Sabino Gadaleta

Batch Maximum Likelihood (ML) and Maximum A Posteriori (MAP) estimation with process noise for tracking applications

Batch maximum likelihood (ML) and maximum a posteriori (MAP) estimation with process noise is now more than thirty-five years old, and its use in multiple target tracking has long been considered to be too computationally intensive for real-time applications. While this may still be true for general usage, it is ideally suited for special needs such as bias estimation, track initiation and spawning, long-term prediction of track states, and state estimation during periods of rapidly changing target dynamics. In this paper, we examine the batch estimator formulation for several cases: nonlinear and linear models, with and without a prior state estimate (MAP vs. ML), and with and without process noise. For the nonlinear case, we show that a single pass of an extended Kalman smoother-filter over the data corresponds to a Gauss-Newton step of the corresponding nonlinear least-squares problem. Even the iterated extended Kalman filter can be viewed within this framework. For the linear case, we develop a compact least squares solution that can incorporate process noise and the prior state when available. With these new views on the batch approach, one may reconsider its usage in tracking because it provides a robust framework for the solution of the aforementioned problems. Finally, we provide some examples comparing linear batch initiation with and without process noise to show the value of the new approach.

Multiple hypothesis clustering and multiple frame assignment tracking

Tracking and initiating large numbers of closely spaced objects can pose significant real-time challenges to current state-of-the-art tracking systems. Cluster or group tracking has been suggested to reduce the computational complexity when closely spaced targets move with similar dynamical properties. While modern individual object tracking systems make association decisions over multiple frames of data, most cluster tracking systems make single-frame clustering decisions. In this paper we illustrate an extension of multiple frame assignment (MFA) individual object tracking to multiple frame cluster MFA tracking. In our approach, multiple single-frame clustering hypotheses are formed and the best clustering is selected over multiple frames of data. In recent work we formulated multiple frame cluster tracking assignment problems and demonstrated a single-frame cluster MFA tracking architecture. The work discussed in this paper extends the previous work and illustrates a multiple hypothesis clustering, multiple frame assignment (MHC-MFA), tracking system. We present simulations studies that motivate the benefits of the multiple frame cluster tracking approach over single-frame cluster tracking and discuss the computational efficiency of the multiple frame cluster tracking approach.

Hierarchical closely spaced object (CSO) resolution for IR sensor surveillance

The observation of closely-spaced objects using limited-resolution Infrared (IR) sensor systems can result in merged object measurements on the focal plane. These Unresolved Closely-Spaced Objects (UCSOs) can significantly hamper the performance of surveillance systems. Algorithms are desired which robustly resolve UCSO signals such that (1) the number of targets, (2) the target locations on the focal plane, (3) the uncertainty in the location estimates, and (4) the target intensity signals are correctly preserved in the resolution process. This paper presents a framework for obtaining UCSO resolution while meeting tracker real-time computing requirements by applying processing algorithms in a hierarchical fashion. Image restoration techniques, which are often quite cheap, will be applied first to help reduce noise and improve resolution of UCSO objects on the focal plane. The CLEAN algorithm, developed to restore images of point targets, is used for illustration. Then, when processor constraints allow, more intensive algorithms are applied to further resolve USCO objects. A novel pixel-cluster decomposition algorithm that uses a particle distribution representative of the pixel-cluster intensities to feed the Expectation Maximization (EM) is used in this work. We will present simulation studies that illustrate the capability of this framework to improve correct object count on the focal plane while meeting the four goals listed above. In the presence of processing time constraints, the hierarchical framework provides an interruptible mechanism which can satisfy real-time run-time constraints while improving tracking performance.

Multiple frame cluster tracking

Tracking large number of closely spaced objects is a challenging problem for any tracking system. In missile defense systems, countermeasures in the form of debris, chaff, spent fuel, and balloons can overwhelm tracking systems that track only individual objects. Thus, tracking these groups or clusters of objects followed by transitions to individual object tracking (if and when individual objects separate from the groups) is a necessary capability for a robust and real-time tracking system. The objectives of this paper are to describe the group tracking problem in the context of multiple frame target tracking and to formulate a general assignment problem for the multiple frame cluster/group tracking problem. The proposed approach forms multiple clustering hypotheses on each frame of data and base individual frame clustering decisions on the information from multiple frames of data in much the same way that MFA or MHT work for individual object tracking. The formulation of the assignment problem for resolved object tracking and candidate clustering methods for use in multiple frame cluster tracking are briefly reviewed. Then, three different formulations are presented for the combination of multiple clustering hypotheses on each frame of data and the multiple frame assignments of clusters between frames.

Short arc gating in multiple hypothesis tracking for space surveillance

Multiple hypothesis tracking methods are under development for space surveillance and one challenge is the accurate and timely orbit initiation from sets of uncorrelated optical observations. This paper develops gating methods for correlation of optical observations in space surveillance. A pair gate based on the concept of an admissible region is introduced. By implementing a hierarchy from fast, but coarse, to more expensive, but accurate gates, the number of hypotheses to be considered for initial orbit determination is reduced considerably. Simulation results demonstrate the effectiveness of the gating procedure, address gate parameter determination, and study the accuracy of initial orbits.

Pixel-cluster decomposition tracking for multiple IR-sensor surveillance

Tracking midcourse objects in multiple IR-sensor environments is a significant and difficult scientific problem that must be solved to provide a consistent set of tracks to discrimination. For IR sensors, the resolution is limited due to the geometry and distance from the sensors to the targets. Viewed on the focal plane for a single IR sensor, the targets appear to transition from an unresolved phase (merged measurements) involving pixel-clusters into a mostly resolved phase through a possibly long partially unresolved phase. What is more, targets can appear in different resolution phases at the same time for different sensors. These resolution problems make multi-sensor tracking most difficult. Considering a centralized multi-sensor tracking architecture we discuss robust methods for identification of merged measurements at the fusion node and develop a method for pixel-cluster decomposition that allows the tracking system to re-process focal-plane image data for improved tracking performance. The resulting system can avoid inconsistent measurement data at the fusion node. We then present a more general multiple hypothesis pixel-cluster decomposition approach based on finding k-best assignments and solving a number of

Multiple Hypothesis Correlation in Track-to-Track Fusion Management

n

Integration of IR sensor clutter rejection techniques with pixel cluster frame manipulation

-dimensional assignment problems over n frames to find a decomposition among several pixel-cluster decomposition hypotheses that best represents a frame of data based on the information from n frames of data.

Group assignment problem

Track to track fusion systems require a capability to perform track matching across the reporting sensors. In conditions where significant ambiguity exists, for example due to closely spaced objects, a simple single frame assignment algorithm can produce poor results. For measurement-to-track fusion this has long been recognized and sophisticated multiple hypothesis, multiple frame, data association methods considerably improve tracking performance in these challenging scenarios. The most successful of the multiple frame methods are multiple hypothesis tracking (MHT) and multiple frame assignments (MFA), which is formulated as a multidimensional assignment problem. The performance advantage of the multiple frame methods over the single frame methods follows from the ability to hold difficult decisions in abeyance until more information is available and the opportunity to change past decisions to improve current decisions. In this chapter, the multiple source track correlation and fusion problem is formulated as a multidimensional assignment problem. The computation of cost coefficients for the multiple frame correlation assignments is based on a novel batch MAP estimation approach. Based on the multidimensional assignments we introduce a novel multiple hypothesis track correlation approach that allows one to make robust track management decisions over multiple frames of data. The use of the proposed multiple hypothesis, multiple frame correlation system, is expected to improve the fusion system performance in scenarios where significant track assignment ambiguity exists. In the same way that multiple frame processing has shown improvements in the tracking performance in measurement-to-track fusion applications, we expect to achieve improvements in the track-to-track fusion problem.

Some assignment problems arising from multiple target tracking

Track initiation in dense clutter can result in severe algorithm runtime performance degradation, particularly when using advanced tracking algorithms such as the Multiple-Frame Assignment (MFA) tracker. This is due to the exponential growth in the number of initiation hypotheses to be considered as the initiation window length increases. However, longer track initiation windows produce significantly improved track association. In balancing the need for robust track initiation with real-world runtime constraints, several possible approaches might be considered. This paper discusses basic single and multiple-sensor infrared clutter rejection techniques, and then goes on to discuss integration of those techniques with a full measurement preprocessing stage suitable for use with pixel cluster decomposition and group tracking frameworks. Clutter rejection processing inherently overlaps the track initiation function; in both cases, candidate measurement sequences (arcs) are developed that then undergo some form of batch estimation. In considering clutter rejection at the same time as pixel processing, we note that uncertainty exists in the validity of the measurement (whether or not the measurement is of a clutter point or a true target), in the measurement state (position and intensity), and in the degree of resolution (whether a measurement represents one underlying object, or multiple). An integrated clutter rejection and pixel processing subsystem must take into account all of these processes in generating an accurate sequence of measurement frames, while minimizing the amount of unrejected clutter. We present a mechanism for combining clutter rejection with focal plane processing, and provide simulation results showing the impact of clutter processing on the runtime and tracking performance of a typical space-based infrared tracking system.