Edmund Førland Brekke

Tracking Small Targets in Heavy-Tailed Clutter Using Amplitude Information

Harbor surveillance above and below the sea surface depends on sensors such as surveillance radar and multibeam sonar. These sensors attempt to detect and track moderately observable targets such as small boats or human divers in environments which often are characterized by heavy-tailed backgrounds. Target tracking in heavy-tailed environments is challenging even for moderate signal-to-noise ratios (SNRs) due to the increased frequency of target-like outliers. A tracking method operating in such an environment should exploit as much of the data as possible to ensure robustness. Still, conventional tracking methods rely on kinematic measurements such as range, bearing, and Doppler only. The performance of the tracking method can be improved by using the backscattered signal strengths together with the kinematic measurements. This is done in the probabilistic data association filter with amplitude information (PDAFAI). We propose new conservative amplitude likelihoods for the PDAFAI with improved robustness compared to existing methods. The first likelihood works by incorporating the uncertainty of the background estimate. The second likelihood explicitly treats the background as heavy tailed using the -distribution. Extensive and realistic Monte Carlo simulations show that both our conservative likelihoods give significant reductions in track loss. Furthermore, we provide a quantitative evaluation of the difficulties encountered by tracking methods in heavy-tailed clutter. To the best of our knowledge, such an analysis does not yet exist in the open literature.

The Modified Riccati Equation for Amplitude-Aided Target Tracking in Heavy-Tailed Clutter

The performance of tracking methods can most often only be assessed by means of Monte-Carlo simulations. An exception to this rule is the popular probabilistic data association filter (PDAF), whose root mean square error (RMSE) can be predicted by means of the modified Riccati equation (MRE). To the best of our knowledge, the first treatment along these lines for the PDAF with amplitude information (PDAFAI) is presented here. We evaluate the MRE with amplitude information (AI) for the case of a Swerling I target in heavy-tailed, or more precisely K-distributed, background noise. The MRE can be used to determine an optimal nominal false alarm rate. To the best of our knowledge, the first systematic approach to the determination of false alarm rates in heavy-tailed clutter is presented here. In particular, it is indicated that the PDAFAI can safely operate in the presence of very abundant clutter, while the PDAF only can cope with limited amounts of clutter.

Tracking dim targets using integrated clutter estimation

In this paper we address the problem of detecting and tracking a single dim target in unknown background noise. Several methodologies have been developed for this problem, including track-before-detect (TBD) methods which work directly on unthresholded sensor data. The utilization of unthresholded data is essential when signal-to-noise ratio (SNR) is low, since the target amplitude may never be strong enough to exceed any reasonable threshold. Several problems arise when working with unthresholded data. Blurring and non-Gaussian noise can easily lead to very complicated likelihood expressions. The background noise also needs to be estimated. This estimate is a random variable due to the random nature of the background noise. We propose a recursive TBD method which estimates the background noise as part of its likelihood evaluation. The background noise is estimated by averaging over nearby sensor cells not affected by the target. The uncertainty of this estimate is taken into account by the likelihood evaluation, thereby yielding a more robust TBD method. The method is implemented using sequential Monte Carlo evaluation of the optimal Bayes equations, also known as particle filtering. Simulation results show how our method allows detection and tracking to be carried out in an uncertain environment where current recursive TBD methods fail.

The signal-to-noise ratio of human divers

A challenging problem in underwater acoustics is the detection and tracking of human divers. In order to assess the suitability of different tracking methods on this problem, an evaluation of the signal-to-noise ratio (SNR) is required.

A novel formulation of the Bayes recursion for single-cluster filtering

In this paper we address the problem of tracking several moving targets with a sensor whose location and orientation are uncertain. This is a generalization of the well-known problem of feature-based simultaneous localization and mapping (SLAM). It is also a generalization of multitarget tracking (MTT) in general, and related to sensor bias estimation. We address such problems from the perspective of finite set statistics (FISST) and point process theory, and develop general expressions for the posterior multiobject density, as represented by probability-generating functionals (p.g.fl.s). We discuss how this general solution relates to approximative solutions previously suggested in the literature, and we also discuss how the p.g.fl. should be defined for such problems. To the best of our knowledge, this is the first paper to outline a FISST-based treatment of explicit data association for SLAM and related problems.

Robust underwater obstacle detection and collision avoidance

A robust obstacle detection and avoidance system is essential for long term autonomy of autonomous underwater vehicles (AUVs). Forward looking sonars are usually used to detect and localize obstacles. However, high amounts of background noise and clutter present in underwater environments makes it difficult to detect obstacles reliably. Moreover, lack of GPS signals in underwater environments leads to poor localization of the AUV. This translates to uncertainty in the position of the obstacle relative to a global frame of reference. We propose an obstacle detection and avoidance algorithm for AUVs which differs from existing techniques in two aspects. First, we use a local occupancy grid that is attached to the body frame of the AUV, and not to the global frame in order to localize the obstacle accurately with respect to the AUV alone. Second, our technique adopts a probabilistic framework which makes use of probabilities of detection and false alarm to deal with the high amounts of noise and clutter present in the sonar data. This local probabilistic occupancy grid is used to extract potential obstacles which are then sent to the command and control (C2) system of the AUV. The C2 system checks for possible collision and carries out an evasive maneuver accordingly. Experiments are carried out to show the viability of the proposed algorithm.

Spatially indexed clustering for scalable tracking of remotely sensed drift ice

For operations in the Arctic, drift ice can be a major hazard. To be able to mitigate this, it is essential to know the position of viable threats. Many sensors can be employed, such as satellite Synthetic Aperture Radar (SAR), marine radar, air surveillance et cetera. At the core of the fusion of this sensor data is a Multi-Target Tracking (MTT) problem. This problem is studied in this paper through the implementation and application of the Multiple Hypothesis Tracking (MHT) algorithm. A major limiting factor in the application of multi-target tracking is scalability. A common method of handling the scaling is clustering, which separates the MHT filter into smaller independent parts. However, with growing scale, the association of sensor data to the “right” cluster can become resource intensive in itself. A method is explored, based on rectangular lower probability bounds, to efficiently index the clusters and compartmentalize the measurement update of the MHT. The method uses the bounding box of the lower probability bound of tracks and reports respectively, to perform an intersection lookup against the sensor field-of-view, efficiently selecting clusters of relevance. The method, as well as the MHT algorithm, has been implemented and published online under an open-source license. In this report, the implementation is described and tested on simulated data for statistics. Further, it is tested against data extracted from the polarimetric classification of ice using satellite imagery of the Arctic. Results show that computational speed improvements can be achieved, in comparison to the linear complexity of a naive search, but that comparable performance can be obtained using standard database lookups.

A multi-hypothesis solution to data association for the two-frame SLAM problem

We propose a multi-hypothesis solution to the simplified problem of simultaneous localization and mapping (SLAM) that arises when only two measurement frames are available. The proposed solution is obtained through direct evaluation of the posterior density as given by finite set statistics. We show that hypothesis probabilities can be evaluated within reasonable accuracy by means of a closed-form expression. Consistency properties are discussed extensively. We overcome inconsistency problems of the extended Kalman filter by means of natural gradient optimization, and we demonstrate through implementations on simulated and real data that the proposed approach has better consistency properties than alternative approaches when applied to the two-frame SLAM problem.

Improved Target Tracking in the Presence of Wakes

Tracking methods attempt to follow the movement of a target of interest while suppressing irrelevant clutter. A particularly troublesome source of clutter is wakes that appear behind the target. This problem arises in sonar tracking of human divers, in the tracking of boats using surveillance radars, and also in radar tracking of ballistic missiles. Previous research has integrated a solution to this problem in the popular probabilistic data association filter (PDAF). A new solution to this problem in the same framework is proposed here. While previous research has used an approach described as probabilistic editing, the new solution solves the wake problem in a Bayesian framework by means of marginalization. Monte-Carlo simulations show that the new solution provides significantly increased robustness as compared with both the standard PDAF and the probabilistic editing approach. As the new solution has improved theoretical underpinnings, we hope that it can be useful for further research on tracking in the presence of wake clutter.

AIS-based vessel trajectory prediction

In order for autonomous surface vessels (ASVs) to avoid collisions at sea it is necessary to predict the future trajectories of surrounding vessels. This paper investigate the use of historical automatic identification system (AIS) data to predict such trajectories. The availability of AIS data have steadily increased in the last years as a result of more regulations, together with wider coverage through AIS integration on satellites and more land based receivers. Several AIS-based methods for predicting vessel trajectories already exist. However, these prediction techniques tend to focus on time horizons in the level of hours. The prediction time of our interest typically ranges from a few minutes up to about 15 minutes, depending on the maneuverability of the ASV. This paper presents a novel datadriven approach which recursively use historical AIS data in the neighborhood of a predicted position to predict next position and time. Three course and speed prediction methods are compared for one time step predictions. Lastly, the algorithm is briefly tested for multiple time steps in curved environments and shows good potential.