Abstract:
Distance and velocity measuring at a plurality of objects using FMCW radar includes repeating measurements using different frequency ramps and including mixing transmitted and received signals, and recording the mixed signal&#39;s spectrum. A matching includes recording spectra peaks for ramps, if belonging to the same object, allocating them to each other, and calculating distances and velocities from peak frequencies. A tracking includes identifying with one another objects measured at various times based on distance and velocity consistency. Each measuring cycle includes less than four measurements with different frequency ramps. For each plausible two peak combination recorded, respectively, during first and second measurements of a cycle, distance and velocity of one possible object represented by these peaks are calculated. A measurement&#39;s anticipated result, is calculated from distance and velocity of the possible object, discarded if an anticipated result does not agree with the measured result.

Description:
FIELD OF THE INVENTION 
   The present invention relates to a method for measuring distance and velocity at a plurality of objects using FMCW radar. 
   BACKGROUND INFORMATION 
   Discussed herein is a method for measuring distance and velocity at a plurality of objects using FMCW radar, in which:
         measurements are repeated cyclically with at least two different frequency ramps,   in each measurement, the transmitted signal is mixed with the received signal, and the spectrum of the mixed signal is recorded,   in a matching procedure, the peaks that are in the spectra recorded for various ramps and that belong to the same object are allocated to each other, and the distances and velocities of the objects are calculated from the frequencies of the peaks, and   in a tracking procedure, the objects measured at various times are identified with one another on the basis of the consistency of their distance and velocity data.       

   In particular, discussed herein is a method of this type which is used in ranging systems or distance-control systems for motor vehicles. 
   From practice, a distance-control system, a so-called ACC (adaptive cruise control) system for motor vehicles is known which works with an FMCW (frequency modulated continuous wave) radar. The functioning principle is described in Winner: “Adaptive Cruise Control”, Automotive Electronics Handbook, published by Ronald K. Jurgen, 2 nd  edition, McGraw-Hill Inc., Chapter 30.1 (1999). The radar waves are emitted continuously, and the frequency is modulated in accordance with a ramp function made up of a cyclical sequence of four ramps having different slopes. The ramps form two pairs, each made up of a rising and a falling ramp. The amounts of the slopes are identical within each pair, but differ from pair to pair. By mixing the transmitted signal with the received signal, which is obtained by reflection of the radar waves at a plurality of objects, a low-frequency signal is formed whose frequency corresponds to the difference between the frequency of the transmitted signal and the frequency of the reflected signal. In each individual measurement, the spectrum of the low-frequency signal is recorded during the duration of one frequency ramp with constant slope. In this spectrum, each object is represented by a peak whose frequency f, according to the following equation, is a function of the distance d and the velocity v (relative velocity) of the object:
 
 f =|(2* F/c*T )* d +(2* f   s   /c )* v|   (1)
 
   Meanings of equation terms:
         f peak frequency in the low-frequency signal   F frequency deviation (frequency at the end of the ramp−frequency at the beginning of the ramp)   c speed of light   T modulation duration (of the ramp)   f s  frequency of the transmitted signal       

   The first term in equation (1) is proportional to the signal propagation time, d/c and the ramp slope F/T. The second term corresponds to the Doppler shift of the reflected signal. 
   If only one reflecting object is present, distance d and relative velocity v of this object may be calculated from peak frequencies f 1  and f 2 , which are obtained by two measurements with different ramp slopes. To that end, the following equation system is solved:
 
 f   1   =α*d+β*v  
 
 f   2   =γ*d+β*v   (2)
 
with:
 
α=2 *f/c*T  for the first ramp,
 
β=2 *f   s   /c  
 
γ=2 *F/c*T  for the second ramp
 
   Given a plurality of objects, however, ambiguities occur, because it is not clear which peak belongs to which object. In the known method, this ambiguity is eliminated by performing two additional measurements using a different ramp slope. Since the distances and relative velocities of the objects change slightly at most within the time in which the four measurements are performed, the allocation between the peaks and the objects must be carried out so that the same distances and relative velocities are obtained for the first two measurements as for the last two measurements. This allocation of the peaks to the objects is called matching. 
   For practical applications, for example, in an ACC system, it is generally necessary to be able to track the measured distances and relative velocities of the various objects over a longer period of time. Therefore, in a procedure known as tracking, the objects measured in one measuring cycle must be identified with the objects measured in a preceding cycle. This tracking procedure is based on the criterion that the distances and relative velocities for each object, measured at various times, must yield a plausible and, in particular, physically possible movement of the object. 
   The U.S. Pat. No. 5,600,561 discusses a method in which only the distances are measured with the aid of radar, and the object velocities are calculated from the changes in distance. The distances measured for various objects are allocated to the individual objects in such a way that the newly recorded distance data are consistent with the previously calculated velocities. 
   In contrast, an FMCW radar has the advantage that the relative velocities of the objects can be measured directly. However, it is only possible to differentiate various objects from each other both with respect to their distances and with respect to their relative velocities with a limited resolution. 
   SUMMARY OF THE INVENTION 
   An object of the present invention is to provide a method for measuring distance and velocity using FMCW radar that permits improved object resolution. 
   This objective may be achieved according to the present invention in a method of the type indicated at the outset, in that
         each measuring cycle includes not more than three measurements with different frequency ramps,   for each plausible combination of two peaks, of which one was recorded during a first measurement and the other was recorded during a second measurement of the same cycle, the distance and the velocity of one possible object represented by these peaks are calculated,   the anticipated result of at least one further measurement is calculated from the distance and the velocity of the possible object, and   the possible object is discarded if at least one anticipated result does not agree with the measured result.       

   One reason for the limited resolution capability of FMCW radar is that the peaks occurring in the individual spectra each have a finite width. In this context, a “blur relation” exists between the width of these peaks and the time available for recording the spectra. If, for example, the low-frequency signals are sampled to obtain discrete spectra with a number n of sampling values, then sampling time T/n (T=modulation duration) is available for each sampling value. In this case, the resolution with respect to the distance is proportional to modulation amplitude F, and the resolution with respect to the relative velocity is proportional to modulation duration T. 
   Compared to the other method discussed above, the exemplary method of the present invention now has the advantage that not four, but rather at most three measurements are performed within each measuring cycle, so that given the same cycle duration, a greater modulation duration is available, and better resolution with respect to the relative velocity is achieved accordingly. 
   Ambiguities in the case of a plurality of objects are eliminated in the method according to the present invention by linking the matching procedure and the tracking procedure to each other. If m objects are in the locating range of the radar, during the first measurement, one obtains peaks at the frequencies f(1,i), i=1 . . . m, and during the second measurement, peak frequencies f(2,j), j=1, . . . , m are obtained. Each pair (i, j) of peaks is regarded as a possible object which can be assigned a distance d i ,j and a relative velocity v i ,j. From the distance and relative velocity data thus obtained for each possible object, it is possible to calculate what result ought to be anticipated for this object in a further measurement. Depending on the embodiment variant of the method, this further measurement may be a distance and velocity measurement in a different measuring cycle or a third measurement within the same cycle, using a ramp slope different from the two first measurements. The anticipated result is then compared to the result actually obtained during the further measurement, and if these results do not match, the object in question is discarded. Therefore, only the distance and velocity data remain for those peak pairs which correspond to real objects. 
   In one specific embodiment, the measuring cycle includes only two measurements with equal and opposite ramp slopes. In the case of the given cycle duration, the modulation duration is then twice as great as for the conventional methods which work with four measurements. Accordingly, the resolution with respect to the relative velocities is improved by a factor of 2. Another advantage is that all measurements may be performed with a maximum frequency deviation, in which the available frequency range of the microwave transmitter is fully utilized. Correspondingly, a maximum resolution with respect to the distance is also achieved in each measurement, while when working with the conventional method, two of the four measurements had to be performed with a smaller ramp slope, and accordingly, with a smaller frequency deviation. Overall, therefore, given a relatively small cycle duration—and correspondingly high time resolution in the object search and object tracking—a high resolution may be achieved both with respect to the distance measurement and with respect to the relative-velocity measurement. 
   In this specific embodiment, the further measurement, whose result is compared to the anticipated result, is a distance and relative-velocity measurement in an earlier or later measuring cycle. The agreement of the results then means not only that the possible object in question is a real object, but at the same time means that the object was also identified with an object in the earlier or later measuring cycle, so that the tracking procedure was successful. 
   For example, from the distance measured in the current cycle and the appertaining relative velocity, it is calculated what distance the same object would have to have had in the immediately preceding measuring cycle. In so doing, it may be assumed in the simplest case that the change in relative velocity is negligibly small from measuring cycle to measuring cycle. 
   Alternatively, however, an expanded tracking procedure may also be used, in which not only the immediately preceding measuring cycle, but rather a larger number of previous measuring cycles is taken into account. It is possible that, because of interference effects, no echo was received from a real object within a single measuring cycle. In this case, the expanded tracking procedure with consideration of a plurality of measuring cycles offers the advantage that the object can nevertheless be recognized as a real object and successfully tracked. 
   Instead of calculating the anticipated distance and the anticipated relative velocity of the object for a previous measuring cycle and comparing them to the actually measured values, in a modified specific embodiment, it is also possible, from the data measured in the instantaneous cycle, to directly calculate the frequency at which the peak for this object ought to be found in the other (earlier or later) cycle. The result can then be very easily verified by specifically searching for a peak at this location. An expanded tracking with consideration of a plurality of measuring cycles is possible in this variant, as well. 
   In the specific embodiment of the method which works with three measurements within one measuring cycle, the third measurement which may have a greater modulation duration than the two first measurements. In this way, a particularly high resolution with respect to the relative velocity is achieved especially in the third measurement. It is again possible to also work with maximum frequency deviation in the third measurement, so that here as well, a maximum distance resolution is achieved in all measurements. 
   This specific embodiment may also be combined with the tracking, taking into account the immediately preceding measuring cycle or a plurality of preceding measuring cycles. For example, it can be required for real objects that the corresponding frequency was measured in two successive measurements in all three spectra. Alternatively, however, this method may also be combined with the tracking in such a way that the confirmation as to whether a real object is involved is carried out depending on the situation with the aid of the simple tracking, with the aid of the third frequency ramp, or with both. In this context, the third ramp and the tracking may also be linked by “or”, so that an object is recognized as real if only one of the anticipated results is confirmed, be it the result for the previous measuring cycle or the result for the measurement with the third frequency ramp. An expanded tracking with consideration of more than two measuring cycles is possible in all combinations when working with these variants, as well. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a frequency/time diagram for clarifying the functioning method of an FMCW radar. 
       FIG. 2  shows examples for spectra that are recorded using the FMCW radar. 
       FIG. 3  shows a diagram for clarifying a method for determining the object distance. 
       FIG. 4  shows a diagram analogous to  FIG. 3 , but for a larger frequency deviation of the radar signal. 
       FIG. 5  shows a diagram for clarifying a method for determining the relative velocities of objects. 
       FIG. 6  shows a diagram analogous to  FIG. 5 , but for a larger frequency deviation of the radar signal. 
       FIG. 7  shows a flow chart for clarifying the general principle of a first specific embodiment of the method according to the present invention. 
       FIG. 8  shows a detailed flow chart of the method according to  FIG. 7 . 
       FIG. 9  shows a flow chart of a subroutine in the method according to  FIG. 8 . 
       FIG. 10  shows an exemplary embodiment for a further subroutine in the method according to  FIG. 8 . 
       FIG. 11  shows another exemplary embodiment for a further subroutine in the method according to  FIG. 8 . 
       FIG. 12  shows a flow chart for a modification of the method according to  FIG. 8 . 
       FIG. 13  shows an example for a subroutine in the method according to  FIG. 12 . 
       FIG. 14  shows another example for a subroutine in the method according to  FIG. 12 . 
       FIG. 15  shops a frequency/time diagram for another specific embodiment of the method. 
       FIG. 16  shows a flowchart for a variant of the method according to  FIG. 15 . 
       FIG. 17  shows a flowchart for another variant of the method according to  FIG. 15 . 
       FIG. 18  shows a flowchart for another variant of the method according to  FIG. 15 . 
   

   DETAILED DESCRIPTION 
   According to  FIG. 1 , when working with an FMCW radar, radar waves are continually emitted with variable frequency f s . Curve  10  drawn in bold indicates the time dependency of frequency f s . This frequency is varied periodically according to a ramp function having a rising first ramp  12  and a falling second ramp  14 . Ramps  12 ,  14  belong to two measurements M 1  and M 2 , which are repeated cyclically. The ramps for both measurements have the same frequency deviation F and identical modulation durations T 1  and T 2 , and consequently their slopes are equal and opposite. 
   Frequency curve  16  for the associated radar echo of a single object is shown with a broken line. This curve has the same ramps  18  and  20 , but with a time shift Δt, which is given by the object distance, and with a frequency shift Δf determined by the Doppler shift. 
   In the radar sensor, the emitted wave is mixed with the received radar echo, so that a low-frequency beat signal (LF signal) is obtained having a frequency f which corresponds to the frequency difference between the emitted waves and the received waves. During each measurement M 1 , M 2 , a frequency spectrum is recorded from this beat signal, e.g. by rapid Fourier transform. 
     FIG. 2  shows examples for two frequency spectra  22 ,  24  obtained in the two measurements M 1  and M 2  when a single object, e.g. a preceding vehicle, is located in the radar locating range. In this case, each spectrum has a peak with an apex at the peak frequency f 1  and f 2 , respectively, which corresponds to the frequency difference of curves  10  and  16  on respective ramps  12  and  18  or  14  and  20 . The frequency difference is substantially dependent on the product of time shift Δt (signal propagation time) and the ramp slope; however during rising flanks  12 ,  18 , it is reduced by the Doppler frequency, whereas during falling flanks  14 ,  20 , it is increased by the Doppler frequency (given positive Doppler shift to greater frequencies, corresponding to an approach of the radar target). The average value of frequencies f 1  and f 2 , at which the two peaks  22 ,  24  lie in  FIG. 2 , therefore corresponds to the signal propagation time, and thus indicates distance d of the object, while half the difference between these two frequencies indicates the Doppler shift, and therefore the amount and algebraic sign of relative velocity v of the object. Relative velocity v is proportional to (f 1 −f 2 )/2. 
   During the duration of a single measurement M 1  or M 2 , the frequency of the LF-signal whose spectrum is shown in  FIG. 2  is largely constant. Nevertheless, even given sharply defined object distances d and relative velocities v, peaks  22 ,  24  have a certain width which, because of the properties of the Fourier transform, is approximately inversely proportional to the measuring time. On its part, the measuring time available is proportional to modulation duration T 1  and T 2 , respectively. 
   When, in the radar locating range, there are two objects whose peaks are so close to each other that their distance is small in relation to the width of the peaks, then the corresponding peaks in the spectrum can no longer be resolved, and consequently both objects can no longer be differentiated from each other. The more sharply the peaks are defined, i.e., the greater the modulation durations T 1 , T 2 , the better the resolution is. 
   The resolution with respect to the object distance may be improved by enlarging frequency deviation F. This shall be clarified with reference to  FIGS. 3 and 4 . 
   In  FIG. 3 , in addition to curve  10 , curves  26 ,  28  of two radar echoes, which are received from two different objects, are drawn in. For each curve  26 ,  28 , differences D 26  and D 28 , respectively, between the peak frequencies are indicated on the first and second ramp. This difference is independent of the Doppler shift, and therefore solely represents the propagation time, and thus object distance d. 
     FIG. 4  shows the same for a larger frequency deviation F. One can see that here, differences D 26  and D 28  are enlarged proportionally to the frequency deviation, so that the peaks can be differentiated more clearly. The same spread of differences D 26  and D 28  could also be achieved by reducing the modulation durations and leaving frequency deviation F unchanged, so that the same ramp slopes are attained as in  FIG. 4 . However, the larger spread would then not lead to a higher resolution, since because of the shorter measuring duration, the peaks would widen accordingly. The decisive parameter for the resolution of the distances is therefore frequency deviation F. In the example described here, in both measurements M 1  and M 2 , use is made of the maximum frequency deviation achievable based on the design of the radar device. 
     FIGS. 5 and 6  illustrate that no better resolution with respect to the relative velocities can be achieved by increasing frequency deviation F. In  FIG. 5 , sums S 26  and S 28  of the frequency differences are indicated on the two ramps for the two curves  26  and  28 . The distance-dependent propagation-time differences have the exactly opposite effect on the frequency difference in the two ramps, and therefore cancel each other out in the summation, so that sums S 26  and S 28  solely represent the Doppler shift for the objects in question. Since this Doppler shift is not a function of the frequency deviation, sums S 26  and S 28  in  FIG. 6  are not greater than in  FIG. 5 . Therefore, improved resolution with respect to the relative velocities may only be achieved by longer modulation durations T 1 , T 2 . 
   On the other hand, however, the total cycle time T=T 1 +T 2  should not be too great, so that the objects detected in one measuring cycle are able to be detected again in the next measuring cycle with the aid of a tracking procedure based on similar distances and relative velocities, and so that the movements of the objects may be tracked with high time resolution. In the specific embodiment shown here, it is possible to satisfy these contradictory demands, since only two measurements need to be carried out during one measuring cycle, so that the modulation duration is relatively great (half as great as the cycle duration). However, a matching procedure is needed which, based on the two measurements per measuring cycle, permits the elimination of ambiguities in the detection of a plurality of objects, by correctly allocating the peaks recorded during the first measurement and the peaks recorded during the second measurement to each other. 
   This is achieved in the method described here by combining the matching procedure with the tracking procedure, as presented in broad outline in  FIG. 7 . 
   To that end, in step S 1  in  FIG. 7 , first of all the distances and relative velocities are calculated for all “possible objects” [i, j]. In this context, all pairs [i, j] of peaks are regarded as “possible objects”, i being the current number of all peaks from the spectrum recorded in the first measurement M 1 , and j being the current number of all peaks from the spectrum recorded in measurement M 2 . If a total of m objects are present, there are m peaks in each spectrum, and the number of possible objects is m 2 . The real objects are represented by a subset, made up of m pairs, of the quantity of all possible objects. 
   In step S 2 , the real objects are differentiated from the unreal objects by utilizing the history, i.e., the results of preceding measurements. In so doing, the criterion is that for real objects, a plausible connection must exist between the results of the current measurement and the results of one of the previous measurements. For example, it is possible to compare the distances and relative velocities from the instantaneous measuring cycle to the distances and relative velocities from the preceding measuring cycle, as is also usually done in a tracking procedure. For real objects, the relative velocities should then be nearly identical, and the difference between the distances must agree approximately with the product of the relative velocity and cycle duration T. Peak pairs for which no partner satisfying these criteria is found in at least one of the preceding measurements are sorted out as “false solution”, i.e., as unreal objects. In so doing, however, real objects which were detected by the radar device for the first time in the current measuring cycle are also mistakenly sorted out. So that these objects can be recognized in later measuring cycles, in step S 3 , the results for all possible objects are stored. For the further evaluation, however, e.g. for the distance control in a motor vehicle, in step S 4  only the “plausible” peak pairs recognized as real objects are utilized. 
     FIG. 8  shows the method sequence in greater detail. 
   Following step S 1 , in step S 21  the first possible object is selected from the list of all possible objects. In step S 22 , it is then estimated what distance and what relative velocity this object would have to have had in the preceding measuring cycle. Based on the results which were stored in the preceding measuring cycle in step S 3 , it is then checked in step S 23  whether an object with appropriate distance and appropriate relative velocity is actually found among the objects from the preceding cycle. If this is the case, then in step S 24 , the object which was selected in step S 21  is entered into the list of real objects. Otherwise, the object is discarded. 
   In step S 25 , it is checked whether all objects of the instantaneous cycle have already been verified. If this is not the case, in step S 26 , the next object is selected from the current list and there is a return to step S 22 . All objects are then verified in this manner one after another in a loop using steps S 22 -S 26 . After the last object is checked, the loop is left after step S 25 . 
   It is possible that the list of possible objects which was stored in the preceding cycle will still contain objects not found again in the current cycle. These objects are now deleted in step S 27 . Therefore, in this specific embodiment, only simple tracking is carried out in which the current objects are compared only to the objects from the immediately preceding measuring cycle. 
   Step S 1  in  FIGS. 7 and 8  is made up of a subroutine whose flow chart is shown in  FIG. 9 . In this context, it is assumed that the spectra recorded in the instantaneous cycle during the first measurement and during the second measurement each have a number of peaks corresponding to the number of objects and in each case lying at a certain frequency. Therefore, given m objects, each spectrum contains m frequencies at which a peak is located. In step S 11 , the first of these frequencies is selected from the first spectrum. Correspondingly, in step S 12 , the first frequency is selected from the second spectrum. In step S 13 , a first plausibility check is carried out based on the criterion that the amplitudes in the case of the first frequency in the first spectrum and the first frequency in the second spectrum must have similar values, if the peak pair in question is a real object. If the amplitudes clearly differ, they are obviously not echoes from the same object, so that the peak pair in question may be discarded from the start. 
   In step S 14 , a second plausibility check is carried out on the basis of the criterion that the signals which were reflected by the same object must also come from a similar direction. If this criterion is not met for the peak pair being considered, this peak pair may likewise be discarded. The checks in steps S 13  and S 14  make it possible to reduce the computing expenditure, however are not essential for the method. 
   In step S 15 , the actual calculation of distance d and relative velocity v is then carried out for the possible object represented by the peak pair being examined. This calculation is performed by solving the system of equations (2) indicated in the introductory section of the Specification. Here, frequency f (1,i) is the frequency for peak i in the first spectrum, and frequency f (2,j) is the frequency of peak j in the second spectrum. If the plausibility check in step S 13  or S 14  was negative, step S 15  is skipped. Therefore, the calculations in step S 15  are not carried out for each combination of peaks, but rather only for those combinations of peaks which are plausible in the sense that they satisfy the criteria checked in steps S 13  and S 14 . Only these peak pairs remain stored in the list of possible objects. 
   Steps S 16  through S 19  control the program run in two loops nested in one another, in which all combinations of peaks i and j in the two spectra are checked in succession. 
   After distances d and relative velocities v have been calculated in this way for all possible, at least for all plausible, objects, in light of this data, step S 22  in  FIG. 8  may be carried out in which, based on the relative velocities, there is a calculation back to find what distances the objects in question had in the preceding measuring cycle. Conversely, it is naturally also possible to proceed so that, based on the distance and velocity data obtained in the instantaneous cycle, the distances and relative velocities to be anticipated for these objects in the next measuring cycle are precalculated.  FIG. 10  shows a possible implementation of step S 23  in  FIG. 8  based on the latter principle. 
   In step S 231 , the values predicted in the preceding measuring cycle for the distance and the relative velocity and optionally also for the lateral displacement of the first possible object are read. In step S 232 , these predicted values are then compared to the values which were obtained in the instantaneous cycle for the currently observed object (selected in step S 21  in  FIG. 8 ). If the deviations are within permissible tolerance limits, in step S 233 , the two objects are linked to each other (tracking). Otherwise, step S 233  is skipped. 
   Steps S 234  and S 235  control a loop with which the above-described checks are repeated in succession for each possible object from the previous measuring cycle. If it was possible to link the instantaneous object in step S 233  to one of the objects from the previous measuring cycle, then the query in S 23  is answered with “yes”, and the method is continued with step S 24 . Otherwise, the query must be answered with “no”, and there is a jump to step S 25 . 
     FIG. 11  shows another possible implementation of step S 23  in  FIG. 8 . From the distance of the object, estimated in step S 22 , at the moment of the preceding measuring cycle, and from the relative velocity of this object (assumed as approximately constant), in step S 231 ′, the frequencies are calculated at which the peaks in the two spectra recorded in the preceding cycle would have had to be situated. The frequency calculation is performed according to equation (1) indicated in the introductory part of the Specification. In step S 232 ′, it is then checked whether these frequencies have actually been measured. If this is the case, step S 23  ends with the response “yes” (step S 233 ′), otherwise with the response “no” (step S 234 ′). 
   Naturally, the variant according to  FIG. 11  may also be carried out “forwards” by calculating the frequencies to be anticipated for the following measuring cycle. 
     FIG. 12  shows a variant with respect to the program sequence according to  FIG. 8 . This variant differs from  FIG. 8  essentially in that step S 27  in  FIG. 8  is replaced by a step S 28  in which a so-called expanded tracking is carried out. In this context, the check test in step S 23  may be performed both according to the method in accordance with  FIG. 10  (object matching) and according to the method in accordance with  FIG. 11  (frequency matching).  FIG. 13  shows one possible implementation of step S 28  for the first case. 
   In  FIG. 13 , the first element is selected from the list of real objects in step S 281 . In step S 282 , it is checked whether this object was found again in the current measuring cycle (positive result in response to the query in step S 23 ). If this is not the case, there is a certain probability that this object has disappeared from the locating range of the radar, i.e., it is less plausible that this object will appear again in later measurements. Accordingly, in step S 283 , a plausibility parameter for this object is decreased. In step S 284 , it is then checked whether the plausibility is still above a specific threshold value. If this is not the case, the object is discarded in step S 285 , i.e., it is permanently removed from the list of real objects. 
   In the event of a positive result in step S 284 , the object continues to be handled as a real object, but no current measuring data exists for the distance and the relative velocity. Therefore, this data is estimated in step S 286  by extrapolating the previous measuring data. 
   If the object was found again in step S 282 , in step S 287 , it is checked whether the plausibility parameter for this object has already reached an upper limiting value. If this is not the case, the plausibility is increased in step S 288 . Otherwise, step S 288  is skipped. 
   Steps S 289  and S 290  again control a loop, in which the above check tests are repeated for each object in the list of real objects. 
     FIG. 14  shows an implementation of step S 28  for the case when frequency matching according to  FIG. 11  is used in step S 23 . In comparison to  FIG. 13 , the subroutine according to  FIG. 14  has an additional step S 291  in which, from the estimated data for the position and relative velocity of the object not found again, the associated frequencies in the first and second spectrum are calculated. These frequencies are then regarded as “measured” in the next measuring cycle in the case of step S 282 ′. 
   The expanded tracking in step S 28  makes the method more robust with respect to a temporary loss of an object. The more frequently the object is found again, the higher its plausibility becomes—up to an upper limiting value. Temporary loss of the object leads to a reduction in plausibility, and the object remains in the list of real objects until the plausibility has decreased to below a lower limiting value. 
   With respect to the matching in step S 23  and in  FIG. 10  or  11 , however, a slight modification is necessary in the methods according to  FIGS. 12 through 14 . During the check test in step S 23 , it is necessary to take into account not only the immediately preceding measurement, but rather all objects still contained in the list of real objects must be included here as well, even if they were temporarily lost during the immediately preceding measurement. As an alternative, in step S 282  ( FIG. 13 ), the check test may be extended to those objects of the current cycle which were initially discarded in step S 23 . For these objects, step S 24  (inclusion in the list of real objects) can then optionally be retrieved. 
   Another specific embodiment of the method shall now be described with reference to  FIGS. 15 through 18 . 
     FIG. 15  shows a modified form of frequency curve  10  in  FIG. 1 . In this frequency curve, a rising ramp  30  again adjoins falling ramp  14  before the measuring cycle is repeated. Accordingly, three measurements M 1 , M 2  and M 3  are carried out here within one measuring cycle. In the third measurement M 3 , modulation duration T 3  is twice as great as in the two other measurements. The slope of ramp  30  is only half as great as for ramp  12 . Consequently, frequency deviation F is also at its maximum in third measurement M 3 . The object distances are therefore able to be measured with optimal resolution in the third measurement, as well. With respect to the relative velocities, because of the greater modulation duration, a resolution is achieved in the third measurement which is twice as high as in measurements M 1  and M 2 . The cycle duration is precisely as great here as in the conventional method, in which four measurements are performed within one cycle. The advantage of the method according to  FIG. 15  compared to the conventional method is that the object distances may be measured three times with maximum resolution within one cycle, and the relative velocities even one time with double the resolution. 
   Instead of the results of measurements M 1  and M 2  in the preceding cycles or in addition thereto, the result of measurement M 3  in the current cycle or in a preceding or subsequent cycle is utilized here for the matching. 
   An example for the method sequence is shown in  FIG. 16 . Steps S 101  and S 102  in  FIG. 16  correspond to steps S 1  and S 21  in  FIG. 8 . In step S 103 , for each possible object whose distances and relative velocities were calculated in step S 101  on the basis of measurements M 1  and M 2  in the current cycle, the anticipated frequency of the respective peak in the spectrum, which is recorded in measurement M 3  for ramp  30 , is calculated in accordance with equation (1). In step S 104 , it is then checked whether a peak is actually found at this frequency in the third measurement. If this is the case, in step S 105 , the possible object is entered into the list of real objects. Otherwise, step S 105  is skipped. Steps S 106  and S 107  are again used for loop control. 
     FIG. 17  shows a variant in which, in comparison to  FIG. 16 , in response to a negative result of the query in step S 104 , two steps S 108  and S 109  are carried out. Here, the matching with the aid of third measurement M 3  is supplemented by simple tracking and object matching analogous to  FIG. 8 . To that end, based on the measured distance and velocity data for the considered object, it is estimated in step S 108  what distance and what relative velocity this object had in the preceding measuring cycle. In step S 109 , it is checked whether an object with this distance and this relative velocity was present in the preceding cycle. If this was the case, step S 105  is carried out, although the calculated frequency could not be confirmed in the third measurement. Only if the query in step S 109  is also negative, is step S 105  skipped. 
     FIG. 18  shows a modification with respect to  FIG. 17  in which additionally, at the end of the procedure, an expanded tracking analogous to  FIGS. 12 through 14  is carried out in step S 110 .