Implementation of a Viterbi Data Association Tracker for Manoeuvring ...

Implementation of a Viterbi Data Association Tracker for Manoeuvring Targets in Over-the-Horizon Radar:  B. F. La Scala and G. W. Pulford Cooperative Research Centre for Sensor Signal and Information Processing and the Department of Electrical and Electronic Engineering University of Melbourne 19 May 1997



Research supported by High Frequency Radar Division, DSTO

1

Contents 1 Background

3

2 Tracking Scenario

5

3 Summary of Progress During this Phase

6

4 Manoeuvre Onset Detection and Tracking

8

4.1 4.2 4.3 4.4

General Aspects : : : : : : : : : : : Trellis Con dence Drop Detector : : Missed Measurement Node Detector Doppler Bias Detector : : : : : : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: : : :

: 8 : 10 : 11 : 12

5 Manoeuvring VDA Algorithm Summary

13

6 Manoeuvring Target Simulations

14

6.1 Methodology : : : : : : : : : : : : : : : : : : : : : 6.2 Results on Simulated Data : : : : : : : : : : : : : 6.2.1 Maximum Acceleration Rates : : : : : : : : 6.2.2 False Alarm Rates : : : : : : : : : : : : : : 6.2.3 Average Manoeuvre Tracking Performance 6.3 Results of Real Data Tests : : : : : : : : : : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

: : : : : :

14 15 15 21 22 23

7 Conclusions

24

8 Further Work

25

2

1 Background The development of the Viterbi data association (VDA) tracker [1, 2, 3] for over-the-horizon radar is continued in this report. The work described herein has been carried out over a period of 5 months. The objective of this phase of the work was \to incorporate the chosen manoeuvre tracking technique into the VDA tracker and test on real single region data containing manoeuvring targets". We are therefore concerned with the algorithmic and implementational details of the manoeuvre detection and tracking methods identi ed in the last report [4] within the VDA tracker framework. In addition we describe the tuning, testing and evaluation of the selected methods on simulated data. The results of 4 tests on real, peak-detected OTHR data are also brie y described. The previous report [4] dealt with the performance evaluation of 3 manoeuvre tracking methods, selected in [3]: 1. multi-level white noise lter (MLWN); 2. two-stage Kalman lter (TSKF); 3. variable-dimension Kalman lter (VDKF); and 4 manoeuvre detection methods appropriate to the VDA framework1 : 1. 2. 3. 4.

monitoring the missed measurement node (the missed measurement node detector); thresholding the trellis con dence (trellis con dence drop detector); innovations-based detector (bias detector); Doppler bias detector.

The assessment was based on the results of Monte Carlo simulations performed on simulated OTHR peak data for a representative scenario. For transparency, the manoeuvre tracking techniques were tested independently of the manoeuvre detection methods. Four kinds of target manoeuvre models were chosen for the tests 1. 2. 3. 4.

step change in speed with constant heading (jerk manoeuvre); step change in speed and heading (kink manoeuvre); sustained acceleration with constant heading (thrust manoeuvre); sustained acceleration with change in heading (turn manoeuvre).

The assumed changes in speed and the target accelerations in range r and azimuth a are summarised below in Table 1. 1

A description of the VDA algorithm and associated terminology is contained in [2].

3

Jerk
r_ = 0:1 km/s
_a = 0:0083 degree/s Kink
r_ = 0:1 km/s
_a = 0:005 degree/s 2 Thrust r = 0:0005 km/s a = 4:167  10,5 degree / s2 Turn r = 0:0005 km/s2 a = 7:5  10,5 degree / s2 Table 1: Accelerations and velocity changes assumed for manoeuvre detection and tracking simulations. It was decided to test the candidate manoeuvre tracking methods in the absence of clutter and for unity probability of detection. The results therefore represented the best achievable performance of each method, without the complications of data association or missed target detections. Each of the manoeuvre tracking methods was tuned to give the best overall performance on the 4 manoeuvre types. For known manoeuvre onset and termination times, the Monte Carlo simulations led to the following conclusions. 1. The TSKF has the best performance in azimuth and range for all manoeuvres considered and has a relatively large initial error for step changes in Doppler. 2. The VDKF performs well in azimuth, but poorly in range for all manoeuvres considered and has the largest errors for step changes in Doppler. 3. The MLWN lter gives intermediate performance but is relatively robust. 4. All lters have increased tracking errors during the manoeuvring phase when the manoeuvre onset time is underestimated. On the basis of these tests, the relative performance of the three trackers was established as 1. two-stage Kalman lter 2. multi-level white noise lter 3. variable-dimension Kalman lter with the VDKF having the worst performance. The complexity of implementation of the three lters is 1. multi-level white noise lter 2. two-stage Kalman lter 3. variable-dimension Kalman lter with MLWN being by far the simplest to implement and the TSKF and VDKF having similar complexity for the OTHR tracking problem. The MLWN and TSKF were therefore selected for further development during this phase of the work. The manoeuvre detectors were tested in the VDA framework with an average of 30 false measurements per dwell at both low and high probability of detection. The results for the manoeuvre detector tests were less conclusive. It was found that all the detectors tended to underestimate 4

the manoeuvre onset time. This outcome was later found to be due to the inclusion of false alarms in the test results (i.e., triggering of the detectors by clutter or excessive measurement noise when there was no manoeuvre). We have attended to this shortcoming in the present report.

2 Tracking Scenario Based on examination of several sets of real peak-detected OTHR data from the Jindalee radar, the following test scenario has been developed for this report. The focus of the current phase is tracking within a single region, with tracking across multiple regions (within a single radar \task") the subject of the next contract phase.

 The radar is operating in aircraft mode under \stable ionospheric conditions".  Measurement resolutions are 20 km (slant range), 0.005 km/s (Doppler) and 0.5 degree         

(azimuth). The region size is: 1000 | 1600 km (slant range), 0 | 0.3 km/s (Doppler) and 0 | 10 degree (azimuth). Multipath propagation is absent. The revisit period is 20 seconds. The simulation length is 40 dwells. Measured Doppler is ambiguous. False measurements are uniformly distributed (outside the central clutter band in Doppler) with an average number of 100 per dwell. Target SNR is not used in the tracker. There is a stationary target (calibration signal or beacon) with a probability of detection PD = 0:98 present throughout the simulation. There is a single in-bound, manoeuvring target present with PD = 0:61. Target Doppler remains outside the central clutter band.

The manoeuvring target has the following characteristics:

 The target follows a straight line course, then executes a turn manoeuvre at dwell 20 and

range 1320 km.  The initial target velocity (at dwell 0) is 0.3 km/s (range) and 0.008 degree/s (azimuth). The initial range is 1500 km and initial azimuth 2 degree.  During the manoeuvre the azimuthal acceleration is zero. The radial acceleration is in the range ,0:001 | ,0:003 km/s/s. 5

 The turn lasts for 3 dwells (60 seconds) after which the target resumes a straight line course.

The assumed target manoeuvre corresponds to a turn to the left while decelerating. The range of radial accelerations chosen corresponds to changes in heading of 6 and 26 degrees with changes in speed of -178 and -476 km/h respectively. 1600

1500

Range (km)

1400

1300 ] 1200

1100

1000 0

1

2

3

4 5 6 Azimuth (degrees)

7

8

9

10

Figure 1: Typical \turn" manoeuvre. The square bracket denotes the head of the track (the current position). The stationary target is marked by the symbol \o".

3 Summary of Progress During this Phase Before describing the algorithmic details of the VDA tracker for manoeuvring targets, we mention a number of modi cations to the tracker software which have been eected during this phase. These modi cations were prompted by implementation considerations for the manoeuvre tracking methods in question and by ongoing testing with real OTHR data.

 Bounded Measurement Noise: The adoption of the standard white Gaussian mea-

surement noise model in the previous report [4] was inappropriate and gave rise to unrealistically large deviations in azimuth. This resulted in a coarseness of track estimates not re ected in real data. Consequently, the measurement noise used in simulations in this phase was assumed to be bounded. Noise samples, taken from a multivariate Gaussian density, were required to lie within two resolution cells in range, azimuth and Doppler. 6

 False Manoeuvre Declarations: In all simulations of the VDA tracker for manoeuvring 

 







targets we make the distinction between (i) the estimated manoeuvre onset time for the true target track; and (ii) false manoeuvre declarations due to measurement noise, clutter and/or missed target detections. Manoeuvre Detectors: The following manoeuvre detectors have been implemented in the VDA tracker: trellis con dence drop detector, missed measurement node detector, Doppler bias detector. The current Doppler bias detector combines aspects of the innovations-based and Doppler bias detectors used in [4]. The detector is chosen by compilation ag (see Appendix 2). Only non-stationary targets are tested for manoeuvring. Manoeuvre Trackers: The following tracking lters have been implemented in the VDA tracker: MLWN and TSKF. The tracking lter to be used is selected at compilation time. Initiation using Doppler binning: During tracking, all trellises have access to all the measurements in the dwell for the speci ed region. Measurements for which the path con dence (as distinct from the overall trellis con dence) is below a threshold are marked as unused by that trellis or unassociated. An earlier implementation of the VDA tracker initiated only one set of 3 trellises (for in-bound/stationary/out-bound velocity ambiguity) per dwell. This resulted in an unacceptably long initiation delay on some targets in a multi-target environment. To overcome this de ciency, at the rst dwell and on all subsequent dwells where unassociated measurements exist, these measurements are sorted into a predetermined number of Doppler bins. Trellises are initiated (for each velocity ambiguity) in each Doppler bin. The optimal number of Doppler bins was found to be between 3 and 5 for the assumed number of targets and clutter density in the simulations. The previous trellis initiation method corresponds to a single Doppler bin. Multiple Regions & Time Handling: A multiple region data structure has been set up to handle ARDS data from more than a single region within the radar's coverage. The method of time handling in the tracker has also been modi ed. Dwell data are numbered sequentially. Each block of dwell data contains a header (see [5]) which identi es the region and the physical time of the dwell. Track life in now is de ned as the number of revisits to the speci ed region between initiation and the current dwell. The lter prediction calculation also takes into account the time since the last revisit for each region. A tracking methodology for multiple regions is to be established in the next phase of the work. Measurement Backtracking: Manoeuvre detection tests are generally based on observations over a time window of length w (the detector window length). If a manoeuvre is detected at time kd = k, then the actual manoeuvre is declared to have started at time k^m = k , w + 1 (the start of the window). This situation is depicted in Fig. 2. Assuming the track has not been deleted prior to detection of the manoeuvre, the measurements from time k , w through to k must be reprocessed (see section 4). This necessitates the storage of w , 1 dwells of past data in addition to the current dwell data for the region. Dwell storage and backtracking have been implemented in the current version of the tracker with a proportional increase in memory overheads. Rescaling of log Costs: Recall that the computation of the path con dences cj (kjk) at time k in each VDA trellis depends on the path probabilities dj (k) according to [2]  cj (kjk) = Pnkdj (kd) (k) j =,1 j 7

where dj (k) = expf,dj (k)g, dj (k) is the log cost of the path to node j at time k and nk is the number of measurements in the dwell. For long tracks, the log cost can become large enough to cause numerical under ow in the computation of the probabilities dj (k), leading to a divide-by-zero in the evaluation of cj (kjk). It is therefore necessary to rescale the log costs periodically to avoid under ow. The following rule has been adopted for this: Let dj (k)min = minj dj (k). If dj (k)min  30, then dj (k) := dj (k) , dj (k)min 8j . A further numerical problem was encountered when the azimuth units were changed from degrees to milliradians. Numerical conditioning in the lter calculations appears to be better for the choice of units: km (range), km/s (Doppler), degree (azimuth).  Duplicate Track Deletion: In the previous version of the VDA tracker, it was observed that multiple copies of tracks were often formed from dierent initial points. The current tracker tests for duplicate tracks and deletes them according to the test [^xi (kjk) , x^j (kjk)]0 fP i (kjk) + P j (kjk)g,1 [^xi (kjk) , x^j (kjk)] < 2nx where x^i (kjk) and x^j (kjk) are the ltered states for tracks i and j , with covariances P i (kjk) and P j (kjk) respectively, 2nx is the 95% con dence limit for a chi-squared random variable with nx degrees of freedom and nx = 4 is the dimension of the state vector. The chi square value is denoted critical point for new track decision in the parameter les listed in the Appendix. Note that this test does not properly account for the statistical dependence of the estimation errors for the two tracks [6]. A more reliable test would take account of the previous state estimates also, as the tracks in question may be from separate targets which are close at time k.

4 Manoeuvre Onset Detection and Tracking 4.1 General Aspects The principle of conventional manoeuvre detection is depicted in Fig. 2 for a target manoeuvre in a hypothetical 2 dimensional space. The target travels at constant velocity until time km , 1 and then accelerates uniformly. The manoeuvre detector, which is based on observations over a window of length w, is triggered at time k and estimates the manoeuvre onset time as k , w +1. The measurements from time k , w + 1 must be reprocessed by the manoeuvre tracking lter, using the constant-velocity estimates at time k , w as the initial point. The manoeuvre lter remains in use until a manoeuvre termination condition is met. Manoeuvre termination may be judged by testing the signi cance of the acceleration estimates, or more simply by declaring the manoeuvre nished after a given maximum time has elapsed. In the present implementation the parameter assumed maximum manoeuvre length is used to determine when to revert to the constant-velocity lter. It is important that the track estimates have \stabilised" before an attempt is made to detect a manoeuvre, otherwise premature triggering of the detector may result. To help ensure that this condition is met, the manoeuvre detection test is only applied to con rmed trellises. 8

01

11 00

11 00 00 11

01

km-1

0110

0110

constant acceleration

constant velocity

km

01

01

11 00 00 11

km+1

0110

01

11 00

k = k

d

k-1

k-2

^ k = k-w+1 m

k-w

Figure 2: Manoeuvre timing and detection over a window for a unity sampling interval. The upper diagram represents the track of the true target which starts accelerating during the time interval [ m , 1 m ], having had constant velocity up to time m , 1. In the lower diagram, the manoeuvre has been k

;k

k

detected at time d . With a window length of , the estimated manoeuvre onset time is then ^m . k

w

k

Since it was not possible to select a single best manoeuvre detection method from the preliminary test results in [4], we have implemented three manoeuvre detectors in the VDA tracker to allow further comparison to take place. The three detectors are: (i) the trellis con dence drop detector; (ii) the missed measurement node detector; and (iii) the Doppler bias detector. These are treated in detail subsequently. Concerning manoeuvre tracking lters, it was clear from [4] that the VDKF should be eliminated, leaving the TSKF and MLWN. Both of the latter have been implemented in the VDA tracker and either may be selected via a compilation ag (see Appendix). For the simpler MLWN approach, two user-de ned parameters (process noise in ation factors) determine the increase in process noise in the range and azimuth lters during the manoeuvre. The requirement of re-initialisation of the TSKF with acceleration estimates for azimuth and range seems to be a potential cause of track loss not encountered in the simulations in [4]. Further investigation is required to determine whether the TSKF is suited to manoeuvring target tracking in the present application. 9

It is of interest to determine the performance of each manoeuvre detection and tracking method with regard to (i) its ability to detect the target manoeuvre and correctly estimate its onset time; (ii) maintain track during and after the manoeuvre, while (iii) minimising the false alarm rate for manoeuvre declarations in the presence of clutter (false measurements). Clearly there is a trade-o in the sensitivity of the manoeuvre detector and its ability to reject clutter. The problem of manoeuvre detection is further complicated when the target detection probability is low and the density of false measurements is high, as is often the case in OTHR. This is because (i) a series of missed target detections could be due to a failure to detect the target or to termination of the track; (ii) a false measurement or series of false measurements may trigger the manoeuvre detector. Missed target detections during the manoeuvring phase are particularly dicult to deal with since then there is no statistical innovation on which to base the manoeuvre hypothesis test. Many of the innovations-based signi cance and goodness of t tests mentioned in [6] for detecting and tracking manoeuvring targets in clutter are not appropriate for low probabilities of target detection due to the absence of data. As an example, consider a statistical test that requires three target detections at the start of the manoeuvring phase in order to decide whether or not to declare a manoeuvre. If the probability of target detection is 0.6, the probability of receiving three detections in a row is 0:6  0:6  0:6 = 0:216. Thus the manoeuvre detector can only be expected to give a decision in 21.6% of cases at this PD . Of this percentage, a further fraction, say 5%, will correspond to false manoeuvre declarations (due to measurement noise and clutter), with the remainder, or 16.6%, being the success rate for the manoeuvre detector! It is clear then that the probability of target detection sets fundamental limits on what can be expected of the manoeuvre detection part of the tracker. The reader is referred to [3] for further discussions on the manoeuvring target tracking problem. Discrete-time models for the target dynamics and measurement processes appropriate to OTHR tracking are covered in [4]. Details of the three manoeuvre detection methods are now covered, together with some general observations on their behaviour. Further evidence for these observations is presented in the simulations section 6.2.

4.2 Trellis Con dence Drop Detector The trellis con dence or probability of existence is de ned as

Pe (kjk) = c,1(kjk) = 1 ,

n X c (kjk) k

i=0

i

where ci (kjk) are the path con dences for the nodes ,1; 0; 1; : : : ; nk and nk is the number of measurements in dwell k. Two sliding window averages of the trellis con dence are de ned: (i) the average over the con rmation delay - used to con rm or delete a trellis; (ii) the average over the manoeuvre window length. The test consists of computing the average trellis con dence over the manoeuvre window for a given con rmed trellis. A manoeuvre is declared if the average falls below a preset threshold. It is important that the manoeuvre window length be less than the con rmation delay to avoid deleting a trellis corresponding to a manoeuvring target. The manoeuvre window length and the con dence threshold for manoeuvre declaration are the only tuning parameters required for this approach. 10

The trellis con dence drop detector typically has a high false alarm rate since it may be triggered by any event that results in a reduction of the average trellis con dence. Such reductions are not always associated with a target manoeuvre. The con dence drop detector is very sensitive to manoeuvres when they occur and does not involve a test of lter innovations, which is an advantage at low PD . The increased sensitivity comes at the price of a higher computational overhead and an increased tendency of track loss, especially for non-manoeuvring tracks on which false manoeuvres are declared. Whereas the con dence drop detector does not consider the characteristics of individual tracks, the following two manoeuvre detectors are linked to the behaviour of the best, or highest con dence, track in the trellis.

4.3 Missed Measurement Node Detector The missed-measurement-node detector monitors the track with the highest path con dence in the trellis and tests for successive occurrences of so-called \dummy nodes" along the track. The dummy nodes in the VDA correspond to a missed target detection (node 0) and to non-existence of the target (node ,1). When the 0 node is selected by the VDA algorithm as the most likely current association for the best track, this implies that either the gate is empty or any detections falling inside the gate had a lower association probability than the \missed detection" hypothesis (i.e., the target was either not been detected or was not inside the gate). Unlike the nearest-neighbour Kalman lter, a dummy measurement may be preferred to a measurement falling inside the gate. A series of dummy nodes, leading to track loss, is indicative of termination of the track or that a manoeuvre has occurred. In the previous report [4] the \dummy-node detector" was designed around this principle. It is now recognised that this detector is too prone to false alarms of the type produced by constant-velocity targets with low PD . The missed-measurement-node detector is an improved version of the dummy detector. To declare a target manoeuvre, three events are required: (i) the constant-velocity gate at time k , 1 must contain a measurement that is associated with the best track in the trellis; (ii) starting from time k the number of successive dummy nodes on the best track must equal or exceed the data window length; and (iii) there must be a measurement contained in the manoeuvre gate at time k . As illustrated in Fig. 3, the manoeuvre gate is a gate containing the constant-velocity gate, obtained by increasing the gate size (as set by the squared number of standard deviations [6]) by the manoeuvre gate factor. This is to allow for the fact that, during a manoeuvre, larger innovations are possible than in the constant-velocity case. Clearly the data window length must be chosen less than the confirmation delay (for con dence averaging) to ensure that the track is not deleted before a possible manoeuvre has been detected. The missed-measurement node detector addresses some of the weaknesses of the trellis con dence drop detector in that it directly monitors the most likely track in the trellis and looks for the presence of a candidate target measurement at the onset of the manoeuvre. A shortcoming of the missed-measurement node detector is that it may be falsely triggered by a succession of dummy nodes that do not correspond to a target manoeuvre. On the other hand, it may fail to 11

01

11 00

0110

11 00 00 11

11 00 00 11

x

11 00

x

constant velocity gate

manoeuvre gate

Figure 3: Constant-velocity and manoeuvre gates. be triggered if there is no candidate detection in the rst manoeuvre gate.

4.4 Doppler Bias Detector To reduce the probability of false manoeuvre declaration inherent in the two detection methods described above, consideration must be given not only to the size of the normalised innovation but to the size its the Doppler component. The Doppler (radial velocity) is by far the most accurate measurement in OTHR and is also the most sensitive and rapid indicator of a target manoeuvre. The Doppler bias detector implemented during this phase diers from that de ned in [4], which required a test statistic to be formed over a window. It is not clear that a sensible de nition of lter innovation is possible in the OTHR context when the PD is low and there is heavy clutter. The revised Doppler bias detector has the requirements of the missed measurement node detector, namely: (i) the constant-velocity gate at time k , 1 must contain a measurement that is associated with the best track in the trellis; (ii) starting from time k the number of successive dummy nodes on the best track must equal or exceed the data window length; (iii) there must be a measurement contained in the manoeuvre gate at time k; and in addition, (iv) the Doppler innovation of the measurement in the manoeuvre gate at time k must be less than the manoeuvre detection theshold. The fourth requirement adds considerable discriminatory power to the manoeuvre detector, since it recognises that a target (aircraft) has a maximum acceleration that limits the change in (radial) speed over one dwell. The price to be paid for the lower false alarm rate achievable with the Doppler bias detector is a lower rate of manoeuvre detection when PD is low, since a target detection is required at the manoeuvre onset time to trigger the detector. It should be straightforward to alleviate this problem by allowing for a single detection in a series of (increasing) manoeuvre gates. We have not eected this change in the current phase, but the potential advantages should be obvious from the following example. 12

Suppose the probability of detection PD = 0:6. The probability of receiving one detection in 2 successive manoeuvre gates is PD + (1 , PD )  PD = 0:84. The probability of a detection in 3 successive manoeuvre gates is PD + (1 , PD )  PD + (1 , PD )2  PD = 0:936, and so on. The potential improvement in manoeuvre detection performance with this method has not yet been assessed.

5 Manoeuvring VDA Algorithm Summary The VDA algorithm for single-region tracking of manoeuvring targets is summarised below. This includes provisions for range-Doppler coupling, measurement gating, automatic track initiation and maintenance, inbound/outbound/stationary velocity ambiguity, multiple constant velocity and manoeuvring targets with arbitrary start and termination times. The generic manoeuvre detection and tracking steps can be implemented using any one of the three above manoeuvre detectors in conjunction with either MLWN or the TSKF. The terminology is consistent with [2]. 1. For the rst dwell k = 0, sort all ARDS measurements into nD Doppler bins. In each Doppler bin which contains measurements, initiate 3 Viterbi trellises, one each for inbound, outbound and stationary targets. 2. For the current dwell k = 1; 2; : : : (a) For each trellis: i. Add new layer to current trellis corresponding to current dwell using the appropriate velocity ambiguity for that trellis. ii. If trellis is marked as manoeuvring, test for manoeuvre termination and set the lter type (constant velocity or constant acceleration) as appropriate. iii. For each node i in dwell k , 1 in the current trellis: A. Calculate the measurement prediction and the measurement prediction covariance. B. Determine the gate and the set of validated measurements. C. For each node j in dwell k in the current trellis: 1 Calculate the transition probabilities and the transition costs for nodes in the gate. 2 Determine the best path to each node j in dwell k. 3 Update the path history and store the path cost. 4 Compute for j  0 the associated Kalman lter state estimate and error covariance. 5 Calculate path con dence. iv. Prune nodes from trellis which have a path con dence less than the track deletion threshold. Mark measurements corresponding to each node as used or unused by current trellis as appropriate. v. Trim nodes in previous layers of the trellis which are no longer on any surviving path and check if and when the paths have merged. vi. Calculate the trellis con dence and the averaged trellis con dence over the confirmation delay. 13

A. If the averaged trellis con dence is less than the trellis deletion threshold, delete the trellis and mark all associated measurements in current measurement set as unused by this trellis. If trellis was con rmed previously mark the trellis and the associated track as lost. B. If the averaged trellis con dence is greater than the trellis confirmation threshold, and the confirmation delay has been exceeded, mark trellis as con rmed and add the best track in the trellis to the track database. C. If trellis is con rmed and not for a stationary target, apply the manoeuvre detection test and mark as manoeuvring or non-manoeuvring as appropriate. If a manoeuvre has been declared, calculate the estimated manoeuvre onset time as k^m = k , w where w is the detector window length. D. Else mark the trellis as tentative. vii. Proceed to next trellis. (b) If any trellis is marked as manoeuvring i. Delete all trellises initiated since dwell k , w + 1 and revise the track database accordingly. ii. Disable the manoeuvre detector. iii. Backtrack to dwell k , w + 1 iv. Initialise the manoeuvring lter by increasing the process noise in azimuth and range by their respective inflation factors (for MLWN). Initialise the bias lter with the range and azimuth accelerations (for the TSKF) based on the constant velocity estimates from time k , w and the new measurement at time k , w + 1. v. Return to step a(i) and reprocess (steps (a), (c) and (d)) the dwell measurements from time k , w + 1 to k. vi. Re-enable the manoeuvre detector. (c) Sort all unused measurements in dwell k into nD Doppler bins. Create and initialise new trellises, one for each velocity ambiguity and non-empty Doppler bin, using all measurements which are not used in any existing trellis. (d) Update the track database with the best track to time k from each trellis that has either merged or been con rmed. These tracks may be displayed. 3. Proceed to dwell k + 1.

6 Manoeuvring Target Simulations 6.1 Methodology A number of simulations were performed to give an indication of the performance characteristics of the manoeuvring VDA tracker using the Multi-Level White Noise lter under each manoeuvre detection technique. The three main features of interest were: 1. the maximum manoeuvre acceleration (or deceleration) that could be tracked; 14

2. the false alarm rate of each detector; and 3. the average performance of the VDA tracker for a realistic manoeuvre scenario. Simulations were performed under the following conditions: S1 single non-manoeuvring target with realistic clutter and PD = 0:6; S2 single manoeuvring target with realistic clutter and PD = 0:6; and S3 single manoeuvring target with low clutter and PD = 1. As in section 2 realistic clutter is taken to mean an average of 100 uniformly distributed false measurements per dwell. Scenario S1 was chosen to give an indication of the false alarm statistics of the manoeuvre detectors. Scenario S2 tests the combination of manoeuvre detector and tracker in a typical OTHR tracking situation. Scenario S3 is useful as a reference scenario in which to compare the capabilities of the three manoeuvre detection methods without the added complications of missed target detections and false alarms.

6.2 Results on Simulated Data 6.2.1 Maximum Acceleration Rates The rst case examined was that of determining how abrupt a manoeuvre the VDA tracker was able to handle. Scenario S2 was used in this calculation. The region contained a single manoeuvring target with a low probability of detection (PD = 0:6). In addition, there was a strong, stationary target (PD = 0:98). There were an average of 100 false measurements per dwell. The moving target executed a short manoeuvre, lasting 3 dwells, beginning at dwell 20. There was no acceleration in azimuth but six data sets were generated each with a dierent acceleration in range. These ranged from ,0:001 km=s2 to ,0:003 km=s2 , corresponding to a change in heading of between 6 and 26 degrees with an associated deceleration. Each manoeuvre detector was tuned to give a minimum false alarm rate while retaining sucient sensitivity to detect the manoeuvre. For all three detectors it was found that selecting the manoeuvre window length to be one dwell less than the con rmation delay (i.e., 3 dwells) gave the best performance. Shorter windows increased the false alarm rate to unacceptable levels, while a window length equal to the con rmation delay led to frequent track deletion prior to the manoeuvre being detected. The other tuning parameters that were adjusted included the manoeuvre detection threshold (for the trellis con dence drop and the missed measurement node detector) and the manoeuvre gate factor (for the missed measurement node and Doppler bias detectors). These parameters were chosen through a process of trial and error. The same range and azimuth process noise in ation factors were used for each manoeuvre detector so that dierences due to the latter could be isolated. For all range decelerations examined it was possible to tune all three detectors so that they estimated the manoeuvre onset time to within 1 dwell of the correct time. With this degree of accuracy in the onset time estimate, the MLWN tracker was able to track the target through the manoeuvre in all cases. 15

It was found that the MLWN tracker was particularly sensitive to the lter process noise in ation factor for azimuth. This was due to the high variance of the azimuth measurement which led to a correspondingly high degree of uncertainty in the azimuth and azimuth rate estimates. The process noise in ation factor for azimuth was held at a relatively small, xed value. Larger values increased the gate to the entire region in the azimuth dimension, leading to frequent track loss. The required process noise in ation factor for range varied for each of the deceleration levels examined. The range in ation factor was gradually increased until a minimum value was found which permitted the tracker to track through the manoeuvre. Due to the relatively high degree of accuracy in the Doppler measurements, and the coupling of Doppler to range rate, the gate size in the range dimension tended to be very small. The suitable minimum value for the range process noise in ation factor was typically O(100) { O(1000) times larger than the azimuth process noise factor. Figures 4 to 6 show the estimated and true target tracks in range-azimuth space for the trellis con dence drop, missed measurement node and Doppler bias detectors (all using the MLWN lter). In this example, the range acceleration was ,0:003 km=s2 .

1600

1500

Range (km)

1400 ] 1073

1300

1200

1100

O 5183

1000 2

3

4 5 Azimuth (deg)

6

7

Figure 4: Range-azimuth display for the Trellis Con dence Drop Detector with MLWN tracker

16

1600

1500

Range (km)

1400 ] 1073

1300

1200

1100

O 5183

1000 2

3

4 5 Azimuth (deg)

6

7

Figure 5: Range-azimuth display for the Missed Measurement Node Detector with MLWN tracker

1600

1500

Range (km)

1400 ] 1073

1300

1200

1100

O 5183

1000 2

3

4 5 Azimuth (deg)

6

7

Figure 6: Range-azimuth display for the Doppler Bias Detector with MLWN tracker

17

The true location of the stationary target is marked with a \" and the true track of the moving target by the dashed line. The track estimates are given by solid lines with the track head marked by \o" for a stationary track and by \]"for an inbound or outbound target track. Track numbers are assigned as described in the Appendix. False tracks have been removed manually from the display for clarity. Figures 7 to 12 show the corresponding state estimates, 3 envelopes and trellis- and trackcon dence measures for the estimated target track. The times at which the VDA tracker selected the missed-detection node are indicated by \o" and by \+" for the non-existent target node.

1600

0.4 Range Rate (km/s)

Range (km)

1500 1400 1300 1200 1100 1000 0

10

20 Dwell no.

30

0.2 0 −0.2 −0.4 0

40

10

20 Dwell no.

30

40

10

20 Dwell no.

30

40

0.1 Azimuth Rate (deg/s)

Azimuth (deg)

6 5 4 3 2 1 0 0

10

20 Dwell no.

30

0.05 0 −0.05 −0.1 0

40

Figure 7: State estimates for the Trellis Con dence Drop Detector with MLWN tracker

18

1600

0.4 Range Rate (km/s)

Range (km)

1500 1400 1300 1200 1100 1000 0

10

20 Dwell no.

30

0.2 0 −0.2 −0.4 0

40

10

20 Dwell no.

30

40

10

20 Dwell no.

30

40

0.1 Azimuth Rate (deg/s)

Azimuth (deg)

6 5 4 3 2 1 0 0

10

20 Dwell no.

30

0.05 0 −0.05 −0.1 0

40

Figure 8: State estimates for the Missed Measurement Node Detector with MLWN tracker

1600

0.4 Range Rate (km/s)

Range (km)

1500 1400 1300 1200 1100 1000 0

10

20 Dwell no.

30

0.2 0 −0.2 −0.4 0

40

10

20 Dwell no.

30

40

10

20 Dwell no.

30

40

0.1 Azimuth Rate (deg/s)

Azimuth (deg)

6 5 4 3 2 1 0 0

10

20 Dwell no.

30

0.05 0 −0.05 −0.1 0

40

Figure 9: State estimates for the Doppler Bias Detector with MLWN tracker

19

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

Prob of existence Track confidence

0.1 0 0

5

10

15

20 Dwell no.

25

30

35

40

Figure 10: Trellis and track con dence for the Trellis Con dence Drop Detector with MLWN tracker

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 Prob of existence Track confidence

0.1 0 0

5

10

15

20 Dwell no.

25

30

35

40

Figure 11: Trellis and track con dence for the Missed Measurement Node Detector with MLWN tracker

20

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

Prob of existence Track confidence

0.1 0 0

5

10

15

20 Dwell no.

25

30

35

40

Figure 12: Trellis and track con dence for the Doppler Bias Detector with MLWN tracker

6.2.2 False Alarm Rates The next stage of the analysis was to determine approximate false alarms rates for each detector and to gauge how often false alarms lead to track loss. A Monte Carlo study of approximately 40 runs was used to gather statistics. The scenario (S1) consisted of a single target moving in a straight line with a PD = 0:6 in a single region with realistic clutter. The three manoeuvre detectors together with the MLWN lter were used in turn on these data sets. The detector parameters were set as described in the previous section to detect a range acceleration of r = ,0:002 km=s2 . The percentage of false manoeuvre declarations on the target track that led to track loss are summarised in Table 2 below. Detector Track Lost Due to False Alarm Trellis Con dence Drop 17.5% Missed Measurement Node 15.0% Doppler Bias 15.0% Table 2: Percentage of manoeuvre false alarms leading to track loss in clutter by detector type. The Doppler bias and missed measurement node detectors were found to have the same overall false alarm rates (45%) and the same proportion of false alarms leading to track loss (15%). This is understandable since the Doppler bias detector was tuned to give the same manoeuvre detection performance as the other detectors. The false alarm rate of the Doppler bias detector could probably be reduced further by choosing the Doppler dierence threshold to be smaller, while applying the technique in section 4.4 to maintain a good manoeuvre detection rate. 21

The trellis con dence drop detector, as it is relatively easily triggered, has the highest false alarm rate (55%) and the highest proportion of false alarms leading to track loss (17.5%). This detector simply monitors the overall trellis con dence for a particular target. The missed measurement node and Doppler bias detectors, on the other hand, monitor the con dence of the most likely track in a given trellis and would be expected to have greater discriminatory power than the trellis con dence drop detector.

6.2.3 Average Manoeuvre Tracking Performance The third stage of the testing was to compute the average performance of each combination of manoeuvre detector with the MLWN lter. The performance of the three types of VDA manoeuvring target trackers were examined under two scenarios. The rst, idealistic, scenario (S3) contained a single target with high probability of detection, observed in very low clutter and was aimed at determining the best case performance. The second, more realistic, scenario (S2) involved tracking a manoeuvring target at low PD in heavy clutter. The results for the idealistic scenario S3 are given in Table 3. Given the unity probability of detection and the low clutter density, an average of 5 false measurements per dwell, the eects of data association uncertainty and missed target detections are almost entirely eliminated. Under these conditions all three detectors, coupled with the MLWN lter, track in 98{100% of cases with no signi cant dierence in performance. Drop Missed Node Doppler Bias Target tracked for entire life 100% 98% 98% Manoeuvre missed 0% 2% 2% Manoeuvre detected but track lost 0% 0% 0% False alarm rate 5% 9% 9% Estimated manoeuvre onset time 19.9 19.9 19.9 Estimated standard deviation 0.9 0.9 1.0 Table 3: Manoeuvre tracking results by detector type for the idealised scenario S3. For the realistic tracking scenario S2 a Monte Carlo simulation of approximately 40 runs was used to provide an indication of the performance of the VDA tracker. In this case the region contained a single manoeuvring target with a low probability of detection (PD = 0:6), and an average of 100 false measurements per dwell. The moving target executed a short manoeuvre, lasting for 3 dwells, beginning at dwell 20. The acceleration in range was taken to be ,0:003 km=s2 with zero acceleration in azimuth. For each data set and manoeuvre detector combination the estimated manoeuvre onset time, false alarm rates (on the target track) and their incidence times were noted. The ability of the VDA tracker to maintain track on the target before, during and after the manoeuvre was also recorded. The track acceptance test required the true target track to be within the 3 limits of the estimated track. It was relatively common for the VDA to be unable to track accurately during the manoeuvre window, while maintaining track on the target at other times. Failure to track after the manoeuvre was traced to a number of causes. The rst is that poor estimates during the manoeuvre can lead to subsequent track loss. A second cause is that a 22

false alarm after the manoeuvre may lead to track loss despite the VDA having tracked during the manoeuvre. Table 4 gives the results of the Monte Carlo study. Target tracked for entire life Manoeuvre missed Manoeuvre detected but track lost Track loss due to false alarm after the manoeuvre Track loss due to failure to track through manoeuvre Estimated manoeuvre onset time Estimated standard deviation

Drop Missed Node Doppler Bias 39% 39% 29% 10% 10% 20% 51% 51% 51% 52% 43% 48% 48% 57% 52% 19.7 19.7 20.3 1.3 1.4 1.8

Table 4: Manoeuvre tracking results by detector type for the realistic scenario S2. The results point to the trellis con dence drop and missed measurement node detectors having superior performance to the Doppler bias detector: the probability of missing a manoeuvre with Doppler Bias Detector is twice as great as that of other two detectors. This result, which deserves clari cation, is due to the fact that the Doppler bias detector in the current implementation requires a target detection at the start of the manoeuvre and, in this example, the probability of detection is only 0.6. Ways of improving the detection performance, while maintaining good false alarm performance, were outlined in section 4, although these have not been implemented so far. The trellis con dence drop and missed measurement node detectors appear to have similar characteristics in terms of the probability of missing a manoeuvre and the probability maintaining track. A likely explanation for this is the observation that, in practice, a trellis generally contains only one strong candidate target track. Thus the trellis con dence closely matches the track con dence of the best target track. Both con dence gures tend to decrease in proportion to the number of successive missed detection nodes on the path. The number of instances of track loss when the manoeuvre was detected and its onset time was estimated to within 1 { 2 dwells of the correct time is relatively high for all three detection methods. However, track retention is better when the manoeuvre onset time is correctly estimated (although track loss may still occur after the estimated manoeuvre termination time). This can be understood, on the one hand, due to the low probability of target detection which renders manoeuvre detection and tracking dicult: the MLWN lter works best when there are a high proportion of target detections during the manoeuvre. Secondly, the high clutter density can cause track seduction when the true target measurement is absent. This problem is especially prevalent during the manoeuvring phase when the lter bandwidth (and gain) is high and the validation gate is relatively large.

6.3 Results of Real Data Tests The manoeuvring VDA tracker was tested on four sets of real, peak-detected, air-mode OTHR data. None of these data sets was considered to be suciently compatible with the assumed manoeuvre scenario to provide a conclusive result. In data set 1, the target manoeuvre was so slight the VDA tracker was able to maintain a track on the target using the constant velocity 23

lter. In data set 2, the target was not detected at and around the time of the manoeuvre, rendering maoeuvre detection impossible. In this case the target was tracked as two separate, constant-velocity targets. In data set 3, the manoeuvre occurred only a few dwells after initial target detection| during the con rmation window of the VDA tracker. Since the current version of the VDA tests for manoeuvres only on con rmed tracks, it was unable to track this target. Data set 4 consisted of air-mode data collected over the Darwin region. This dense target environment overloaded the VDA track display and, in the absence of truth data, made it dicult to determine if any manoeuvring targets were present. A further complicating factor may have been the presence of crossing targets which is not within the capabilities of the current VDA agorithm. By comparison, the existing PDA-based tracker, developed by HFRD, was able to track the target manoeuvre in data sets 1 and 3, and produced similar output to the VDA tracker on data set 2.

7 Conclusions This report has dealt with the development of a manoeuvring target tracker based on the VDA algorithm. From investigations presented in [3, 4], three candidate manoeuvre detection methods and two tracking lters were singled out for possible inclusion in the VDA tracker during this phase of the work. All three manoeuvre detectors and both manoeuvre tracking lters have now been integrated into the VDA tracker software. The two-stage Kalman lter, although only brie y tested, appears to be sensitive to re-initialisation at the manoeuvre onset time. The MLWN lter does not suer from this drawback and is consequently more robust. Testing was carried out on both simulated and real data. The simulations scenarios chosen were S1 low PD target, high clutter, non-manoeuvring target; S2 low PD target, high clutter, manoeuvring target; S3 high PD target, low clutter, manoeuvring target; In addition, an investigation of the tracker's performance against manoeuvring targets with a range of radial decelerations was carried out for scenario S2. At high probability of target detection with low clutter (S3), a manoeuvre detector window length of 2 dwells was found to be sucient. At low PD (S2), a window length of 3 dwells was required for adequate performance. It appears therefore that 3 dwells of ARDS data per region need to be stored in order to track manoeuvring targets in the VDA framework. The computational burden imposed by backtracking and reprocessing of the previous dwell data over the window was found to be tolerable. Clearly, it is advantageous to keep the false alarm rate of the manoeuvre detector as low as possible. For the high PD , low clutter (idealistic) scenario S3, the VDA tracker was able to track the target in almost all simulation runs using any of the three manoeuvre detectors. The false alarm rate for this case was around 10%, with the trellis con dence drop detector providing the most reliable manoeuvre detection for the small number of Monte Carlo runs considered. In the more realistic low PD , high clutter case, the false alarm rate against a non-manoeuvring target (scenario S1) was found to be in the vicinity of 50% for all three manoeuvre detectors, 24

with the trellis con dence drop detector having the highest false alarm rate. The relatively small number of simulations carried out so far was not considered adequate to to rank the three detectors; however, the trellis con dence drop detector is arguably the least reliable of the three since factors other than a target manoeuvre can cause it to be triggered. For the realistic manoeuvring target scenario S2, the missed measurement node and trellis con dence drop detectors had the best performance and maintained track in around 40% of cases. However, the Doppler bias detector has considerable room for improvement in its manoeuvre detection rate while retaining the best false alarm rate (see section 4.4), and should be able to compete with the other two detectors. Under all three manoeuvre detectors, the VDA tracker was capable of maintaining track on a manoeuvring target in scenario S2 for radial decelerations of up to 0:003 km=s2 . Tracker performance for accelerations outside this range was not considered. The tracker was tested on 4 real data sets. The VDA tracker provided adequate performance in tests 1 and 3, compared with the current HFRD tracker. In test 1, the manoeuvre was so slight that it could be tracked with a constant-velocity lter. In test 3, the target was not detected during the manoeuvre so that the track was lost and then reacquired after the manoeuvre. In test 2, the target manoeuvre occurred within the algorithm's con rmation delay which precluded detection of the manoeuvre. Test 4 was inconclusive due to the large number of tracks produced and the diculty in establishing the presence of a clear manoeuvring target track in the absence of truth data. It is hoped that more suitable data will be obtained for testing during the next phase of the work.

8 Further Work The current implementation of the VDA tracker presented herein gives adequate performance for slowly manoeuvring targets in typical OTHR environments. However, several issues remain to be investigated. While these have not been treated in this phase of the project, they may lead to enhanced performance.

 The two-stage Kalman lter for manoeuvring target tracking: the sensitivity to re-initialisation

at the estimated manoeuvre onset time requires further investigation.  Retention of the constant-velocity trellis when a manoeuvre is declared. This should be used as a backup in case of a false alarm in the manoeuvre detector. If the constant-velocity assumption is incorrect, the trellis should be deleted naturally [6].  More re ned manoeuvre termination tests should be implemented. The current test assumes a maximum manoeuvre duration after which the tracking lter is switched from manoeuvring mode to constant-velocity mode. Accurate estimation of manoeuvre termination time is important as tracking errors are generally greater when the manoeuvring lter is in use. Testing for manoeuvre termination can be implemented easily using significance testing of acceleration estimates or changes in Doppler.  While the false alarm rate for the Doppler bias detector is low, its manoeuvre detection performance in low PD can be greatly enhanced using M/N logic of the type described at the end of section 4.4. The added computational burden would be minimal. 25

There is also considerable scope to enhance the ease of operation of the current implementation of the VDA tracker. These developments are not necessary to the completion of the current contract, but we list them here for completeness. Some of these items may be dealt with in the nal phase of the contract along with the main objective of multiple region tracking.

 The tracker must ensure continuity of tracks that cross region boundaries. A further level    

of track database management is required when the radar is performing multiple tasks, each involving multiple regions. There may be overlap between these tasks and this should be taken into account during the tracking. The replica track deletion logic should be improved. The current version considers only correlation in the most recent state estimate and it is possible that one track in a pair of crossing tracks could be deleted. Correlation over the last few dwells would be a more accurate indicator of duplicate tracks. Target speed and heading information should be calculated from the estimated range rate and azimuth rate and stored in the track structure. More data adaptivity should be introduced into the algorithm to give increased robustness of tracking performance on varying data sets. Ways of selecting parameters that require manual tuning, such as target PD , trellis maintenance thresholds etc., could be looked into. This would require a thorough investigation of tracker performance characteritics. Many enhancements to the VDA tracker output displays are possible. Menu-driven display windows for track editing would make examination of the track database more convenient and aid performance evaluation.

Acknowledgements This work was funded jointly by the Cooperative Research Centre for Sensor Signal and Information Processing (CSSIP) and the Defence Science and Technology Organisation (DSTO), Australia, under DSTO contract number 476189. Mr Efstratios (Stan) Ska das of the University of Melbourne is acknowledged for his assistance in the software development for this phase of the project. The authors also wish to thank Mr Steve Tucker, Dr Branko Ristic and Dr Bren Colegrove of High Frequency Radar Division, DSTO, for the provision of real data and for helpful discussions during the course of this work.

26

References [1] G. W. Pulford, and B. F. La Scala. \Over-The-Horizon Radar Tracking Using The Viterbi Algorithm - Second Report to High Frequency Radar Division", CSSIP Report No. 16/95, Adelaide, August 1995. [2] G. W. Pulford, and B. F. La Scala. \Over-The-Horizon Radar Tracking Using The Viterbi Algorithm - Third Report to High Frequency Radar Division", CSSIP Report No. 27/95, Adelaide, December 1995. [3] G. W. Pulford and B. F. La Scala. \A Survey of Manoeuvring Target Tracking Methods and their Applicability to Over-The-Horizon Radar", CSSIP Report No. 14/96 to High Frequency Radar Division, July 1996. [4] B. F. La Scala and G. W. Pulford. \An Analysis of Manoeuvring Target Detectors and Trackers for Over-The-Horizon Radar", CSSIP Report No. 29/96 to High Frequency Radar Division, Nov. 1996. [5] B. F. La Scala and G. W. Pulford. \Software Speci cation for the Viterbi Data Association Tracker for OTHR", CSSIP Report No. 12/96 to High Frequency Radar Division, May 1996. [6] Y. Bar-Shalom, and T. E. Fortmann. Tracking and Data Association, Academic Press, 1988.

27

Appendix 1: Usage of VDA Tracker Program Data Generation The Unix commands for compiling and running the data generation program are given below. make gend gend param_file data_file truth_file

where param file is the input le containing the target and clutter parameters (as given in Appendix 4), data file is the output le for the simulated ARDS data and truth file is the output le containing the true target state values.

VDA Tracker The Unix commands for compiling and running the VDA tracker program are given below. 1. make vda 2. vda param_file data_file

where param file is one of the following tracker parameter les: params drop, params dummy or params dbias, and data file is a le containing either simulated or real ARDS data in the form speci ed in [5]. The format of the three parameter les is given in Appendix 4.

Appendix 2: Make le Options The following compilation options are de ned for the VDA tracker program. Note that only one manoeuvre detector -DDUMMY, -DDROP, -DBIAS or -DDBIAS may be chosen at a time, and one manoeuvre tracking lter -DMLWN or -DTSKF. A manoeuvre tracking lter must be included if a manoeuvre detector is used.

 -DSNR: includes SNR measurement in transition cost calculations. Appears to degrade      

algorithm performance. -DDUMMY: manoeuvre detection using the missed measurement node method. -DDROP: manoeuvre detection using the trellis con dence drop method. -DBIAS: ARD innovations-based manoeuvre detector. -DDBIAS: manoeuvre detection using revised Doppler bias method. -DMLWN: use Multi-Level White Noise lter for manoeuvre tracking. -DTSKF: use Two-Stage Kalman Filter for manoeuvre tracking.

28

Appendix 3: MatlabTM Tracker Output Display The following commands may be used within MatlabTM to display and manipulate the VDA tracker output le.



rtrackf('track file', num dwells) - read the VDA tracker output a period of num dwells dwells. Returns 1 if le read successfully.



rtruthf('truth file', num tracks, num dwells) - read the true track le truth file generated by gend which contains num tracks target tracks over a period of num dwells

   

le track file for

dwells. Returns 1 if le read successfully. dog - make all variables global for subsequent routines. qadplot - produce slant range-azimuth (coverage) display of tracker output and truth (if available). Individual track state estimates and con dence plots can be viewed by clicking on the desired track label. Plots may be zoomed in or out (Matlab feature). rshort(n) - removes tracks shorter than n dwells. rdummy(p) - removes tracks containing greater than p % dummy (missed measurement) nodes.

Track Notation and Numbering Tracks within one region are given a unique number. This number identi es the time the track was initiated, the corresponding Doppler bin and whether the track is from an in-bound, outbound or stationary target. Track tags are of the form TTDBB where:

TT is the time (dwell) the track was initiated D is the Doppler bin BB is 73 for an in-bound target, 79 for an out-bound target and 83 for a stationary target. In addition, the following symbols are used for the track coverage display. |] = inbound target track |[ = outbound target track |o = stationary target

29

Appendix 4: Samples of Parameter Files Data Generation Parameter File Random number seed = -101 Number of dwells = 50 Minimum time between revisits = 20.0 Maximum time between revisits = 20.0 Number of regions = 1 Region number = 1 Avg number of clutter points = 100 Noise limiting factor = 2 Slant range range = 1000.0 1600.0 Doppler range = 0 0.3 Apparent azimuth range = 0.0 10.0 Max unambiguous doppler value = 0.3 Range resolution = 20.0 Doppler resolution = 0.005 Azimuth resolution = 0.5 Expected clutter power = 7.0 Noise floor = 8.0 Number of targets = 2 Initial state = 1100.0 0.1 0.0 2.0 0.0 0.0 22.0 Signal model measurement variance = 100.0 6.25e-6 0.25 Signal model process variance = 0.0 0.0 Expected SNR value = 22.0 Target initiates at dwell 0 Target terminates at dwell 49 Velocity ambiguity flag = 0 /* Stationary target */ Manoeuvre type = 0 /* Constant velocity */ Initial state = 1500.0 0.3 0.0 0.5 0.008 0.0 8.0 Signal model measurement variance = 100.0 6.25e-6 0.25 Signal model process variance = 0.0 0.0 Expected SNR value = 8.0 Target initiates at dwell 0 Target terminates at dwell 49 Velocity ambiguity flag = -1 /* Inbound target */ Manoeuvre type = 1 /* Constant acceleration */ Acceleration in range = 0.001 Acceleration in azimuth = 0.0 Manoeuvre starts at dwell 30 Manoeuvre ends at dwell 32 Region number 1 Probability of detection for target 0 = 0.980291 Probability of detection for target 1 = 0.606531

30

Parameter File for Trellis Con dence Drop Detector Number of regions = 1 Region number = 1 Probability of detection = 0.8 Initial prob of existence = 0.5 Delta_0 = 0.8 Delta_1 = 0.2 Gate probability = 0.99 Gate limit = 11.3 Alpha = 0.99 Measurement covariance matrix scaling factor = 0.25 SNR measurement noise variance = 1.0 Process noise variances = 1.0e-8 1.0e-8 1.0e-8 Initial state error covariance scaling factor = 1.0 Process noise inflation factor in range = 500.0 Process noise inflation factor in azimuth = 10.0 Assumed maximum manoeuvre length = 6 Confirmation delay = 4 Data window length = 3 Number of doppler bins = 3 Track deletion threshold = 0.05 Trellis confirmation threshold = 0.6 Trellis deletion threshold = 0.1 Manoeuvre detection threshold = 0.3 Critical point for new track decision = 20.0 Interactive or batch mode = 1

Parameter File for Missed Measurement Node Detector Number of regions = 1 Region number = 1 Probability of detection = 0.8 Initial prob of existence = 0.5 Delta_0 = 0.8 Delta_1 = 0.2 Gate probability = 0.99 Gate limit = 11.3 Alpha = 0.99 Measurement covariance matrix scaling factor = 0.25 SNR measurement noise variance = 1.0 Process noise variances = 1.0e-8 1.0e-8 1.0e-8 Initial state error covariance scaling factor = 1.0 Manoeuvre gate factor = 4.0 Process noise inflation factor in range = 500.0 Process noise inflation factor in azimuth = 2.0 Assumed maximum manoeuvre length = 6

31

Confirmation delay = 4 Data window length = 3 Number of doppler bins = 5 Track deletion threshold = 0.05 Trellis confirmation threshold = 0.6 Trellis deletion threshold = 0.1 Critical point for new track decision = 20.0 Interactive or batch mode = 1

Parameter File for Doppler Bias Detector Number of regions = 1 Region number = 1 Probability of detection = 0.8 Initial prob of existence = 0.5 Delta_0 = 0.8 Delta_1 = 0.2 Gate probability = 0.99 Gate limit = 11.3 Alpha = 0.99 Measurement covariance matrix scaling factor = 0.25 SNR measurement noise variance = 1.0 Process noise variances = 1.0e-8 1.0e-8 1.0e-8 Initial state error covariance scaling factor = 1.0 Manoeuvre gate factor = 4.0 Process noise inflation factor in range = 500.0 Process noise inflation factor in azimuth = 2.0 Assumed maximum manoeuvre length = 6 Confirmation delay = 4 Data window length = 3 Number of doppler bins = 5 Track deletion threshold = 0.05 Trellis confirmation threshold = 0.6 Trellis deletion threshold = 0.1 Manoeuvre detection threshold = 3.8 Critical point for new track decision = 20.0 Interactive or batch mode = 1

32

DISTRIBUTION LIST CSSIP 1. Dr Barbara La Scala 2. Dr Graham Pulford 3. CSSIP Library (2 copies)

HFRD DSTO 1. Mr Steve Tucker 2. Dr Branko Ristic 3. Dr Bren Colegrove

33