system (10) with a transmitter (22) and a receiver (19) and a signal source (21) for a clock signal (1) that can be sent by means of the transmitter (22) of the base station (12), the system also comprising a transponder (14), which is arranged on a mobile device (15) and is designed and configured to receive and to modulate the clock signal (1) and to send the modulated clock signal (1) back to the receiver (19) of the base station (1) as a locating signal. A fastening means (150) is also included and is fastened in the shaft, the fastening means (150) comprising a boom (160) extending in front of an opening region of the conduit (100), and the transmitter (22) and the receiver (19) being arranged on the boom.

Claims

1. A system for locating a device (15) in a ducting system comprising a conduit (100) and a shaft (140) arranged next to or above the conduit (100), wherein the system comprises a base station (12) of a radar system (10) with a transmitter (22) and a receiver (19) and also a signal source (21) for an initial signal (1) that can be transmitted by means of the transmitter (22) of the base station (12), and also a transponder (14) arranged on a mobile device (15) and designed and configured to receive and to modulate the initial signal (1) and to transmit the modulated initial signal (1) back to the receiver (19) of the base station (1) as a locating signal, characterized in that a fastening means (150) is comprised and is fastened in the shaft, wherein the fastening means (150) has a cantilever (160) extending in front of an opening region of the conduit (100), the transmitter (22) and the receiver (19) being arranged on said cantilever.

2. The system of claim 1, characterized in that a deflection roller (180) for supply cables of the device (15) is arranged on the cantilever (160) of the fastening means (150).

3. The system of claim 1, characterized in that the transponder has a transmitter (22′) and a receiver (19′) and also an amplifier (17), wherein a first mixer (16) in the transponder (14) modulates onto a received initial signal (1) an amplitude modulation frequency by means of a signal source (23).

4. The system of claim 1, characterized in that a second mixer (18) and preferably a third mixer (20) are connected in the transponder (14) and modulate onto the initial signal (1) a stabilization frequency by means of a further signal source (34).

5. The system of claim 1, characterized in that in the base station a first mixer (24) in the base station (12) mixes a received locating signal (2) with a frequency of the signal source (21), and a filter (28) subsequently filters the mixed signal.

6. The system of claim 5, characterized in that a second mixer (26) in the base station (12) mixes the filtered signal with a further frequency.

7. The system of claim 1, characterized in that the fastening means (150) is embodied in the form of a telescopic arm, which is expanded and braced in the shaft (140) by means of a rotational movement about its own axis and/or a linear movement along its own axis.

8. The system of claim 1, characterized in that the fastening means (150) is arranged above the conduit (100) in the shaft (140), wherein the fastening means (150) is arranged in particular equidirectionally with the conduit beginning of the conduit (100) in the shaft (140).

9. A method for locating a movable device in a conduit system by means of a radar system comprising a base station and a transponder fitted to the device, characterized by the following steps: fitting a fastening device in a shaft fitted next to and above a conduit, wherein the fastening comprises a cantilever extending as far as in front of the opening region of the conduit, and a transmitter and a receiver of the base station being arranged on said cantilever, transmitting a periodic initial signal having a temporally variable initial frequency by means of the base station, receiving the periodic initial signal by means of the transponder fitted to the device, generating and transmitting a periodic locating signal on the basis of the initial signal by means of the transponder, receiving the locating signal by means of the base station, and evaluating the locating signal by means of an analysis for periodic signals in order to locate the device in the conduit system, wherein the distance between the device and the base station is determined.

10. The method of claim 9, furthermore comprising the following step: modulating the initial signal in the transponder in order to generate a locating signal, such that the amplitude of the initial signal oscillates periodically with a fixed amplitude modulation frequency.

11. The method of claim 9, characterized in that the position of the device is controlled and regulated depending on the evaluation of the locating signal.

12. The method of claim 9, characterized in that the device comprises an electric drive, a drilling or milling head, an illuminant for generating radiation for curing a tubular liner and/or a camera.

13. The method of claim 10, characterized in that the modulation is effected by a first mixer in the transponder, which accepts the initial signal and modulates it with a high-frequency constant amplitude modulation frequency in order to output it to a transmitter of the transponder.

14. The use of a system according to claim 1 for ascertaining the position of a device in a conduit of a conduit system, in particular of a ducting.

15. The use as claimed in claim 14, wherein the position of the device is used for exposing a lateral duct in the conduit by means of the device.

16. The use of a method according to claim 9 for ascertaining the position of a device in a conduit of a conduit system, in particular of a ducting.

17. The use as claimed in claim 16, wherein the position of the device is used for exposing a lateral duct in the conduit by means of the device.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The invention is explained in greater detail below on the basis of two exemplary embodiments with reference to the associated drawings.

[0076] In the figures:

[0077] FIG. 1 shows a schematic side view of a radar system according to the invention for determining a distance of an object,

[0078] FIG. 2 shows a schematic embodiment of a system according to the invention with fastening means arranged in a shaft,

[0079] FIG. 3 shows an embodiment according to the invention of a radar system with an amplitude amplifier, but without mixing of the modulated signal with a frequency,

[0080] FIG. 4 shows a frequency analysis of the amplitude-amplified locating signal plus the signal backscattered passively from other objects,

[0081] FIG. 5 shows an embodiment according to the invention of a radar system with amplitude modulation,

[0082] FIG. 6 shows an embodiment according to the invention of a radar system with amplitude modulation,

[0083] FIG. 7 shows a frequency analysis of the amplitude-modulated locating signal plus the signal backscattered passively from other objects,

[0084] FIG. 8 shows a frequency analysis of the amplitude-modulated locating signal with subsequent second mixing in the base station,

[0085] FIG. 9 shows a frequency analysis of the amplitude-modulated locating signal with subsequent self-mixing and an alternative embodiment of the transponder.

DETAILED DESCRIPTION

[0086] FIG. 1 shows a conduit 100 with a branch junction 110, which has been renovated by means of a tubular liner 120. Furthermore, a radar system 10 according to the invention is arranged in the conduit 100, by means of which radar system the distance of an exposing device 15 can be determined. The radar system 10 comprises a base station 12 and transponders 14 fitted to the device 15.

[0087] The base station 12 emits an initial signal 1, which is received by the transponder 14 and is actively modulated in the transponders 14 in order subsequently to be transmitted back to the base station 12.

[0088] According to the invention, the locating signal 2 is amplitude-modulated. The modulation is effected for each transponder 14 with a high-purity dedicated amplitude modulation frequency. The amplitude modulation frequency can be a sine or a cosine. The initial frequency of the initial signal can be implemented in a frequency band of 24 GHz ISM. Since the radar system 10 according to the invention has active transponders, it is not limited just to 150 m, as is the case for conventional passive radar systems.

[0089] The radar system 10 can emit an initial signal 1 comprising a linearly frequency-modulated wave. Furthermore, the radar system 10 is embodied as an SISO, AoA, digital beamforming, MIMO or other imaging radar system. The starting bandwidth of the radar system 10 can be a plurality of megahertz.

[0090] FIG. 2 here shows the installation situation of a fastening means 150 according to the invention in a shaft 140 situated above the conduit. It is clearly evident that that section of the conduit 100 which is to be renovated only begins next to the shaft 140. The materials necessary for the renovation are introduced into the conduit system through the shaft 140. The shaft 140 itself is not repaired during the renovation of the conduit 100, and so possible markings for the positioning of the fastening means 150 are maintained.

[0091] Consequently, according to the invention, the fastening means 150 can be mounted and demounted, and simultaneously represent a secure and reliable reference point for measurements for example before and after the renovation of the conduit 100.

[0092] In this case, it has proved to be advantageous if not only transmitters and receivers of a locating system are arranged on the cantilever 160, but the fastening means also comprises a deflection roller 170 in order to guide supply lines for the mobile device 15.

[0093] FIGS. 1 and 2 thus show a system according to the invention comprising base station 10 with mobile device 15, which system enables conduit systems 100 to be measured exactly and allows the setting of a reproducible starting point of the distance measurement from base station 10 to device 15.

[0094] FIG. 3 shows a very simple radar system 10, in which the transponder 14 merely amplifies the initial signal 1 by means of an amplifier 17. The base station 12 comprises a signal source 21 for the initial signal 1. The signal source 21 is a VCO oscillator (Voltage Controlled Oscillator), which generates a signal having an initial frequency fuW. The initial signal 1 is transmitted in the direction of the transponder 14 by means of a transmitter 22. The transponder 14 receives the initial signal 1 with a receiver 19. In the transponder 14, the initial signal 1 is amplified by the amplifier 17 and forwarded to a transmitter 22 of the transponder 14, which transmits the locating signal 2 thus generated back to a receiver 19 of the base station 12. The base station 12 receives the locating signal 2 and evaluates it. For this purpose, the locating signal 2 is forwarded to a first mixer 24, where it is mixed with the initial frequency fuW of the signal source 21 of the initial signal 1 and forwarded to a filter 28. The filter 28 can be a high-pass filter or a bandpass filter or a low-pass filter which filters the locating signal 2 out of a signal superposed with noise at the receiver 19 of the base station 12. After filtering, the filtered signal is conducted to an output 32 of the base station 12 for evaluation, where it can be analyzed for example by means of a computer in respect of movements, distances, oscillations and directions of movement of the objects 15.

[0095] The initial signal 1 can be calculated as follows if the temporal dependence of the initial frequency is general, wherein y1(t) is the initial signal, A is the amplitude, ω is the frequency, and t and respectively t′ are time. This calculation formula also applies to temporally dependent frequencies ω(t) that are not linear.

y.sub.1(t)A.Math.cos(∫.sub.∞.sup.tω(t′).Math.dt′)

[0096] In the case of slow frequency variations compared with the period duration of the initial signal 1, the emitted initial signal 1 can also approximately be subject to the following relationship, wherein a linear relationship between the time-dependent initial frequency ω(t) and time t is present. Furthermore, a phase shift ϕ0 is contained, which also arises as a result of the integration of the general formula for y1(t).

y.sub.1(t)=A.Math.cos(ω(t).Math.t+φ.sub.0)

[0097] The initial signal 1 emitted by the transmitter 22 of the base station 12, said initial signal following a wave function y1(t), is received by the receiver 19 of the transponder 14 and includes a time of flight delay T of from just the distance between the transponder 14 and the base station 12. In this case, the receiver 19 of the transponder 14 receives a wave function y2(t) with an attenuated amplitude B, which can be described as follows.

y.sub.2(t)=B.Math.cos(ω(t).Math.(t−T.sub.oF)+φ.sub.0)

[0098] Since the change in the time-dependent initial frequency ω(t) can be regarded as very slow or stepwise, the argument of ω(t) is approximately not shifted in time by the time of flight delay ToF. The argument simply remains t.

[0099] The transponder 14 of the embodiment in accordance with FIG. 2 merely amplifies the received signal with the wave function y2(t) and emits a locating signal 2 having an altered amplitude, which, after a renewed time of flight delay Tof and a damping of the amplitude, is received by the receiver 19 of the base station 12 with the wave function y4(t) having an amplitude D and a doubled time of flight delay Tof. The argument of ω(t) can likewise be regarded as approximately not shifted in time by the time of flight delay.

y.sub.4(t)=D.Math.cos(ω(t).Math.(t−2.Math.T.sub.oF)+φ.sub.0)

[0100] In the base station 12, the received locating signal 2 is multiplied by the initial signal 1 by the first mixer 24. The multiplication proceeds on the basis of trigonometrical theorems with respect to the following wave function.

[00001]$y_1\left(t\right).Math.y_4\left(t\right)=\frac{A.Math.D}{2}.Math.\left[(\cos \left(2\omega \left(t\right).Math.T_{\mathrm{oF}}\right)+\cos \left(2.Math.\omega \left(t\right).Math.\left(t-T_{\mathrm{oF}}\right)+2{\phi }_0\right)\right]$

[0101] Afterward, the right-hand term is filtered out by low-pass filtering, such that a filtered function is output to the output 32 for evaluation. The following function is particularly easy to analyze since unnecessary signal components and noise have been filtered out.

[00002]$\begin{array}{cc}\mathrm{filt}\left(y_1\left(t\right).Math.y_4\left(t\right)\right)=\frac{A.Math.D}{2}.Math.\cos \left(2\omega \left(t\right).Math.T_{\mathrm{oF}}\right)& \end{array}$

[0102] By virtue of the constant time of flight delay ToF, the wave functions oscillate harmonically owing to the time-dependent frequency variation of the initial frequency ω(t). In the case of different distances between the transponder 14 and the base station 12, the signal oscillates at different speeds in the case of a linear variation of the initial frequency ω(t). Moreover, an FMCW radar system can process abrupt frequency changes. In the case of a superposition of a plurality of objects 15 with transponders 14, the linear and other components of the signals are separated from one another by a Fourier transformation, thereby enabling an evaluation of the distance and the speed of the individual objects.

[0103] If a linear change in the initial frequency ω(t) is assumed, a temporally linear relationship is obtained, wherein Δ ω represents a change in frequency and ΔT represents a change in time.

[00003]$\omega \left(t\right)=\frac{\mathrm{\Delta \omega }}{\Delta T}.Math.t$

[0104] The wave function y1(t) of the initial signal 1 can be simplified as a result. There follows after an integration of the linear relationship

[00004]$y_1\left(t\right)=A.Math.\cos \left({\int }_{\infty }^t\omega \left(t^{\prime }\right).Math.{\mathrm{dt}}^{\prime }\right)=A.Math.\cos \left(\frac{\mathrm{\Delta \omega }}{2\Delta T}.Math.t^2\right).$

[0105] Furthermore, the following relationship results for the wave function y4(t) of the locating signal 2 received by the base station 12.

[00005]$y_4\left(t\right)=D.Math.\cos \left(\frac{\Delta \omega }{2\Delta T}.Math.{\left(t-2T_{\mathrm{oF}}\right)}^2\right)=D.Math.\cos \left(\frac{\mathrm{\Delta \omega }}{2\Delta T}.Math.\left(t^2-4T_{\mathrm{oF}}.Math.t+4T_{\mathrm{oF}}^2\right)\right)$

[0106] The simplified wave functions y1 and y4 are multiplied together again and subsequently filtered, resulting in the following relationship according to the above explanation of the filtering process.

[00006]$\mathrm{filt}\left(y_1\left(t\right).Math.y_4\left(t\right)\right)=\frac{A.Math.D}{2}.Math.\cos \left(2\underset{\underset{\omega \left(t\right)}{︸}}{\frac{\Delta \omega }{\Delta T}.Math.t}.Math.T_{\mathrm{oF}}-2\frac{\Delta \omega }{\Delta T}.Math.T_{\mathrm{oF}}^2\right)$

[0107] The first term in the argument of the cosine function represents the relationship of the stepwise FMCW method. Supplementarily to the term of the stepwise FMCW method, the second term represents the distance-dependent phase shift, which remains in a steady state in the case of an invariable distance despite the linear time dependence of the initial frequency. This is the case for a stationary object 15.

[0108] If the device 15 is in motion, however, and has a speed, an acceleration or an oscillatory movement, then the time of flight delay Tof is no longer in the steady state, but rather likewise follows a temporal dependence. In the simplest case, this can be linear as follows, wherein v is a constant speed and c0 is the speed of light.

[00007]$T_{\mathrm{oF}}=\frac{v.Math.t}{c_0}$

[0109] For a moving device 15, the filtered multiplication of the wave functions that is passed to the output 32 for evaluation results as

[00008]$\mathrm{filt}\left(y_1\left(t\right).Math.y_4\left(t\right)\right)=\frac{A.Math.D}{2}.Math.\cos \left(2\frac{\Delta \omega }{\Delta T}.Math.\frac{v}{c_0}.Math.t^2.Math.\left(1-\frac{v}{c_0}\right)\right)$

[0110] FIG. 3 shows a frequency analysis of the multiplied signal, said frequency analysis being achieved by the radar system 10 of the embodiment in FIG. 2. The vertical axis 30 indicates the amplitude strength and the horizontal axis 31 indicates the magnitude of the frequency in hertz. The radar system 10 in FIG. 2 does not generate an amplitude modulation with a high-purity periodic function according to the invention.

[0111] If the radar system is now operated in a 24 GHz ISM frequency band, then the linear variation of the initial frequency ω(t) can take place with a bandwidth of 250 MHz. The resultant resolution arises from the following relationship, wherein ΔR is the resolution pattern in a spatial direction and Δf is a change in a frequency.

[00009]$\Delta R=\frac{c_0}{2\Delta f}$

[0112] The number of oscillations while traversing the frequency ramp with ω(t) in the case of a 24 GHz ISM frequency band follows the following relation, wherein NR indicates the number of oscillations and R indicates a distance.

[00010]$N_R=\frac{R}{\Delta R}$

[0113] By way of example, in the case of objects at a distance of 1.8 km from the base station 12, there are up to 3000 oscillations per frequency ramp. Given a ramp repetition frequency which is high enough, and which can be 50 Hz, for example, in order to be able to cleanly resolve movements of the device 15 on the basis of the Doppler effect, a maximum frequency of 150 kHz can be calculated for passive radiating surfaces of the objects. Passive radiating surfaces are surfaces of the objects and of the surroundings thereof which radiate back the radar signals and they arrive at the base station 12 in addition to the locating signal 2 radiated back actively by the transponder 14. These signals 33 radiated back passively are represented as a triangular area in FIG. 3 since these passive reflectors are distributed approximately homogenously and they generate a continuous spectrum from 0 Hz to 150 Hz, the amplitude of this signal 33 decreasing.

[0114] If, then, in accordance with the embodiment in FIG. 3, the locating signal 2 is not modulated with an amplitude modulation and a high-purity frequency, rather the amplitude is merely amplified, the result, as illustrated in the frequency analysis in FIG. 3, is a doubled transmitted-back peak-like signal 27 having discrete distance-dependent frequencies fR which lies in the signal 33 radiated back passively. This results in a superposition of the signals 27, 33 and thus in an evaluation of the distance that is made more difficult. In particular, as the distance increases, the amplitude of the discrete frequency fR can fall below the amplitude of the backscattered signal 33. Such a disadvantageous effect occurs for example in the case of multiply reflective surroundings such as ducts, since there the duct walls constantly reflect owing to the high roughness. This can be a particular hindrance if there is a desire to recognize a duct robot using a radar system.

[0115] A further embodiment of the radar system 10 is illustrated in FIG. 5. In principle, in this embodiment, the initial signal 1 is likewise transmitted by a transmitter 22 of the base station 12 to a receiver 19 of the transponder 14, and the locating signal 2 is transmitted back. In the transponder 14, a first mixer 16 is connected downstream of the amplifier 17 and amplitude-modulates the wave function y2(t) by means of a signal source 23. The signal source 23 impresses a frequency fAM on the amplitude of the wave function y2(t), which results in an altered wave function y3(t) with respect to the embodiment in FIG. 2. The new wave function y3(t) follows the relationship

y.sub.3(t)=k.Math.B.Math.cos(ω(t).Math.(t−T.sub.oF)+φ.sub.0).Math.cos(ω.sub.AM.Math.t+φ.sub.AM)

[0116] In this case, k is a factor by which the new amplitude B is increased or decreased. Furthermore, ωAM is the frequency of the amplitude modulation at which the amplitude oscillates, and φAM is the phase shift of the amplitude modulation. This amplitude modulation frequency fAM and also the factor k for the amplitude modulation can differ in magnitude for different objects 15 with different transponders 14.

[0117] The receiver 19 of the base station 12 receives a wave function y4(t)

y.sub.4(t)=D.Math.cos(ω(t).Math.(t−2.Math.T.sub.oF)+φ.sub.0).Math.cos(ω.sub.AM.Math.(t−T.sub.oF)+φ.sub.AM)

[0118] which is altered according to the amplitude modulation. As in the embodiment in FIG. 3, the wave function y4(t) is mixed with the initial signal 1 by the first mixer 24 and then filtered by the filter 28. The signal that arises as a result of the mixing is a product of two harmonic functions and has the following form.

[00011]$\mathrm{filt}\left(y_1\left(t\right).Math.y_4\left(t\right)\right)=\frac{A.Math.D}{2}.Math.\cos \left[2\omega \left(t\right).Math.T_{{\mathrm{oF}}^{}}\right].Math.\cos \left[{\omega }_{\mathrm{AM}}.Math.\left(t-T_{\mathrm{oF}}\right)+{\phi }_{\mathrm{AM}}\right]$

[0119] The frequency analysis of the received locating signal 2 is illustrated in FIG. 5. The two peak-like transmitted-back doubled signals 27 have been shifted out of the passive signal 33 along the frequency axis 31 around the amplitude modulation frequency fAM and have a frequency component which includes a distance-dependent frequency fR, which is firstly subtracted from the amplitude modulation frequency fAM and secondly added thereto, thus giving rise to two signal peaks 27 around the amplitude modulation frequency fAM. As a result, even in the case of very large distances the amplitudes of the signals 27 are not superposed by the amplitude of the noise of the signal 33.

[0120] Subsequently, for the purpose of signal processing, as illustrated in FIG. 5, in a second mixer 26 in the base station 12, a signal from a signal source 29 for a sampling can be modulated onto the filtered signal. The signal modulated in this way has a frequency fdown that is lower than the modulation frequency fAM. As a result, sampling of the signal after it has been transmitted to the output 32 can be simplified because the data rate can be reduced by means of slow analog-to-digital converters.

[0121] Such a frequency analysis of the signal processing is illustrated in FIG. 7, which shows the mixing of the wave function y4(t) by the second mixer 26 and the impressing of the frequency fdown. In this case, the signals 27 are drawn back again to a range with a low frequency, the signals 27 doubling around the starting frequency of the second mixer 26 in the base station 12 by way of the distance-dependent frequency fR.

[0122] Alternatively, for signal processing purposes, the second mixer 26 and the signal source 29 can be dispensed with, wherein the signal transmitted to the output 32 then has to be analyzed by means of fast analog-to-digital converters.

[0123] A third alternative for a subsequent treatment for the signal processing of the filtered signal includes just the use of slow analog-to-digital converters, but without the mixing with a slow frequency fdown by means of a signal source 29.

[0124] A fourth alternative for the subsequent signal processing of the filtered signal includes a self-mixing of the signal in a baseband signal and a sampling of the signal with very low sampling rates. In this case, firstly only the relevant frequency band around fAM is bandpass-filtered. In particular, frequencies in the lower frequency range but also higher frequencies are filtered out as a result. The self-mixing results in the following expression, the expression containing, read from left to right, a DC component, the pure distance information in the argument of a harmonic function with the frequency 2fR but with a factor of 2 compared with the traditional radar equation, the doubled amplitude modulation frequency fAM and two discrete signal peaks 27 with respect to the doubled amplitude modulation frequency fAM on account of the amplitude modulation with the locating signal 2.

[00012]${\left[\mathrm{filt}\left(y_1\left(t\right).Math.y_4\left(t\right)\right)\right]}^2={\left(\frac{A.Math.D}{2}.Math.\cos \left[2\omega \left(t\right).Math.T_{\mathrm{oF}}\right].Math.\cos \left[{\omega }_{\mathrm{AM}}.Math.\left(t-T_{\mathrm{oF}}\right)+{\phi }_{\mathrm{AM}}\right]\right)}^2=\frac{{\left(A.Math.D\right)}^2}{4}.Math.{\left(\cos \left[2\omega \left(t\right).Math.T_{\mathrm{oF}}\right]\right)}^2.Math.{\left(\cos \left[{\omega }_{\mathrm{AM}}.Math.\left(t-T_{\mathrm{oF}}\right)+{\phi }_{\mathrm{AM}}\right]\right)}^2=\frac{{\left(A.Math.D\right)}^2}{8}.Math.\left(1+\cos \left[4\omega \left(t\right).Math.T_{\mathrm{oF}}\right]\right).Math.\left(1+\cos \left[2.Math.{\omega }_{\mathrm{AM}}.Math.\left(t-T_{\mathrm{oF}}\right)+{\phi }_{\mathrm{AM}}\right]\right)=\frac{{\left(A.Math.D\right)}^2}{8}.Math.\left(1+\cos \left[4\omega \left(t\right).Math.T_{\mathrm{oF}}\right]+\cos \left[2.Math.{\omega }_{\mathrm{AM}}.Math.\left(t-T_{\mathrm{oF}}\right)+{\phi }_{\mathrm{AM}}\right]+\cos \left[4\omega \left(t\right).Math.T_{\mathrm{oF}}\right].Math.\cos \left[2.Math.{\omega }_{\mathrm{AM}}.Math.\left(t-T_{\mathrm{oF}}\right)+{\phi }_{\mathrm{AM}}\right]\right)$

[0125] FIG. 8 shows the frequency analysis of the self-mixing, the distance-dependent frequency fR being determined by the filtering of the high-frequency frequencies by means of a simple data acquisition. A doubled resolution capability is achieved by means of the self-mixing because the distance axis is extended by a factor of 2 by comparison with other radar methods.

[0126] In order to simplify the following calculations, it is assumed that only one transponder 14 in the radar system 10 communicates with the base station 12. The phase angle of the mixed amplitude-modulated locating signal 2 of the base station 12 is not known; moreover, fluctuations of the high-purity amplitude modulation frequency can occur on account of component tolerances.

[0127] However, the emitted frequency can be calculated on the basis of the doubled signal 27 transmitted back, by means of the averaging of the two distance-dependent frequencies fR and −fR. Furthermore, the distance from the base station 12 to the transponder 14 and thus to the object 15 can be calculated by way of the difference between the two distance-dependent frequencies fR and −fR of the two peak-like signals 27. The following relationship can be used for this purpose, wherein fright indicates the frequency of the right peak and fleft indicates the frequency of the left peak.

[00013]$R=\frac{c_0}{4.Math.\Delta f/\Delta T}.Math.\left(f_{\mathrm{right}}-f_{t\backslash \mathrm{left}}\right)$

[0128] The Doppler effect and/or the phase rotation which can arise on account of small movements of the object 15 are determined by the measurement of the phase difference Δω(t) between the two signals 27 transmitted back, wherein φ right(t) indicates the phase of the right peak and φ left(t) indicates the phase of the left peak.

Δφ(t)=f.sub.right(t)−f.sub.left(t)

[0129] A further embodiment includes a plurality of transponders 14 used with just one base station 12. In this case, each transponder 14 amplitude-modulates with a dedicated amplitude modulation frequency fAM,i, wherein i is the index of the respective transponder 14 where i=1, 2, 3 . . . N. The respective amplitude modulation frequencies fAM,i=≈fAM differ from one another in their phase angle and the frequencies, but they are preferably distributed around the frequency fAM. In order that the objects can be reliably differentiated, the distances R must differ at least by one to two times the distance resolution A R. It is only if these conditions are met that the left and right peaks of the signal 27 of the individual transponders 14 can be unambiguously differentiated from one another. Otherwise, the peaks of the signals 27 of the different transponders 14 merge and can therefore no longer be assigned to the respective transponders 14.

[0130] If the locating signal is then self-mixed for evaluation in accordance with the fourth alternative of the signal processing, the transponder systems 14 can operate with significantly different amplitude modulation frequencies fAM,i. These amplitude modulation frequencies fAM,i can include the multiple of the fundamental amplitude modulation frequencies fAM. Furthermore, the self-mixing results in coupled multiplication terms between the individual transponders 14, the multiplication terms of the different amplitude modulation frequencies fAM,i being manifested with multiples of the fundamental amplitude modulation frequencies fAM. Therefore, they are easy to filter out, such that the uncoupled multiplication terms are mixed into the low frequency band and are superposed there with the signals of the other transponders 14. If all of the transponders 14 were operated with the same amplitude modulation frequencies fAM, so-called “ghost objects” would arise which do not represent real interference.

[0131] Furthermore, the base station 12 can be either an SISO system having preferably one TX antenna and one RX antenna or an imaging MIMO system. The use of a corresponding system presupposes that in each case only one of the four signal processing methods above can be used.

[0132] Alternatively, instead of a linear frequency variation that is typical in a radar system, some other modulation method of the kind that are customary in conventional communication systems can be used in the base station.

[0133] FIG. 9 illustrates an alternative transponder 14. The transponder 14 mixes the wave function y2(t), after amplification by the amplifier 17, with a stabilization frequency fRF by means of a second mixer 18, said stabilization frequency being generated by a signal source 34. After being mixed in the second mixer 18, the signal is forwarded to the first mixer 16 in the transponder 14, where the amplitude modulation is effected. After the amplitude modulation, the signal is forwarded further to a third mixer 20, where it is mixed with the stabilization frequency fRF in a repeated manner and as wave function y3(t) is transmitted by the transmitter 22 as locating signal 2 to the base station 12. The stabilization frequency fRF is in the microwave range and has approximately the same frequency fuW as the initial signal 1.