Tài liệu Tracking and Kalman filtering made easy P3 pdf

Tracking and Kalman Filtering Made Easy Eli Brookner Copyright # 1998 John Wiley & Sons, Inc ISBNs: 0-471-18407-1 (Hardback); 0-471-22419-7 (Electronic) PRACTICAL ISSUES FOR RADAR TRACKING 3.1 TRACK INITIATION AND CLUTTER REJECTION The problems of clutter rejection and track initiation are very much interwined It is possible to use track initiation to help in the rejection of clutter On the other hand it is possible to use appropriate clutter rejection techniques to reduce the track initiation load Examples of these are discussed in the following sections 3.1.1 Use of Track Initiation to Eliminate Clutter The radar track initiator can be used to eliminate clutter by passing the clutter returns as well as target returns, which are indistinguishable initially, into the track initiation filter However, only those returns that behave like a moving target would be passed into track at the output of the track initiation filter, thus finally eliminating the clutter returns For example, the stationary clutter returns would be dropped by the track initiation filter (or classified as clutter returns for association with future such returns) The use of this approach can in some cases potentially provide about an order of magnitude or more increase in system sensitivity This is the case when dealing with spiky clutter In order to achieve a low false-alarm probability due to spiky clutter returns at the input to the track initiation filter, it is necessary that the detector threshold be increased by 10 dB or more above what would be required if the clutter were not spiky, that is, if the clutter were Rayleigh distributed at the output of the receiver envelope detector (which implies that it has a Gaussian distribution at the input to the envelope detector) This is shown to be the case in Figure 3.1-1 for spiky sea clutter, rain clutter, lognormal 111 112 PRACTICAL ISSUES FOR RADAR TRACKING Figure 3.1-1 Typical measured and theoretical clutter probability distributions (After Prengaman, et al., ‘‘A Retrospective Detection Algorithm for Extraction of Weak Targets in Clutter and Interference Environments,’’ IEE 1982 International Radar Conference, London, 1982.) clutter, and Weibull clutter for low probabilities of false alarm of 10
6 For mountain land clutter the situation is even worse Here the threshold has to be increased 20 dB for a 20-dB worse sensitivity than for Rayleigh clutter when a low probability of false alarm of 10
5 is desired Extrapolating the curve of Figure 3.1-1 indicates that if a higher false-alarm probability of  10
3 is used, then there is essentially no loss of sensitivity for spiky sea and rain clutter and a low loss for lognormal clutter and Weibull clutter The idea is to use a higher false-alarm probability for detection and to then use the track initiator to eliminate the false alarms resulting from the spiky clutter The APL retrospective detection is an example of such a system It uses the track initiator to eliminate spiky sea clutter for an ocean surveillance radar TRACK INITIATION AND CLUTTER REJECTION 113 without penalizing system sensitivity [32, 33] In fact system sensitivity is increased because scan-to-scan video integration is used For the retrospective detector the returns from eight successive scans are examined to determine if they form a moving-target track If they do, a target is declared present If they not, then it is assumed that only clutter was observed (As we shall see shortly, the retrospective detector even permits the detection of stationary targets, such as buoys, and zero Doppler targets.) The details of the procedure now follows The radar coverage is broken down into small range and bearing regions For each of these regions the returns from eight scan are stored By way of illustration, Figure 3.1-2 plots an example set of such returns seen as range versus bearing and time These are the returns from one of the range–bearing regions mentioned It is next determined if any set of these returns correspond to a target having a constant velocity Return numbers 1, 4, 6, 10, 12, and 14 form the returns from such a constant-velocity target, the target having a velocity in the band between 28 and 35 knots The rule used for declaring a target present in a Doppler band is that M out of N returns be detected in the band Here N ¼ and typically M would be of the order of The retrospective detector was implemented by APL on the AN/FPS-114 radar mounted on Laguna Peak on the California coast This S-band radar has a range resolution of 50 ft and azimuth beamwidth of 0.9  Its scan period is sec with no coherent Doppler processing being used Figure 3.1-3 shows the raw data observed in the lower southwest quadrant after constant false-alarm rate (CFAR) processing The returns from 100 scans are displayed in the figure The coverage is out to a range of nmi A digital range-averaging logarithmic CFAR was used by the system for the results shown in Figure 3.1-3 The results shown in Figure 3.1-3 were obtained without the use of the retrospective detector A high false-alarm rate, about 10
3 , was used in obtaining the results of Figure 3.1-3 This resulted in about 2000 false alarms per scan In this figure the sea clutter false alarms are indistinguishable from small target returns resulting from a single scan Figure 3.1-4 shows the results obtained after retrospective detector processing; again 100 scans of data are displayed The retrospective detector has reduced the false-alarm rate by at least four orders of magnitude The ships and boats in the channel are clearly visible The reduction in the false-alarm rate provided by the retrospective detector is further demonstrated in Figure 3.1-5, which displays 1000 scans of data (about h of data) Very few false alarms are displayed The echo from a clutter spike generally will not generated a false-alarm return at the output of the retrospective detector this is because a spiky echo return typically does not have a duration of more than about 10 sec [34–36] If it did, a retrospective detector with a longer integration time and higher threshold M would be used As mentioned, the detector even allows the detection of targets having a zero Doppler velocity Such returns could arise from ships moving perpendicularly to the radar line of sight and from buoys The detection of buoys is essential for shipboard radars navigating shallow waters 114 PRACTICAL ISSUES FOR RADAR TRACKING TRACK INITIATION AND CLUTTER REJECTION 115 Figure 3.1-3 Raw data observed in lower southwest quadrant after CFAR processing (100 scans of data; nmi total range) (After Prengaman, et al., ‘‘A Retrospective Detection Algorithm for Extraction of Weak Targets in Clutter and Interference Environments,’’ IEE 1982 International Radar Conference, London, 1982.) The above data showed the effectiveness of the retrospective detector in detection of targets in an ocean clutter This type of detector would also be very effective in detecting targets over spiky land clutter, potentially reducing or eliminating the large detection sensitivity loss otherwise needed to eliminate spiky clutter The hardware implementation of the above retrospective detector for the AN/FPS-114 radar consisted of  6-in wire wrap cards containing 250 small and medium-scale integrated circuits (late 1970s/early 1980s technology) The total power consumption is 30 W This implementation is limited to 2000 contacts per scan by the memory size available With the use of modern very large scale integrated (VLSI) circuitry, the size of the signal processor will decrease and its capability increase Table 3.1-1 summarizes the characteristics of the retrospective detector and its performance Figure 3.1-2 Operation of retrospective processor: (a) returns from single scan; (b) returns from Eight Scans; (c) eight scans of data with trajectory filters applied (After Prengaman, et al., ‘‘A Retrospective Detection Algornithm for Extraction of Weak Targets in Clutter and Interference Environments,’’ IEE 1982 International Radar Conference, London, 1982.) 116 PRACTICAL ISSUES FOR RADAR TRACKING Figure 3.1-4 Results obtained after retrospective detector processing using 100 scans of data (After Prengaman, et al., ‘‘A Retrospective Detection Algorithm for Extraction of Weak Targets in Clutter and Interference Environments,’’ IEE 1982 International Radar Conference, London, 1982.) Figure 3.1-5 Retrospective detector output after 1000 scans of data (about hr of data) (After Prengaman, et al., ‘‘A Retrospective Detection Algorithm for Extraction of Weak Targets in Clutter and Interference Environments,’’ IEE 1982 International Radar Conference, London, 1982.) 3.1.2 Clutter Rejection and Observation-Merging Algorithms for Reducing Track Initiation Load In this section we shall describe how clutter rejection and observation-merging algorithms are used to reduce the track initiation load for a coherent ground two-dimensional surveillance radar A two-dimensional radar typically is a radar that has a vertically oriented narrow fan beam (see Figure 1.1-1) that is TRACK INITIATION AND CLUTTER REJECTION 117 TABLE 3.1-1 Retrospective Detector Radar demonstrated on: S-band AN/FPS-114 at Laguna Peak, CA Resolution: 0.1 msec 0:9  4-sec scan-to-scan period 1500 ft altitude Retrospective processor: special purpose, consisting of six  6-in wire wrap cards containing 250 small and medium integrated circuits; total power: 30 W (Late–1970s/early–1980s technology.) Performance results: with single-scan false-alarm rate set at 2000 per scan, after 100 scans false-alarm rate reduced by at least four orders of magnitude, after 1000 scans ( hr) only a few alarms visible scanned 360  mechanically in azimuth about the local vertical axis [1] Such a radar provides two-dimensional information: slant range and the bearing angle to the target (These algorithms are also applicable to three-dimensional radars, that is, radars that measure target range, azimuth, and elevation simultaneously as done with the GE AN/FPS-117 [1, 37], the Marconi Martello stacked beam radars [1, 38– 40], and the Westinghouse ARSR-4 [1].) The next four paragraphs will describe how the Lincoln Laboratory moving-target detector (MTD) Doppler suppression technique works [41, 42] 3.1.2.1 Moving-Target Detector For a radar using the Lincoln Laboratory MTD clutter rejection technique, the radar pulse repetition rate (PRF), that is, the rate at which the radar pulses are transmitted measured in pulses per second, and antenna scan rate are chosen so that the target is illuminated by more than 2N pulses on one scan across the target For the first N pulses PRF ¼ PRF1 is used For the second set of N pulses PRF ¼ PRF is used The purpose of the two PRFs is to remove pulse-Doppler ambiguities and blind velocities that result if only are PRF is used as shall be explained shortly Briefly the pulse Doppler velocity ambiguity and blind velocities arise because typically the PRFs used are too low to permit unambiguous pulse Doppler velocity measurements, that is, the PRF is lower than the Nyquist sampling rate needed to measure the maximum Doppler shift from the target unambiguously An MTD system is coherent, meaning the transmitted train of N pulses can be thought of as generated by gating a stable radio frequency (RF) oscillator The system can be thought of as a sample data system where the sampling is done on transmit One could just as well have transmitted a continuous wave (CW) and done the sampling on receive However, range information would then not be available In order not to have range ambiguities, the pulse-to-pulse period is made larger than the round-trip distance to the longest range target 118 PRACTICAL ISSUES FOR RADAR TRACKING from which echoes are expected For example, if the maximum range for the radar is 100 nmi, then the pulse-to-pulse period would be (100 nmi) (12.355 nmi/msec) ¼ 1235 msec or greater The system PRF would then be 1=1235 msec ¼ 810 Hz For a 1.3-GHz carrier frequency L-band radar an approaching target having a Doppler velocity of 182 knots would give rise to a Doppler-shifted echo having a Doppler shift equal to the PRF of 810 Hz Because we have in effect a sampled data system with a sample data rate of 810 Hz, any target having a target velocity producing a Doppler shift higher than the sampling rate would be ambiguous with a target having a Doppler shift lower than the sampling rate For example, a target having a Doppler velocity of 202 knots would appear as a Doppler-shifted signal produced by a target having a Doppler velocity of 202 knots modulo the sampling rate of 182 knots, or equivalent 20 knots Thus we would not know if the target actually was going at 202 knots or 20 knots, hence the ambiguity The use of the second PRF for the second set of N pulses removes this ambiguity problem This is done by the application of the Chinese remainder theorem A blind velocity problem also arises from the Doppler ambiguity problem If the target had a Doppler velocity of 182 knots, that is, equal to the sampling rate, then it would be ambiguous with the zero Doppler echo returns But the zero Doppler returns are primarily from strong ground clutter Hence, the echo from a 182-knot target is ambiguous with the strong ground clutter As a result, often if would be most likely masked by the ground clutter return This results in the second reason for use of the second set of N pulses at a second PRF A target ambiguous in Doppler with the zero Doppler clutter on the first PRF will not be ambiguous on the second PRF This same problem occurs for near zero Doppler rain clutter and a Doppler ambiguous aircraft echo The rain could mask the ambiguous aircraft echo This masking also is eliminated by the second set of N pulses having the second PRF A typical value for N is To measure the Doppler velocity of the target in a given range cell, the N ¼ echoes from this range cell are passed into a bank of N ¼ narrow Doppler filters covering the band from to 182 knots, with each filter having a bandwidth of (182 knots)/8 ¼ 22.8 knots The nonzero Doppler filters would have a frequency transfer characteristic with a notch at zero Doppler frequency so as to better reject the zero Doppler ground clutter while at the same time passing the signal in the Doppler band of that filter One would think that the output of the zero Doppler filter is ignored, having the strong ground clutter return Actually it is not ignored Instead the filter centered at zero Doppler is used to detect aircraft targets moving perpendicularly to the radar line of sight, which as a result have a zero Doppler velocity Such targets can often be detected in the clutter because when the target has a zero Doppler velocity it is being viewed broadside For this aspect angle the target generally has a very large cross section Hence it is possible that its return echo will be stronger than that of the ground clutter When this occurs, the target is detected To prevent the detection of ground clutter echoes in the zero Doppler filter, the threshold in this filter is set higher than the ground clutter The setting of this TRACK INITIATION AND CLUTTER REJECTION 119 threshold varies with range and azimuth since the clutter strength varies with range and azimuth To determine what value the threshold should be set at for a given range–azimuth cell, a clutter map is generated For this clutter map the strength of the clutter for each range–azimuth cell of the radar is stored in memory Typically the power of the echo in a particular range–azimuth cell from the last H scans (where H might be of the order of to 10) are averaged to generate the clutter strength for this cell An exponentially decaying average is typically used for ease of implementation, it then being possible to implement the filter with a simple feedback infinite-impulse response filter rather than the more complicated finite-impulse response filter The above described processor is the Lincoln Laboratory MTD [41, 42] Lincoln Laboratory first implemented an MTD for the FAA experimental AN/FPS-18 air traffic control radar at the National Aviation Facilities Engineering Center (NAFEC) It was installed in 1975 The FPS-18 is an S-band (2.7 to 2.9 GHz) radar having a PRF of 1000 to 1200 Hz [41, 42, 44] For this radar, in effect, N ¼ 8, with eight Doppler filters used to process eight echo pulses The coherent processing of a set of N ¼ echoes having a specified PRF is called a coherent procesing interval (CPI) There are thus eight Doppler outputs per range cell per CPI Figure 3.1-6 shows a typical system Figure 3.1-6 Typical ASR single-scan return from single target Radar range nmi while Doppler resolution was about 16 knots (From Castella, resolution was 16 F R and J T Miller, Jr., ‘‘Moving Target Detector Data Utilization Study,’’ IEE Radar—77, London, 1977.) 120 PRACTICAL ISSUES FOR RADAR TRACKING return for a single target resulting from a single scan across the target with a two-dimensional TWS radar Each dot represents a Doppler filter crossing For the first range cell return from the target there are four CPIs observed for the target For the next range cell three CPI detections are observed for the same target For each CPI the target is also detected in more than one Doppler cell In some cases all eight Doppler cells show detections Apparently a low detection threshold was used for the illustrated scan given 3.1.2.2 Observation Merging (Redundancy-Elimination, Clustering) Castella and Miller [44] noticed that in general, for a single scan across a target, detection occurred for more than one range–Doppler–azimuth cell It is imperative that all these detections from the same targets not be reported as separate target returns as this would lead to an overload of the tracker The association of such detections, called redundant detections, with a single target and reporting them as a single range–Doppler–bearing report for one target is called observation merging [8], redundancy elimination [8], and clustering [16] Techniques to be used for observation merging are discussed in detail in reference Redundant detections, while being a problem, can be used to effectively eliminate false clutter returns Very effective algorithms developed by Castella and Miller (of the Johns Hopkins University APL) for doing this are described in reference 44 These are now summarized Castella and Miller found that aircraft targets on which there is a firm track typically give rise to responses in two or more of either range cells, Doppler cells, or azimuth cells during one pass across the target Clutter returns on the other hand typically give rise to only one range, Doppler, or azimuth cell response As a result they suggested the use of this characteristic to eliminate clutter returns before they have passed onto the track initiator Table 3.1-2 shows the statistics for single range, Doppler, and bearing CPI returns for aircraft targets for which there is a firm track and for cell echoes which are primarily comprised of clutter returns About 79% of the clutter echoes consist of only one range cell response, one Doppler cell response, or one bearing cell response In contrast, for aircraft targets for which there is a firm track, only 15 TABLE 3.1-2 Sample Centroid Statistics Characteristics Number of CPIs ¼ Maximum number of Doppler cell detections per CPI per range cell ¼ Maximum range extent ¼ Total centroids considered Source: After Castella and Miller [44] Percent of All Centroids Percent of Firm Track Centroids Only 78.7 78.7 15.2 13.7 79.3 34,445.0 21.0 3485.0 ... 3.1.4 Combined Clutter Suppression and Track Initiation It is apparent from Sections 3.1.1 and 3.1.2 that clutter suppression and track initiation go hand in hand Often the engineer generating... 12, and 14 form the returns from such a constant-velocity target, the target having a velocity in the band between 28 and 35 knots The rule used for declaring a target present in a Doppler band... sensitivity for spiky sea and rain clutter and a low loss for lognormal clutter and Weibull clutter The idea is to use a higher false-alarm probability for detection and to then use the track