Distributed versus Centralised Tracking in Networked Anti-Submarine Warfare J. M. Thredgold and M. P. Fewell Maritime Operations Division Defence Science and Technology Organisation DSTO-TR-2373 ABSTRACT This report describes a study of active sonar tracking, which explores the effect of networking sonars on tracking performance. We compare the tracking performance when sonars share detections (centralised tracking) with the performance when sonars share tracks (distributed tracking). Provided that the sonar layout and detection probabilities are such that multiple sonars have a reasonable probability (~30%) of obtaining detections from a target, we show that centralised tracking decreases the time to confirm a track on a target and improves the continuity of the target track. These improvements in target tracking occur at the expense of an increase in false track rate. RELEASE LIMITATION Approved for public release Published by Maritime Operations Division DSTO Defence Science and Technology Organisation PO Box 1500 Edinburgh South Australia 5111 Australia Telephone: (08) 8259 5555 Fax: (08) 8259 6567 © Commonwealth of Australia 2010 AR-014-687 January 2010 APPROVED FOR PUBLIC RELEASE Distributed versus Centralised Tracking in Networked Anti-Submarine Warfare Executive Summary A previous report (DSTO-TR-2086) suggests that appropriate networking of sonars may be able to make significant inroads on the problem of submarine detection. Of the many assumptions in this simple analytical approach, the avoidance of the issue of false alarms is perhaps the most serious. The present report seeks to address this by comparing distributed and centralised tracking in a scenario that explicitly includes false detections at a rate that leads to false tracks. We compare tracking performance when sonars share detections (centralised tracking) with the performance when sonars share tracks (distributed tracking). The model builds on the earlier analytical work, which found that detection probabilities as low as 30% could be useful for track initiation, if there was a network of sonars such that these detections could be shared with other sonars with similar probabilities of detection. The simulation model used for the analysis in this report was developed in order to see if this networking advantage carries through to other stages of the tracking process. The simulation model is documented in a separate report (DSTO-TR-2372). Using this model, we show that centralised tracking decreases the time to confirm a track on a target and can also improve the continuity of the target tracks. These improvements in target tracking occur at the expense of an increase in false track rate. The majority of false tracks formed by the centralised tracker have similar characteristics to tracks formed by distributed tracking, and so are not more difficult to identify as false tracks. Classifying tracks by length alone, centralised tracking results in a small increase in the number of false tracks wrongly classified as potential targets (from 7 to 11%) but this is offset by the decrease (from 33 to 26%) in the number of target tracks which fail to be identified as such. These results indicate the potential for false detections and false tracks to cause difficulties when sonar systems are networked. It points to a need to improve detection classification techniques if networking is to achieve its full potential in anti-submarine warfare. Authors J.M. Thredgold Maritime Operations Division Jane Thredgold commenced working in the Maritime Operations Division at DSTO in early 2007, after completing a PhD in Mathematics at the University of South Australia. She is currently performing operations analysis work relevant to anti-submarine warfare. ____________________ ________________________________________________ M.P. Fewell Maritime Operations Division Matthew Fewell joined DSTO in 2001, coming from an academic physics background. He has worked and published in experimental nuclear structure physics, gaseous electronics, atom–photon interactions including coherent effects, laser physics, plasma processing of materials, the theory of network-centric warfare and its modelling at the operational level (including cognitive issues), human-in-the-loop experimentation, and weapon–target allocation in ship air defence. He is at present working on issues in anti-submarine warfare from surface-ship and maritime-patrol perspectives. ____________________ ________________________________________________ Contents VARIABLES 1. INTRODUCTION...............................................................................................................1 2. STUDY METHOD..............................................................................................................2 2.1 Summary of the Simulation Model.......................................................................2 2.2 Data Fusion................................................................................................................3 2.3 Scenario.......................................................................................................................4 2.4 Tracking Assessment Method................................................................................5 2.4.1 Track Classification Schemes.................................................................5 2.4.2 Metrics.......................................................................................................6 2.4.3 Track Coalescence...................................................................................7 3. COMPARISON OF CENTRALISED AND DISTRIBUTED TRACKING..............8 3.1 Simulation Results...................................................................................................8 3.1.1 Track Establishment Delay....................................................................8 3.1.2 Number of False Tracks..........................................................................9 3.1.3 Length of False Tracks..........................................................................10 3.1.4 Length of Target Tracks........................................................................11 3.1.5 Number of Tracks Occurring at Each Time Step during a Simulation Run......................................................................................12 3.1.6 System Confusion Matrix.....................................................................13 3.2 False Track Behaviour............................................................................................14 4. SUMMARY AND CONCLUSIONS..............................................................................18 5. REFERENCES....................................................................................................................20 Variables L track classification length threshold P probability of detection per ensonification d P probability of a false detection fa P probability of false track initiation per 5 consecutive fti ensonifications  DSTO-TR-2373 1. Introduction The prevailing paradigm governing concepts of command and control — network-centric warfare [1,2] — makes it natural to look to networking for solutions to the antisubmarine- warfare (ASW) problem [3]. In a previous report [4], we described some analytical studies comparing the ASW effectiveness of forming tracks on detections from a group of sonars (centralised tracking) with the case where each individual sonar forms tracks using only its own detections (distributed tracking). This report describes a further study of the problem, motivated by limitations arising from some of the assumptions made in the earlier analytical work. The previous work focussed on track initiation. Results from this analytical study indicated that networking sonars increases the area in which we can reasonably expect to start a track on a target, with the greatest networking benefits seen when the sonar probability of detection (P ) versus range curves have long tails of low, but not too low, probability (P ~ 0.3). d d However the approach taken in the previous work did not consider measurement errors or the effect of false detections, nor the resulting difficulties in associating a detection with other detections to form tracks. In the analytic work, we assumed that, if the target is detected three times in five pings, then we always start a track. In reality this may not always occur, as measurement errors mean that the detections may not be close enough together or a false detection may interfere with the track formation process by confusing the picture. In short, the analytical study doesn’t give sufficient consideration to the issue of data association. Also the significant issue of the increased false track rate arising from centralised tracking was ignored. The previous work included an analytical study of false-detection rate in the centralised case. However this study was inconclusive and did not address at all the issue of the false detections leading to false tracks. Because of these shortcomings, a simulation model was designed and implemented to address these issues. The model is described in detail in a companion paper [5]. It allows us to investigate the impact of measurement errors and false detections on ASW effectiveness. The false (i.e. non-target) detections in the model are assumed to be ‘noise’ detections which are not associated with any nearby real object. The presence of recurrent clutter type detections which result from objects, such as bottom features or fish schools, is a separate issue that is not addressed in this report. The simulation model includes data association, track maintenance and track termination, not just the track initiation step. Section 2 of this report describes the analytical method adopted for the study and Section 3 gives results, including some analysis of how the number of sensors in the network and the probability of a false detection affect the false track rate. 1 DSTO-TR-2373 2. Study Method The aim of the study is to examine the extent to which the conclusions of the earlier analytical study [4] stand up to the inclusion of false detections and measurement errors. This was approached by constructing a simulation model explicitly including these features. The model is summarised in Section 2.1; details appear elsewhere [5]. Compared with an analytical study, a simulation-based study has the disadvantage that it must work with a physical scenario, leading to the potential criticism that the results are scenario-specific. This criticism is difficult to counter, short of running many different scenarios. Our approach is to choose a scenario that represents a generic ASW task, as described in Section 2.3. We choose the simplest (from the modelling point of view) of the four generic ASW scenarios [6], open-ocean transit. The conclusions of an operations-research study can be strongly influenced by the metrics chosen. The earlier analytical work [4] examined a range of metrics, none of which are well adapted to analysis of scenarios with false alarms. Since the present work is exploratory, we decided that its main thrust would involve a comparison of tracking metrics. The metrics chosen, detailed in Section 2.4.2, were based on metrics used in the surveillance-radar domain [7]. 2.1 Summary of the Simulation Model Given a scenario, such as that described in Section 2.3 below, the elements that define the model can be grouped under the following topics:  type and operation of the sonars modelled  model of sonar performance  manner in which target and false detections are generated  method of initiating a track  how to decide whether a detection should be associated with an existing track  the tracking algorithm  track termination These are summarised in the following paragraphs. Full details are given in a companion report [5]. Since our interest is not in improving tracker performance but rather in comparing ASW effectiveness when tracking is performed centrally as opposed to fusing the tracks from individual sonars, we use standard algorithms for tracking and data association. We model a field of active sonars with multiple monostatic operation. The performance of the modelled sonars is defined by probability of detection versus range curves, with no bearing or depth dependence. For simplicity and ease of comparison with the analytical study, and to keep the modelling unclassified, in the work reported here we use exponential functions as the probability of detection versus range curves. Whether or not a sonar ping produces a target detection is determined by a draw from a uniform random distribution compared with the detection probability at the relevant range. If the target is detected, then the recorded position is generated using additional random numbers to introduce measurement error. Measurement errors have a zero-mean bivariate normal distribution in range and bearing. The covariance matrix of the errors is set so that the 2 DSTO-TR-2373 standard deviations correspond to the Cramér–Rao lower bound [8], approximately 1 metre in range and 2.5° in bearing. The false detections generated differ for each run of the simulation. The number of false detections occurring at each ping is drawn from a Poisson distribution with the expected value depending on the probability P of a false detection per range–bearing cell per ping set fa by the user. In practice an operator who is concerned by a high false alarm rate would raise the detection threshold (hence decreasing the probability P of a false detection) to reduce the fa number of tracks they need to consider. One option in our simulation model would be to make the false track rates with the two different tracking options equal by adjusting the probability of obtaining a false detection. However we have not done this, as we preferred to keep the detection lists passed to the trackers identical for the two tracking options. We used P = 10–5 with the scenario described in Section 2.3 below to give the results presented in fa Section 3. The track-initiation rule specifies three detections in five consecutive pings of the active-sonar field. False detections and measurement errors complicate the application of this rule: we require a way of deciding whether a detection ought to be associated with an existing track, or whether it is a candidate for forming a new track. For this, we use Mahalanobis distance [9] from the detection to the current track position. We require this distance to be small enough that there is a 95% probability of the detection being a target detection. Where more than one detection fulfils this criterion, we pick the one with the smallest distance. This is done with each existing track, which means that a detection might be associated with more than one track. After all tracks have been processed, any detection that is not associated with an existing track is considered as a potential source of a new track. Given an isolated detection, the algorithm will search for a second detection within the next three time steps using an expanding, almost square, gate centred on the initial detection. The size of the gate is primarily determined by the length of time elapsed since the initial detection and the maximum relative velocity with which it is estimated potential targets could be travelling. The tracking algorithm used is relatively simple as our interest is not in improving tracker performance but in comparing the tracks produced when tracking is performed centrally with those obtained by fusing the tracks from individual sonars. We use a standard Kalman filter [10]. The 3-in-5 rule is used not only for track initiation, but also for track maintenance and termination. 2.2 Data Fusion Within each simulation run the same detections (both target and false) are used by the two tracking options. The only difference is in how these detections are processed to form tracks, as described below. For centralised tracking, the detection lists from each sensor are combined and passed to the tracker as a single set. The combination rule is the equivalent of a simple logical ‘or’, except for the case where two detections occur at the same time very close to one another. Detections 3 DSTO-TR-2373 from two sonars are fused into a single detection if the Mahalanobis distance between them is consistent with zero at the 95% confidence level. For distributed tracking, the tracking algorithm is applied separately to the detections recorded by each sensor. The tracks are then fused into a single list. If two sensors are tracking the target at the same time, and the track position estimates are close enough together, the tracks will be fused into a single track. For example if sonar 1 has a track on the target from ping 10 to ping 14 and sonar 2 has a track on the target from ping 12 to ping 17, for analysis purposes this is regarded as a single track on the target from ping 10 to ping 17, as Figure 1 illustrates. Sensor 2 track Sensor 1 track Fused track 10 11 12 13 14 15 16 17 Ping number Figure 1: Illustration of track fusion for distributed tracking 2.3 Scenario The scenario used in this study is shown in Figure 2. This scenario comprises a network of three sonars. There is a single submarine target present. The positions of the sonars and the submarine at the beginning of the simulation are shown in the figure, together with their relative motion, which is constant throughout the simulation. If the sonars were hull mounted sonars attached to ships, then this scenario could be considered as representative of a task Red sub Relative velocity 30 11 m/s (21 kn) 40 km 30 km Blue task group (3 frigates) 5 km 10√3 km Figure 2: The positions of the three sensors and the submarine at the beginning of the simulation. The relative velocity is constant throughout the simulation. 4