Apparatus and method for detecting alignment of sensor and calibrating antenna pattern response in an automotive detection system

A method for calibrating an antenna pattern of a sensor in an automotive detection system includes receiving reflected signals and generating receive signals indicative of the reflected signals. Processing the receive signals to generate detections of objects including one or more ground-stationary clutter objects, each of the detections being associated with a detected azimuth and detected relative velocity of each ground-stationary clutter object. For each of a plurality of angles with respect to a boresight of an antenna of the sensor, processing the detected azimuth and detected velocity of one of the ground-stationary clutter objects and a signal indicative of velocity of the sensor to generate an actual antenna pattern for the antenna of the sensor. A calibrated antenna pattern for the antenna of the sensor is generated using the actual antenna pattern to adjust an assumed antenna pattern.

BACKGROUND

1. Technical Field

The present disclosure is related to automotive detection systems such as automotive radar systems, and, in particular, to an apparatus and method for detecting and correcting for misalignment of a sensor, and calibrating the antenna pattern response in an automotive detection system.

2. Discussion of Related Art

In automotive detection systems, such as radar systems or LiDAR systems, the sensor, i.e., radar sensor or LiDAR sensor, can be mounted, i.e., physically attached, to the vehicle body or frame. Detection system performance is typically characterized by detection of reflections from objects in proximity to the vehicle to enable implementation of speed control, collision prevention, and/or other system functions. In such automotive detection systems, it is typically desirable to determine an azimuth angle in the form of a target object bearing angle, the range or distance with respect to the objects, and a Doppler relative velocity between the vehicle and these objects.

For typical vehicle detection applications, it is important to measure the target bearing angle with very high precision. The angle accuracy of a detection system depends on fundamental parameters such as modulation technique, antenna design, component tolerances, assembly precision and/or installation conditions. Furthermore, due to various environmental influences such as mechanical stress or temperature variations, the angle estimation performance might be degraded. Also, alignment of a sensor may be affected by installation of the sensor in the host vehicle, since certain features of the vehicle can alter the electromagnetic performance characteristics of the antenna when it is placed in proximity to these vehicle features. Some of these error sources exhibit a random statistical distribution, while others result in a fixed-angle offset of the sensor module. Monitoring and correcting for misalignment or bias angle can be important in vehicle detection applications.

SUMMARY

According to one aspect, a method for calibrating an antenna pattern of a sensor in an automotive detection system is provided. The method includes: transmitting transmitted signals into a region; receiving reflected signals generated by reflection of the transmitted signals and generating receive signals indicative of the reflected signals; receiving the receive signals; generating a signal indicative of velocity of the sensor; processing the receive signals to generate detections of objects in the region, the objects in the region including one or more ground-stationary clutter objects in the region, each of the detections being associated with a detected azimuth and detected relative velocity of each ground-stationary clutter object; for each of a plurality of angles with respect to a boresight of an antenna of the sensor, processing the detected azimuth and detected velocity of one of the one or more ground-stationary clutter objects and the signal indicative of velocity of the sensor to generate an actual antenna pattern for the antenna of the sensor; using the actual antenna pattern to adjust an assumed antenna pattern to generate a calibrated antenna pattern for the antenna of the sensor.

In some embodiments, the method further comprises, using the calibrated antenna pattern, determining an angle of misalignment of the sensor.

In some embodiments, the objects in the region comprise objects which are moving with respect to ground.

In some embodiments, the method further comprises filtering the detections of objects in the region to substantially eliminate detections of objects which are moving with respect to ground. In some embodiments, the filtering is a statistical filtering. In some embodiments, the filtering comprises using an order statistic.

In some embodiments, the method further comprises generating a correlation azimuth estimate.

According to another aspect, an automotive radar sensor with calibration of an antenna pattern is provided. A transmitter transmits signals into a region. A receiver receives reflected signals generated by reflection of the transmitted signals and generates receive signals indicative of the reflected signals. A processor: (i) receives the receive signals; (ii) generates a signal indicative of velocity of the sensor; iii) processes the receive signals to generate detections of objects in the region, the objects in the region including one or more ground-stationary clutter objects in the region, each of the detections being associated with a detected azimuth and detected relative velocity of each ground-stationary clutter object; (iv) for each of a plurality of angles with respect to a boresight of an antenna of the sensor, processes the detected azimuth and detected velocity of one of the one or more ground-stationary clutter objects and the signal indicative of velocity of the sensor to generate an actual antenna pattern for the antenna of the sensor; and (v) uses the actual antenna pattern to adjust an assumed antenna pattern to generate a calibrated antenna pattern for the antenna of the sensor.

In some embodiments, the processor uses the calibrated antenna pattern to determine an angle of misalignment of the sensor.

In some embodiments, the objects in the region further comprise objects which are moving with respect to ground.

In some embodiments, the processor filters the detections of objects in the region to substantially eliminate detections of objects which are moving with respect to ground. In some embodiments, filtering performed by the processor comprises statistical filtering. In some embodiments, filtering performed by the processor uses an order statistic.

In some embodiments, the processor generates a correlation azimuth estimate.

DETAILED DESCRIPTION

FIG. 1Aincludes a schematic block diagram of an automotive detection system10A, such as an automotive radar system, according to some exemplary embodiments. It is noted that, although the following detailed description refers to system10A as an automotive radar system as an exemplary illustrative embodiment, the present disclosure is directed to automotive detection systems in general and can be, for example, automotive radar systems, automotive LiDAR systems, or other such detection systems. The description herein of radar system components and signal processing are applicable to analogous components and signal processing of LiDAR systems. System10A ofFIG. 1Aincludes one or more detection modules such as radar sensor modules12A for processing automotive radar signals, in accordance with some exemplary embodiments. Referring toFIG. 1A, system10A includes one or more radar modules12A, which process radar transmit and receive signals which are compatible with the radar detection and monitoring system10A in the host automobile. Radar module12A generates and transmits radar signals into the region adjacent to the host vehicle that is being monitored by system10A. Generation and transmission of signals is accomplished by RF signal generator24A, radar transmit circuitry20A and transmit antenna16A. Radar transmit circuitry20A generally includes any circuitry required to generate the signals transmitted via transmit antenna16A, such as pulse shaping/timing circuitry, transmit trigger circuitry, RF switch circuitry, or any other appropriate transmit circuitry used by radar system10A.

Radar module12A also receives returning radar signals at radar receive circuitry22A via receive antenna18A. Radar receive circuitry22A generally includes any circuitry required to process the signals received via receive antenna18A, such as pulse shaping/timing circuitry, receive trigger circuitry, RF switch circuitry, or any other appropriate receive circuitry used by the radar system. The received radar signals are processed by radar receive circuitry22A to generate processed receive signals, which are forwarded to a mixer28A, which mixes the processed receive signals with an RF signal from RF signal generator24A. The resulting difference signals may be further filtered as required by filtering circuitry32A to generate baseband signals, which are digitized by analog-to-digital converter circuitry (ADC)34A to generate receive signals. These digitized baseband receive signals are processed by a processor, such as a digital signal processor (DSP)36A, to generate target object detections related to objects in the region being monitored by detection system10A. In some exemplary embodiments, the DSP36A can perform any and/or all of the processing tasks required to implement the sensor alignment monitoring, compensation and/or correction described herein according to the exemplary embodiments.

FIG. 1Bincludes a schematic block diagram of an alternative automotive detection system10B, such as an automotive radar system, according to some exemplary embodiments. Referring toFIG. 1B, system10B includes a radar sensor module12B, which processes radar transmit and receive signals which are compatible with the radar detection and monitoring system in the host automobile. Radar module12B generates and transmits radar signals into the region adjacent to the host vehicle that is being monitored by the radar system. Generation and transmission of signals is accomplished by RF signal generator24B, radar transmit circuitry20B and transmit antenna16B. Radar transmit circuitry20B generally includes any circuitry required to generate the signals transmitted via transmit antenna16B, such as pulse shaping circuitry, transmit trigger circuitry, RF switch circuitry, or any other appropriate transmit circuitry used by the radar system.

Radar module12B also receives returning radar signals at radar receive circuitry22B via receive antenna18B. Radar receive circuitry22B generally includes any circuitry required to process the signals received via receive antenna18B, such as pulse shaping circuitry, receive trigger circuitry, RF switch circuitry, or any other appropriate receive circuitry used by the radar system. In some exemplary embodiments, the received signals processed by radar receive circuitry22B are forwarded to phase shifter circuitry26B, which generates two signals having a predetermined phase difference. These two signals, referred to as an inphase (I) signal and a quadrature (Q) signal, are mixed with an RF signal from RF signal generator24B by mixers28B and30B, respectively. The resulting difference signals are further filtered as required by filtering circuitry32B to generate baseband I and Q signals, labeled “I” and “Q” inFIG. 1B. The baseband I and Q signals are digitized by analog-to-digital converter circuitry (ADC)34B. These digitized I and Q baseband signals are processed by a processor36B, which can include such circuitry as a digital signal processor (DSP), associated memory, associated I/O circuitry, communication bus circuitry, and any other circuitry required for carrying out any processing functions of system10B and/or radar sensor12B. In some exemplary embodiments, the DSP36B can perform any and/or all of the processing tasks required to implement the sensor alignment monitoring, compensation and/or correction described herein according to the exemplary embodiments.

In some exemplary embodiments, processor36B can perform processing such as a fast Fourier Transform (FFT) to generate a plurality of Doppler range bins, which include range, bearing and velocity information for detections during multiple sweeps, i.e., frequency-modulated (FM) chirps, of the radar illumination signal transmitted into the region around the vehicle being analyzed. In some exemplary embodiments, radar sweeps are performed at a rate of approximately 12 Hz. It will be understood that other sweep rates can be used.

FIG. 2includes a schematic top view of an automobile or vehicle50equipped with an automotive detection system10A,10B illustrated inFIGS. 1A and/or 1B, respectively, and referred to herein collectively as automotive detection system10, which includes one or more radar sensor modules12A,12B, referred to herein collectively as radar sensor modules12, according to some exemplary embodiments. A first radar sensor module12-1can be connected via a bus60, which in some exemplary embodiments is a standard automotive controller area network (CAN) bus, to a first CAN bus electronic control unit (ECU)56. Object detections from radar sensor module12-1can be reported to ECU56, which processes the detections and can provide detection alerts via CAN bus60. In some exemplary embodiments, the alerts can be in the form of a visible indicator, such as a light-emitting diode (LED) in side mirror64, which is visible to the driver. Similarly, in some exemplary embodiments, a second radar sensor module12-2can be connected via CAN bus60, to a second CAN bus electronic control unit (ECU)58. Object detections from radar sensor module12-2can be reported to ECU58, which processes the detections and can provide detection alerts via CAN bus60to a visible indicator, such as a light-emitting diode (LED) in side mirror66. In the particular embodiment illustrated inFIG. 2, first and second radar sensor modules12-1and12-2of radar system10can be part of a blind spot system for reporting object detections in one or both blind spots of automobile50. It will be understood that the present disclosure is applicable to other types of radar systems10. For example, in some exemplary embodiments, one or more forward-looking radar sensor modules12-3can be connected via CAN bus60to a third CAN bus electronic control unit (ECU)59, and one or more rear-looking radar sensor modules12-4can be connected via CAN bus60to a fourth CAN bus electronic control unit (ECU)57. ECUs57and59can process target object detections from radar sensor modules12-3and12-4, respectively, and can provide detection alerts to a visible indicator or to a vehicle system process for appropriate processing and management of detections.

It will be understood that, according to the present disclosure, detection system10can have many configurations, each including different numbers and locations of sensor modules12. For example, detection system10can include one or more forward-looking sensor modules12, one or more rear-looking sensor modules12, and/or one or more side-looking sensor modules12. Data gathered by sensor modules12can be processed by one or more processors, e.g., ECUs(s), to carry out the various features implemented by detection system10. These features can include, but are not limited to, at least one or any combination of any subset of: a blind spot detection feature, a rear cross traffic detection feature, a lane change assistance feature, a trailer detection feature, a safe door opening feature an adaptive cruise control feature, and an autonomous braking feature.

In general, sensor modules12in automotive detection systems such as detection system10described herein in detail are mounted at specified positions and point at a specified angle with respect to the host vehicle.FIG. 3includes a schematic top view of automobile or vehicle50equipped with an automotive detection system10A and/or10B, including an exemplary front corner radar sensor module12, according to some exemplary embodiments. Referring toFIG. 3, front, right corner radar sensor module12can be mounted inside the front bumper at the front right corner of vehicle50. As illustrated in the exemplary configuration ofFIG. 3, sensor module12can be mounted to point into a region74along a pointing direction72, which forms an angle of, for example, 45°, with respect to a center line70of vehicle50.

In automotive detection systems such as detection system10, sensor module alignment is important to proper operation. The system and each sensor module should have verification of alignment of each sensor module in the system. To that end, according to the present disclosure, a fast, efficient and accurate means for determining and compensating for antenna pattern distortion, calibrating the antenna pattern and thereby correcting for sensor module misalignment is provided.

This disclosure relates to an approach to calibrating and aligning bearing angle measurement in automotive detection systems such as automotive radar systems. It removes or minimizes the angle measurement bias and errors caused by the lack of the positional knowledge of the radar antennas due to either mechanical mounting tolerance or errors, or distortion of the antenna radiation pattern caused by the structures surrounding the radar antenna.

The approach of the disclosure uses the Doppler information of the radar measurements from ground-stationary clutter target returns and the radar motion measurements to establish the antenna response as a function of azimuthal angle (sometimes also referred as “bearing”) after the radar sensor is installed on the moving platform (an automobile, for example). This response is the calibrated response as opposed to a response measured in a static environment or an anechoic chamber as is typically done for radar sensors. The static response usually does not include any mounting bias or distortion effect which cause errors after the sensor is installed on a vehicle, while the approach of the disclosure corrects those errors without relying on a priori knowledge.

Prior approaches have attempted to use linear frequency modulated (LFM) waveforms to estimate antenna response or mounting biases. However, due to the effect commonly referred to as range-Doppler-azimuth coupling, it is difficult to separate the antenna response from other influences besides azimuth. Prior approaches have relied on discrete scatterers whose availability cannot be guaranteed with sufficient confidence. The approach of the present disclosure makes use of the much more available ground-stationary clutter returns and provides much more predictable performance and fast convergence in day-to-day operations of the radar sensor.

FIG. 4includes a schematic top view of a portion of an automobile or vehicle50, equipped with an automotive detection system10A and/or10B, which includes at least two front corner radar sensor modules12-5,12-6, according to some exemplary embodiments. Referring toFIG. 4, right front sensor module12-5can be mounted to point into a region174A along a pointing direction172A, and left front sensor module12-6can be mounted to point into a region174B along a pointing direction172B. In general, regions174A and174B may overlap in an overlap region176, which is in the field of view (FOV) of both sensor modules12-5and12-6. Each sensor module12is characterized by an alignment bias, which is an angle defining the extent of the detected misalignment of the sensor module. Long-range radar applications generally require accurate cross-range (if “x” is the direction of travel for the host vehicle, then “y” direction would be cross-range) estimates to make determinations with regard to detections, for example, to determine a lane position of a target with respect to the host vehicle. A single-sensor radar detection approach relies on the responses of individual antenna elements to estimate azimuth, and then converts that azimuth estimate to x and y coordinates. Sources of azimuth error include sensor azimuth bias in which electrical radar boresight is misaligned and/or mounting of the sensor on the vehicle is out of alignment. Sensor azimuth error can also be due to interference from one or more mechanical features of the host vehicle, such as the bumper fascia. Also, vehicle heading errors, in which the velocity vector and a vehicle body reference can be misaligned.

According to the present disclosure, an approach to azimuth measurement uses in-situ clutter Doppler to derive azimuth without knowledge of the antenna element response. It is understood that automobile radar returns are dominated by detections from ground-stationary clutter objects having a well-defined radial-range-rate/azimuth relationship. According to the present disclosure, this relationship is used to extract useful sensor alignment and/or calibration data to align the sensor and/or calibrate the antenna pattern response. That is, according to the present disclosure, in-situ clutter Doppler measurements are used to correct sensor misalignment and/or to calibrate azimuth angle measurement.

In some exemplary embodiments, radar system10uses a continuous wave (CW) waveform and generates 512 samples over a sample interval of 54.4 μsec. The Doppler resolution is 36 Hz, with unambiguous Doppler of ±9.2 kHz. The range rate resolution is 22.4 cm/s, with unambiguous range rate of ±57.4 m/s. Although other waveforms may be used according to the present disclosure, the above waveform provides a long integration time, wide unambiguous Doppler, narrow resolution bandwidth and detects objects without range-Doppler coupling. It will be understood that any waveform which provides a Doppler measurement can be used. These waveforms can include, but are not limited to pulsed Doppler, FMCW, step FM or other waveforms.

FIG. 5includes a schematic diagram of an automobile or vehicle, equipped with an automotive detection system10A and/or10B, which includes a rear-left-facing sensor module12-7, according to some exemplary embodiments. Sensor module12-7ofFIG. 5monitors and receives object detections from a region203at the rear left of host vehicle50. Vehicle50is moving in the direction and speed illustrated by velocity vector V, which can be provided by a velocity monitoring system of vehicle50. As a result, stationary ground clutter in region203will result in a measurable detection signal in Doppler which has the relationship with the velocity V of vehicle50:

∂r∂t=-V⁢⁢cos⁢⁢θ,
where θ is the angle between the line to the detected object and the positive direction of travel of vehicle50, i.e., the azimuth with respect to the vehicle velocity. For example, stationary clutter object detections at direction205form an angle θ of 90 degrees with vector V, resulting in a velocity

∂r∂t=0,i.e.,
the object appears to be at a constant range with respect to vehicle50. Similarly, objects directly behind vehicle50at direction209will have a Doppler velocity V; objects at an angle θ of 30 degrees with respect to vector −V at direction207will have a velocity

∂r∂t=-V⁢⁢cos⁡(180⁢°-30⁢°)=0.866⁢⁢V.
It is noted that, typically, the speed of a vehicle is given as a positive number, for example, 10 m/s). However, the range rate as measured by the radar can have both positive values, indicating an object is moving away, or negative values, meaning the object is moving closer. If the vehicle is moving at 10 m/s forward, for example, then the ground clutter will appear to moving away directly behind the vehicle, therefore having a positive range rate, i.e., range increasing with time.

It is noted that, in general, moving target objects such as other moving vehicles, will be detected in region203. Those objects will generally be statistical outliers, since the large majority of detections will generally be from stationary ground clutter objects. For example, stationary ground clutter targets may account for 90% of the detections, while moving targets may account for only 10% of the detections. According to exemplary embodiments, these moving target object detections can be eliminated from the results by some filtering means, such as a statistical filter, e.g., an order statistic. Alternatively, a threshold Doppler can be applied, and object detections having Doppler velocities above the threshold can be eliminated since they are moving and, therefore, are not stationary ground clutter. That is, according to exemplary embodiments, data from moving targets is filtered out so that only data from stationary ground clutter is used.

Hence, system10will report apparent azimuth based on the signals received at the antenna array and process by system10. According to the present disclosure, a mapping between the reported apparent azimuth and the azimuth relative to velocity, which is determined from the detected Doppler of ground-stationary clutter detections can be generated. This mapping provides a calibration of the antenna pattern of the sensor to providing more accurate azimuth determinations, such that misalignment of the sensor can be compensated for.

FIGS. 6A and 6Binclude curves of phase response for an exemplary four-channel, i.e., four-antenna-element, radar sensor, illustrating phase versus azimuth angle, for three channels, e.g., channels 2, 3 and 4, with respect to a single reference channel, e.g., channel 1.FIG. 6Aillustrates the phase response for a stand-alone sensor, i.e., a sensor that has not been installed in an automobile.FIG. 6Billustrates the phase response for an in-vehicle sensor, i.e., a sensor that is installed in a vehicle. Referring toFIG. 6A, curves220A,222A and224A are actual measured responses for channels (antenna elements) 2, 3 and 4, respectively, and curves220B,222B and224B illustrate the theoretical or ideal responses for channels (antenna elements) 2, 3 and 4, respectively, for the stand-alone sensor. Similarly, referring toFIG. 6B, curves226A,228A and230A are actual measured responses for channels (antenna elements) 2, 3 and 4, respectively, and curves226B,228B and230B illustrate the theoretical or ideal responses for channels (antenna elements) 2, 3 and 4, respectively, for the in-vehicle sensor.

As noted fromFIG. 6A, for the stand-alone sensor, deviations of actual measurements from the theoretical or ideal patterns are relatively small, uniform and predictable. These deviations can be attributable to various expected and predictable factors such as electrical and mechanical tolerances and other factors. In prior systems, these in-factory measured deviations from theoretical expectations are used to generate a theoretical calibration table or curve, which is used later during actual in-vehicle operation to attempt to correct for deviations from theoretical expectations of actual in-vehicle azimuth calculations from actual target object detections. However, as shown inFIG. 6B, after installation of the sensor in a vehicle, due to various distortion factors, deviations of actual measured responses from the theoretical or ideal responses are more pronounced, more variable, and, therefore, less predictable. The theoretical calibration table or curve generated using stand-alone, in-factory sensor measurements results in inaccurate and inconsistent azimuth measurements.

In contrast to these prior approaches, according to the antenna pattern calibration and sensor alignment approach of the present disclosure, these in-vehicle distortions are compensated for in-situ, i.e., in the vehicle during sensor operation, to provide more accurate antenna azimuth determinations. According to the present disclosure, one of the channels (antenna elements) is used as a reference channel to normalize the other channels. The Doppler of detected ground-stationary clutter is used to calculate the “true” azimuth. The large volume of data from clutter detections is filtered, such as by application of an order statistic, to separate data from moving target objects, to generate an antenna phase calibration curve or table. Because this calibration curve or table is generated in-situ, i.e., in the vehicle during operation, it accounts for distortions introduced by installation of the sensor in the vehicle. The newly generated antenna calibration table or curve is used for accurate azimuth estimation for real target objects. This calibration approach of the present disclosure can replace the theoretical or factory or end-of line (EOL) calibration table or curve generated at the sensor point of manufacture.

FIG. 7includes a schematic functional block diagram and logical flow diagram of the approach to radar antenna pattern calibration and radar sensor misalignment compensation, according to some exemplary embodiments. Referring toFIG. 7, as shown at252, sample data for returns received at each of a quantity K channels, i.e., K antenna elements, are received for processing by processing circuitry. In the illustrated embodiments, each channel includes N samples. Frequency transformation processing, such as a Fast Fourier Transform (FFT), is performed on the N samples for each of the K channels. The result of the FFT is generation of a number of Doppler bins, which in the illustrated embodiments is K*N total bins. As indicated at254, a magnitude of each complex value in the Doppler bins is then computed. At256, each magnitude is compared to a threshold, indicated as Threshold_1 inFIG. 7. A tally or count of magnitudes that exceed Threshold_1 is maintained in a table at256. In the exemplary illustration, at the first Doppler bin for each channel, a “1” is entered for channels where the magnitude exceeds Threshold_1, and a “0” is entered for channels where it is not exceeded; with the entries for the first Doppler frequency being illustrated. These entries are made in the illustrated table for each Doppler bin over each channel. Next, as shown at258, the number of channels having a magnitude exceeding Threshold_1 is determined. For example, in the case illustrated at256, this number is three. That number of channels is compared to a second threshold, referred to herein as Threshold_2. If the number of channels exceeds Threshold_2, then it is concluded that a detection is indicated. This process is performed for each channel and Doppler bin to identify detections to generate a detection list.

As indicated at260, clutter detection screening is performed on the detection list to exclude the effects of vehicle dynamics. For example, vehicle dynamics which indicate vehicle steering angles in the case of a turn, or vehicle velocity which would indicate a stopped vehicle, are filtered to ensure that the detections being relied upon are related to ground-stationary clutter. This step results in generation of a filtered detection list.

As illustrated at262, the filtered detection list is used to generate a table of phase per channel for each detection. That is, for each detection, a set of phases, i.e., one phase per channel, is identified. By the nature of this identification, the corresponding azimuth of the detection is associated with the phases of each of the K channels. That is, since the azimuth for each detection is determined, the corresponding set of phases associated with that detection provides an unambiguous identification of the azimuth.

As shown at264, these channel phase-azimuth associations can be used to build an antenna channel phase database, per channel, per azimuth bin. According to exemplary embodiments, the azimuth is calculated from the Doppler measurement from clutter detections. For example, if a clutter object is detected at a Doppler of 5 m/s, while the host vehicle is moving at a speed of 10 m/s, then the azimuth will be 60 degrees, according to

∂r∂t=-V⁢⁢cos⁢⁢θ,
described above. Referring to block264inFIG. 7, the term “Doppler bin” is used instead of azimuth along the horizontal axis, since the relation between azimuth and Doppler bin is one-to-one. The terms “Doppler bins” and “azimuth bins” are used interchangeably. The number of channels herein is referred to as K, and the number of Doppler bins is referred to as D, such that the total number of “buckets” is given by D*K. Block264can be viewed to illustrate a database with D by K buckets. Each bucket contains the electrical phases calculated from the many detections of clutter. For example, in the bucket with D=10 and K=3 (meaning the 10thDoppler bin and 3rdantenna channel), there are 121 phases measured from clutter detection. The order statistic filter using 50% percentile as the threshold will pick the 61stphase of the list of 121 phases arranged in an ascending or descending order. With each of the D bins populated and the order statistic filter applied, then a phase-vs.-azimuth correspondence can be tabulated for each channel K.

During normal operation, the antenna channel phase database is used as a calibration look-up table to account for distortions in azimuth calculations. When actual target detections are generated, the sets of phases associated with the individual channels are identified in the calibration look-up table. The azimuth associated in the calibration look-up table with the measured phases is determined to be the actual azimuth to the target object. Hence, the technique builds a set of K phase-vs-azimuth relations from the database. In an ideal situation, this set of curves226B,228B, and230B generated by the techniques of the present disclosure, follows a known pattern as illustrated inFIG. 6B. This set of curves are used as follows: if there is a true target detection from which a set of K phases are measured, one can look up the K curves as illustrated inFIG. 6Band find the azimuth at which the phases of the curves best match the measured phases.

One way to accomplish this complex table look-up is by using a correlation method. Under this technique of the present disclosure, the set of K measured phases is considered a vector of K elements. The K phase curves are considered a set of D vectors of the same length, each corresponding to a set of phases at a specific azimuth. One can calculate the correlation coefficients of the measured phase vector with all the D vectors of the table, and find the one that is the maximum. The azimuth of this vector can be considered the azimuth of the target.

According to this correlation approach of the present disclosure, from the database of phase response curves illustrated inFIG. 6B, a vector α(θd) can be created at each of the D Doppler bins, i.e., azimuth angles, as follows:

α⁡(θd)=[e-i⁢⁢∅d⁢⁢1e-i⁢⁢∅d⁢⁢2e-i⁢⁢∅dK],d=1,2,…,D;
where θdis the azimuth angle corresponding to the dthDoppler bin, and ØdKis the electrical phase response of the Kthantenna channel. A target detected by the radar system is considered. From this detection, a set of K phases φ1, φ2, . . . , φKcan be calculated to form a vector v, given by:

v=[e-i⁢⁢φ1e-i⁢⁢φ2e-i⁢⁢φK].
The phase response curves ofFIG. 6Bcan be considered to be a set of D vectors, each vector being of length K and corresponding to an azimuth angle as described above. The azimuth angles can be mapped one-to-one to the Doppler bins, and there are D Doppler bins. Accordingly, the correlation coefficient between the measured phase vector v and the D vectors from the database. Specifically, a set of D correlation coefficients ρ(θd) can be calculated, i.e., estimated, from the vector-inner-product, i.e., dot product, between phase vector v and each of the D vectors from the database, resulting in D coefficients, as follows:
ρ(θd)=|α(θd)Hv/K|,d=1,2, . . . ,D.
Note αHis Hermittian transpose of vector α. The angle corresponding to the maximum correlation coefficientis the azimuth bearing for the detection, that is,=argmax(ρ(θ)).