U.S. patent application number 10/618973 was filed with the patent office on 2005-02-17 for method and radar system for determining the directional angle of radar objects.
Invention is credited to Budiscak, Benoit, Eder, Sonja.
Application Number | 20050035902 10/618973 |
Document ID | / |
Family ID | 29723875 |
Filed Date | 2005-02-17 |
United States Patent
Application |
20050035902 |
Kind Code |
A1 |
Eder, Sonja ; et
al. |
February 17, 2005 |
METHOD AND RADAR SYSTEM FOR DETERMINING THE DIRECTIONAL ANGLE OF
RADAR OBJECTS
Abstract
A method for determining the directional angle of radar objects
using a multibeam radar, including the steps of: (a) recording the
frequency spectra of the radar echoes for a plurality of beams; (b)
seeking a measuring frequency near a frequency maximum assigned to
the radar object; and (c) comparing the phases and/or amplitudes of
the radar echoes at the measuring frequency with reference patterns
known for various directional angles, steps (b) and (c) being
executed repeatedly, each time for different measuring frequencies,
and the directional angles obtained for the various measuring
frequencies being checked for consistency.
Inventors: |
Eder, Sonja; (Koengen,
DE) ; Budiscak, Benoit; (Sachsenheim, DE) |
Correspondence
Address: |
KENYON & KENYON
ONE BROADWAY
NEW YORK
NY
10004
US
|
Family ID: |
29723875 |
Appl. No.: |
10/618973 |
Filed: |
July 14, 2003 |
Current U.S.
Class: |
342/147 ;
342/118; 342/128; 342/146; 342/175; 342/192; 342/195; 342/27 |
Current CPC
Class: |
G01S 13/424 20130101;
G01S 13/345 20130101; G01S 13/584 20130101; G01S 13/48
20130101 |
Class at
Publication: |
342/147 ;
342/027; 342/118; 342/128; 342/146; 342/175; 342/192; 342/195 |
International
Class: |
G01S 013/06; G01S
013/93 |
Foreign Application Data
Date |
Code |
Application Number |
Jul 12, 2002 |
DE |
1 02 31597.3 |
Claims
What is claimed is:
1. A method for determining a directional angle of a radar object
using a multibeam radar, the method comprising: (a) recording a
frequency spectra of radar echoes for a plurality of beams; (b)
seeking a measuring frequency near a frequency maximum assigned to
a radar; and (c) comparing at least one of phases and amplitudes of
the radar echoes at the measuring frequency with reference patterns
known for various directional angles, wherein steps (b) and (c) are
executed repeatedly, each time for different measuring frequencies,
and wherein the directional angles obtained for the measuring
frequencies are checked for consistency.
2. The method according to claim 1, wherein in step (c), the
amplitudes of the radar echoes are compared with reference patterns
given by a reference antenna diagram.
3. The method according to claim 1, further comprising modulating a
transmitting frequency of the multibeam radar with different ramps,
and wherein steps (a), (b) and (c) are executed separately for each
ramp, and in the consistency check, directional angles obtained for
the ramps at one of the same and different measuring frequencies
are also checked for consistency.
4. The method according to claim 1, wherein, in step (c),
plausibility variables are calculated for a plurality of possible
directional angles, a plausibility variable for a given directional
angle being the greater the better the directional angle conforms
with a reference pattern, and, as a final directional angle, a
particular directional angle is selected which, in view of the
plausibility variables obtained for the measuring frequencies, has
a greatest plausibility.
5. A radar system comprising: a multibeam radar; and an evaluation
device for determining a directional angle of a radar object, the
evaluation device including: a first device for recording frequency
spectra of radar echoes, a second device for seeking a plurality of
measuring frequencies near a frequency maximum assigned to the
radar object in the frequency spectra, a third device for comparing
at least one of phases and amplitudes of the radar echoes at each
of the measuring frequencies with reference patterns one of stored
and calculated for various directional angles, and a fourth device
for calculating a final directional angle for comparison results
obtained for various measuring frequencies.
Description
FIELD OF THE INVENTION
[0001] The present invention is directed to a method for
determining the directional angle of radar objects using a
multibeam radar, including the steps of:
[0002] (a) recording the frequency spectra of the radar echoes for
a plurality of beams;
[0003] (b) seeking a measuring frequency near a frequency maximum
assigned to the radar object; and
[0004] (c) comparing the phases and/or amplitudes of the radar
echoes at the measuring frequency with reference patterns known for
various directional angles.
BACKGROUND INFORMATION
[0005] A method is known from German Patent Application No. 195 43
813. It is used in a motor vehicle to determine the positions of
radar objects, for example of vehicles driving ahead, using a
static multibeam radar, so that then, within the framework of an
adaptive cruise control (ACC), the velocity of one's own vehicle is
adapted to the velocity of a vehicle driving ahead, and the
distance to the vehicle driving ahead can be regulated to a
suitable value. The positions of the radar objects are indicated in
polar coordinates, thus by distances and directional angles. The
distances can be determined on the basis of the signal propagation
times of the radar echoes. In addition, using the Doppler effect,
the relative velocities of the radar objects can be determined.
However, for an error-free distance control (vehicle-to-vehicle
ranging), the directional (course) angles of the radar objects are
needed in order for a decision to be made as to whether a located
(tracked) radar object is a vehicle driving ahead in one's own
lane, or a vehicle driving in an adjacent lane that is irrelevant
for the distance control. In the context of a static multibeam
radar, the optical axis of the radar system is fixed in relation to
the vehicle. It is preferably parallel to the longitudinal axis of
the vehicle. This optical axis then expediently forms the reference
axis for determining the directional angles. The multibeam radar
system has a plurality of receiving elements, each of whose
sensitivity maxima are in different receiving directions, so that
altogether, therefore, they cover a specific angular range. Since
the sensitivy ranges of the receiving elements overlap one another,
from one single radar object, one receives radar echoes in a
plurality of channels, i.e., in a plurality of receiving elements.
For an idealized, nearly punctiform radar object, at a given
directional angle, a characteristic phase and amplitude relation
exists among the signals received in the various channels. Due to
the differences in the propagation time (delay differences) of the
radar echoes from the radar object to the various receiving
elements, a phase difference is derived which is proportional to
the directional angle and to the distance of the receiving elements
in the right-angled direction to the optical axis, and is inversely
proportional to the wavelength of the radar waves. The amplitude
ratios among the received signals are dependent upon the
directional angle and upon the sensitivity curves of the receiving
elements. They are able to be experimentally determined in advance
for the directional angles of interest and recorded in a reference
antenna diagram. In this way, by evaluating the phase relations or
by evaluating the amplitude relations, or also by combining both
evaluation processes (evaluating the complex amplitudes), it is
possible to determine the directional angle of a located radar
object.
[0006] The high-frequency signals received in the various channels
are able to be evaluated in a mixing process using a reference
frequency, while maintaining the phase and amplitude relations, and
converted into low-frequency signals which are able to be evaluated
in an evaluation electronics. For example, the low-frequency
signals can be digitized using analog/digital converters and then
digitally further processed. A frequency spectrum is first recorded
for each beam of the multibeam radar, i.e., for each of the
low-frequency signals received from the various receiving elements.
Each radar object emerges in the spectrum in the form of a peak,
whose position is dependent upon the Doppler shift and, thus, upon
the relative velocity of the object. When the transmitting
frequency of the radar system is modulated, for example when
working with a FMCW radar (frequency modulated continuous wave),
the position of the peak is also dependent upon the propagation
delay. When the transmitted signal is alternately modulated with
ascending and descending ramps (ramp waves), the relative velocity
of the object can be calculated from the frequency spacing of the
peaks obtained at the various ramps, and the distance of the object
can be calculated from the average value of the peak frequencies.
Any ambiguities in the received signals that arise when
simultaneously locating (finding the position of) a plurality of
objects, are able to be overcome by varying the ramp slopes in the
frequency modulation. Peak pairs which belong together can be
identified by the correspondence of the relative velocities and
object distances obtained at various ramp slopes.
[0007] Since the signals received from the same object in the
plurality of receiving elements of the multibeam radar have
identical Doppler shifts and also at least nearly identical signal
propagation times, the peaks in all the channels are more or less
at the same frequency.
[0008] In the known method, as a measuring frequency for the
angular determination, that frequency is selected which corresponds
to the apex of the peak.
[0009] However, real (tangible) radar objects, in particular large
objects such as trucks, usually have a plurality of centers of
reflection, whose radar echoes are superposed in the various
receiving elements and interfere with one another. This can degrade
the accuracy and reliability of the angular determination.
SUMMARY OF THE INVENTION
[0010] An object of the present invention is to provide a method
for determining directional angles which is more reliable with
respect to the interference effects that occur when working with
real radar objects.
[0011] This objective is-achieved by a method of the type mentioned
at the outset, in which steps (b) and (c) are executed repeatedly,
each time for different measuring frequencies, and in which the
directional angles obtained for the various measuring frequencies
are checked for consistency.
[0012] This approach is based on the observation that the
interference effects occurring in the context of large radar
objects are critically dependent on the frequency, and, therefore,
have different effects at different measuring frequencies. Often,
these interference effects are already eliminated by a slight
change in the measuring frequency, so that, by evaluating a
plurality of measuring frequencies, one obtains a more reliable or
more accurate result, since "outliers" (an observation far from
normality) caused by interference in the context of an unfavorably
selected measuring frequency, are able to be detected and
eliminated or at least mitigated, with respect to their effects, by
averaging the results.
[0013] When the results obtained for various measuring frequencies
are inconsistent to the point where a clear directional angle
cannot be determined, one at least receives the information that a
reliable determination of the directional angle is not possible at
the particular moment, thereby lessening the danger of erroneous
determinations being made with respect to the directional
angle.
[0014] In step (c), to determine the directional angle at the
particular measuring frequency, the complex amplitudes are
evaluated which also contain phase information, or optionally only
the absolute amounts of the amplitudes.
[0015] When, as in the case of an FMCW radar, the frequency of the
transmitted signal is modulated with different ramps, one obtains a
separate frequency spectrum for each ramp, and the method described
above may then be carried out for each peak in each one of these
spectra. For one single object, the directional angles ascertained
on the basis of the various spectra should then conform. When a
plurality of objects is located simultaneously, this holds, of
course, only on the condition that the plurality of peaks in the
various spectra were each assigned to the correct object.
Therefore, a discrepancy in the directional angles may also be used
for examining and, if indicated, for correcting the assignment
between peaks and objects.
[0016] However, even given a proper object assignment, interference
effects can result in more or less substantial deviations in the
directional angles, which are obtained for the same measuring
frequency, from the various spectra. For that reason, for the
consistency check, it is not only the results obtained for the
various measuring frequencies that are compared to one another, but
the results obtained from various spectra, i.e., from various ramps
of the frequency modulation, as well. When, at a given measuring
frequency, the results obtained from the various spectra deviate
from one another, then this indicates that the result for this
special measuring frequency is falsified by interference effects.
In determining the most plausible directional angle, the result
obtained for this measuring result is then weighted less heavily or
completely excluded from the evaluation. Conversely, the
plausibility of an obtained directional angle is rated to be all
the higher, the more frequently this directional angle is confirmed
by the evaluation of other spectra. Altogether, therefore, the
accuracy and reliability can be considerably enhanced in this
way.
[0017] The greater the number of beams of the multibeam radar is,
the greater the angular resolution and the measuring accuracy
generally become. However, as the number of beams increases, the
evaluation on the basis of the reference patterns also becomes more
complex.
[0018] When the frequency spectra exist in the form of discrete
spectra, one obtains amplitude values for discrete frequencies
which are preferably evenly distributed (equally spaced apart) over
the considered frequency range. As a measuring frequency,
preferably that frequency which corresponds to the maximum of the
peak, as well as one or more adjacent frequencies are selected in
the discrete spectrum, when evaluating three measuring frequencies,
thus, for example, the maximum frequency, and the next lower, as
well as the next higher frequency. Accordingly, when evaluating
five measuring frequencies, preferably the maximum frequency and
the two directly adjacent, lower frequencies, as well as the two
directly adjacent higher frequencies are evaluated.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] FIG. 1 shows a block diagram of a radar system for
implementing the method according to the present invention.
[0020] FIG. 2 shows an example of a frequency spectrum having a
peak produced by a single radar object.
[0021] FIG. 3 shows the peak of the spectrum according to FIG. 2
having a higher frequency resolution.
[0022] FIG. 4 shows an example of a reference antenna diagram which
indicates the relation among the amplitudes as a function of the
directional angle.
[0023] FIGS. 5(A)-(E) show diagrams, which are indicative of the
deviation between the measured amplitudes and the reference pattern
as a function of the directional angle, for five different
measuring frequencies and, in each case, for four frequency
ramps.
DETAILED DESCRIPTION
[0024] FIG. 1 schematically depicts a radar sensor of a multibeam
radar 10, which is installed on the front-end section of a motor
vehicle and is used for finding the position of radar objects 12
located ahead of the vehicle. Multibeam radar 10 has three
transmitting and receiving elements 14, referred to in the
following, in short, as receiving elements, of which one is
situated on optical axis 18 defined by an optical system 16 of the
radar sensor, while the two others are configured so as to be
laterally offset from the optical axis. In this manner, three
measuring beams 20 are produced, which are emitted at different
angles with respect to the optical axis. In practice, measuring
beams 20 shown in the drawing only as lines, have the form of radar
lobes which extend over relatively large, overlapping angular
ranges. The lines in FIG. 1 indicate the direction of each
intensity maximum of these radar lobes.
[0025] Radar object 12 is generally hit by all three radar lobes,
and, for each measuring beam, produces a radar echo, which is
focused again through optical system 16 at receiving element 14,
which had emitted the measuring beam in question. The lines
representing measuring beams 20 at the same time indicate the
direction of the sensitivity maxima of receiving elements 14. Thus,
each of the three receiving elements 14 receives a radar echo of
greater or lesser intensity from radar object 12. The relation
among the phases of the received signals, as well as the relation
among their amplitudes are dependent upon directional angle a, at
which radar object 12 is "seen" by multibeam radar 10.
[0026] High-frequency signals HF received by receiving elements 14
are mixed in each instance in a separate mixer 22 with a reference
signal RF, whose frequency is on the same order as that of the
received signal. Reference signal RF may be, for example, the
signal which is fed to transmitting and receiving elements 14 in
order for measuring beams 20 to be generated. The frequency of
reference signal RF is then identical to the frequency of the
transmitted radar waves. Thus, at the output of each mixer 22, one
obtains a low-frequency signal NFr, NFm or NFl, whose frequency
corresponds to the difference between the frequencies of the
transmitted and the received signals.
[0027] A control device 24, which determines the frequency of the
transmitted signal (and thus also reference frequency RF), belongs
to multibeam radar 10. In the illustrated example, multibeam radar
10 is an FMCW radar. The transmitted frequency is modulated with
four different ramps, namely two ascending ramps R1s and R2s and
two descending ramps R1f and R2f. The slopes of ramps R1s and R1f
are inversely equal, as are the slopes of ramps R2s and R2f.
[0028] On the one hand, due to the frequency modulation, the
frequencies of the low-frequency signals at the output of mixers 22
are dependent on the propagation delay of the radar waves to the
radar object and back to receiving elements 14 and, on the other
hand, due to the Doppler effect, they are dependent on the relative
velocity of radar object 12. When, from the frequencies of the
low-frequency signals, which are received during ramps R1s and R1f,
one generates the average value, then the frequency shifts caused
by the differences in the propagation delay cancel each other out,
and one obtains a measure of the relative velocity. Conversely, if
one forms the difference between these frequencies, then the
frequency shifts caused by the Doppler effect cancel each other
out, and one obtains a measure for the propagation delay and, thus,
for the-distance of radar object 12. Ramps R2s and R2f are used to
eliminate ambiguities when simultaneously locating a plurality of
radar objects.
[0029] Low-frequency signals NFr, NFm and NF1 are digitized in an
analog/digital converter 26 and then fed via three parallel
channels, which correspond to the three measuring beams 20, to a
digital evaluation computer 28.
[0030] In a first functional block 30 of the evaluation computer, a
discrete frequency spectrum Sr, Sm or S1 is calculated from the
low-frequency signal for each channel. The measuring time for
recording the frequency spectrum corresponds in each instance to
the duration of ramp R1s, R1f, R2s or R2f, which is precisely the
ramp used to modulate the transmitted frequency. For that reason,
the propagation delay- and velocity-dependent frequency shifts are
substantially constant during recording of the spectrum.
Theoretically, therefore, for each radar object 12, one obtains
exactly one peak in each frequency spectrum. When the signals on
the three channels originate from the same radar object 12, the
propagation delays and also the Doppler shifts are substantially
the same in all three channels, so that the peaks in the three
spectra roughly lie at the same frequency. However, their
amplitudes are different, because the three receiving elements 14
receive radar echoes of different intensity from radar object 12.
Since in the example shown in FIG. 1, radar object 12 is situated
to the right of optical axis 18, the amplitude of low-frequency
signal NFr will be the greatest, and the amplitude of signal NF1
the smallest. The same applies to the height of the peaks in the
spectra.
[0031] In a further functional block 32, a measuring frequency fmax
is then sought, at which the three peaks assume their maximum in
spectra Sr, Sm and Sl. This frequency should be the same for all
three spectra. In the case that slight deviations still exist, the
most suitable frequency is selected as a measuring frequency. When
a plurality of radar objects 12 are simultaneously located, the
spectra contain a plurality of peaks, and, for each peak, the
corresponding measuring frequency f.sub.max is determined.
[0032] The amplitudes of the three low-frequency signals at
measuring frequency f.sub.max are then evaluated in a functional
block 34, in order to determine possible candidates for directional
angle a. For this purpose, using so-called amplitude matching, the
pattern of the amplitudes received on the three channels at
measuring frequency f.sub.max is compared angle for angle with a
stored reference pattern, as is elucidated further below. The
result is a deviation function D.sub.0 which, for each angle,
indicates the extent of the deviation between the measured
amplitude patterns and the reference pattern. The angle or angles
at which deviation function D.sub.0 is at its minimum is/are,
therefore, suitable candidate(s) for directional angle a.
[0033] In the illustrated example, this procedure is not only
carried out for measuring frequency f.sub.max, but also for four
other measuring frequencies f.sub.max-1 f.sub.max-2 f.sub.max+l and
f.sub.max+2, which are directly adjacent to the apex of the peak in
the discrete frequency spectra. For that reason, functional block
34 is shown fivefold in FIG. 1. The altogether five deviation
functions D.sub.0, D.sub.-, D.sub.--, D.sub.+ and D.sub.++, which
one obtains in this way, 10 are temporarily stored in a buffer
36.
[0034] Thus, for each radar object 12, one obtains at least five
candidates for directional angle .alpha.. In the ideal case, for
all five measuring frequencies, the same candidate, namely the
correct directional angle, should result. However, if the amplitude
has been falsified at one or more of the measuring frequencies by
interference or other interference effects, different values may
result for directional angle .alpha.. In such a case, by averaging
the results or by eliminating outliers, the accuracy and
reliability may be enhanced when determining the directional
angle.
[0035] The above described procedure is repeated during each ramp
R1s, R1f, R2s and R2f, so that for one complete measuring cycle
including all four ramps, one finally obtains four sets of
deviation functions D.sub.--, D.sub.-, D.sub.0, D.sub.+ and
D.sub.++in buffer 36. These four times five deviation functions are
compared to one another in a selection block 38, in order to select
the most plausible and thus most probable value for directional
angle a and to output it as a result.
[0036] Since the position of the peaks in the frequency spectra is
dependent on the ramp slope, during each ramp, one obtains
different values for measuring frequencies f.sub.max, f.sub.max+1
etc., in functional block 32. When a plurality of radar objects 12
is simultaneously located, the corresponding peaks, obtained for
the various ramps are properly allocated in the manner that is
customary for a FMCW radar. In selection block 38, only those
deviation functions are then compared to one another which belong
to the same object. Since, typically, different objects are seen at
different directional angles, on the other hand, the intermediate
results that one receives in selection block 38 as candidates for
the directional angle may be used for verifying and, if indicated,
for correcting the object assignment in functional block 32. This
is indicated in FIG. 1 by a feedback arrow 40.
[0037] The principle of operation of the above described radar
system shall now be explained on the basis of an example and with
reference to FIGS. 2 through 5.
[0038] FIG. 1 shows an example of one of the frequency spectra, for
example S.sub.m, calculated in functional block 30. The discrete
frequencies in the spectrum are numbered by a consecutive index f,
which is indicated in FIG. 2 on the horizontal axis. Radar object
12 emerges (stands out) in the spectrum in the form of a single
peak 42, whose apex is at frequency index f=148.
[0039] In FIG. 3, peak 42 is shown with a higher frequency
resolution. In functional block 32 in FIG. 2, the following
measuring frequencies (expressed as frequency indices) are selected
for this peak: f.sub.max=148, f.sub.max-1=147, f.sub.max-2=146,
f.sub.max+1=149 and f.sub.max+2=150.
[0040] FIG. 4 shows a so-called reference antenna diagram 44 which
is stored in evalution computer 28 and is consulted for the
evaluation in functional blocks 34 in FIG. 1. For each directional
angle within the considered angular range, this reference antenna
diagram 44 specifies a reference pattern which indicates which
relation would theoretically have to exist among the amplitudes of
the three low-frequency signals NFr, NFm und NFl, given an ideal
radar object. The directional angles are indicated in FIG. 4 on the
horizontal axis in the form of an angular index I(.alpha.) which,
in the illustrated example, runs from 0 to 100. The allocation to
directional angles .alpha. is dependent on the size of the radar
system's angular sensing range. In-the illustrated example, index
50 corresponds to directional angle .alpha.=0. At an angular
sensing range of .+-.10.degree., index 100 would then correspond to
a directional angle of .alpha.=+10.degree. (deviation to the
right), and index 0 to a directional angle of
.alpha.=-10.degree..
[0041] Since the amplitudes of the received radar echoes differ
from object to object, the measured amplitudes, as well as the
amplitudes in the reference antenna diagram must be normalized to
enable them to be compared to one another. In the illustrated
example, amplitudes A in the reference antenna diagram are also
normalized in accordance with the sum standard, so that the sum of
all three amplitudes always yields value 1. The theoretical
amplitude NFRm for low-frequency signal NFm in the middle channel
is represented in FIG. 4 by a solid, bold curve. It is roughly
symmetrical to index 50 (.alpha.=0) and is also at its maximum at
this index. The theoretical amplitude NFRl for low-frequency signal
NF1 is represented in FIG. 4 by a dotted-line curve, which is at
its maximum at smaller index values, while the theoretical
amplitude NFRr for low-frequency signal NFr is represented by a
thinner continuous curve, which is at its maximum at index values
of more than 50.
[0042] The three horizontal straight lines drawn in a corresponding
line representation in FIG. 4 indicate the corresponding measured
amplitudes of low-frequency signals NFm, NFr and NFl. The object of
the algorithm, which is executed in functional block 34 in FIG. 1,
in principle, is to search the angular index in which the measured
amplitudes best match the theoretical amplitudes. In the
illustrated example, this is the case for angular index
I(.alpha.)=70. For each channel, the corresponding deviations Dm,
Dl and Dr between the theoretical and the measured amplitudes are
indicated in FIG. 4. These deviations are able to be analogously
determined for each angular index. From deviations Dm, Dr and Dl in
the individual channels, deviation function D.sub.0, i.e., D.sub.+,
D.sub.++, D.sub.31 or D.sub.-- is calculated. It indicates the
total deviation., for example in the form of the square sum of
deviations Dm, Dr and Dl.
[0043] Strictly speaking, the exact form of reference antenna
diagram 44 is also dependent on the frequency of the transmitted
and received radar waves. Since, however, the frequency of the
received radar waves differs only little from the transmitted
frequency, generally, it suffices to store one single reference
antenna diagram 44, which is valid for all frequencies and,
accordingly, may be used for evaluation purposes in all five
functional blocks 34 in FIG. 1.
[0044] FIGS. 5(A) through (E) show the total of twenty deviation
functions D.sub.--, D.sub.-, D.sub.0, D.sub.+ and D.sub.++ which
are obtained in this manner during one complete measuring cycle
made up of four ramps and which are stored in buffer 36 and then
compared to one another in selection block 38. Curves 46a and 48a
in FIG. 5(A) indicate deviation functions D that one had obtained
at measuring frequency f.sub.max-2 during ramps Rls and Rlf. Curves
50a and 52a indicate the deviation functions for ramps R2s and R2f
and for the same measuring frequency. The corresponding curves in
FIGS. 5(B)-(E) are characterized with the same reference numerals
and each with a different letter supplement (b-e).
[0045] If one were to undertake the evaluation only at the single
measuring frequency f.sub.max, then one would only have the result
in accordance with FIG. 5(C). Here, curves 46c and 48c have their
minimum at an angular index of about 72, while curves 50c and 52c
have their minimum at an angular index of about 83. For that
reason, it is not possible to clearly decide which directional
angle .alpha. is now the correct one.
[0046] However, if one includes in the consideration those results
which were obtained at measuring frequencies f.sub.max-1 and
f.sub.max+1, then it is very probable that an angular index of
about 70 is the correct one. At f.sub.max-1 (FIG. 5(B)), one does,
in fact, obtain similarly contradictory results as in FIG. 5(C),
however curves 46d and 48d in FIG. 5(D) merely confirm an angular
index near 70, while the minimum of the two other curves 50d and
52d is at a completely different value here (namely at 20).
Therefore, the final angular index could be determined in selection
block 38, for instance, by eliminating curves 50b-50d and 52b-50d,
which yield inconsistent results, and by generating the average
value from the minima of the remaining curves (near 70).
[0047] If one additionally considers the results that were obtained
for-the one-after-the-next adjacent frequencies f.sub.max-2 and
f.sub.max+2 (FIGS. 5(A) and 5(E)), then one discerns that FIG.
5(A), in fact, does not yield a consistent result and is,
therefore, unusable; FIG. 5(E), on the other hand, shows virtually
the same curve shape for all four ramps, having a minimum at an
angular index of about 68. From this, one may conclude, in this
case, that the amplitudes are falsified at frequency f.sub.max+2,
at least by interference or interference effects and, therefore,
yield the most reliable result. Therefore, in this case, the
algorithm in selection block 38 would yield angular index .alpha.
which belongs to angular index 68.
[0048] Different implementations are possible for the selection
algorithm. In the simplest case, the average value is simply
generated from the minima of the altogether twenty curves. A
refinement may provide for eliminating obvious "outliers" before
the averaging operation.
[0049] In accordance with another specific embodiment, the
algorithm may be so conceived that, for each individual measuring
frequency, one or more candidates are initially determined for the
angular index, as well as for the corresponding weightings. In this
context, the weighting of an angular index is all the greater, the
smaller the deviation function is and the better the various curves
conform at this angular index. For example, in FIG. 5(C), angular
indices 72 and 83 would receive an average weighting, since, here,
two of the altogether four curves coincide at their minimum. On the
other hand, in FIG. 5(E), angular index 68 would receive a more
than twice as high weighting, because here the same value is
confirmed by all four curves. In the last selection step, that
angular index would then be selected at which the weighted sum of
the angular indices defined for the individual measuring
frequencies, is at its maximum.
[0050] Conversely, it is also possible to initially determine one
or more candidates for the angular index and corresponding
weightings on the basis of curves 46a-46e, then correspondingly for
curves 48a-48e, etc., and then, finally, to select the angular
index for which the weighted sum of the thus obtained angular
indices is at its maximum.
[0051] Instead of calculating the selection functions in functional
blocks 34, it is also possible, in these functional blocks, to
directly calculate individual candidates for the angular indices,
as well as corresponding weightings or plausibilities and, then, in
selection block 38, to make a selection among these candidates.
* * * * *