Association and fusion of passive direction finding (DF) reports with active radar tracks from airborne targets is challenging
because of the low dimensionality of the common kinematic measurement space. Often, multi-target scenarios lead to
significant data association ambiguity. Classically, the approach to this problem is a simple hypothesis test wherein a
batch of DF sensor measurements is associated with either zero or one of the radar tracks; assignment of multiple DF
tracks to a single radar track is allowed without regard to compatibility, and this can lead to detrimental results. This
paper develops a new approach for managing the ambiguity. The problem is formulated as a two-dimensional assignment,
and any association ambiguity is determined from the k best solutions. Firm association decisions are made only when
the ambiguity is at an acceptable level. The ambiguity information is also available in real time as an output to the
system operator. An improved batch association score, relative to previous works, is formulated that addresses statistical
correlations between individual measurement-to-track residuals; this new score is a likelihood ratio generated from Kalman
Filter residuals. Where previous scoring methods lead to incorrect ambiguity assessments in certain scenarios, the new
approach yields accurate results. Because the score is recursive, the batch may be extended over an arbitrary number of
measurements, helping to manage association ambiguities over time. Simulation results are shown to demonstrate the
Most modern maximum likelihood multiple target tracking systems (e.g., Multiple Hypothesis Tracking (MHT) and Numerica's
Multiple Frame Assignment (MFA)) need to determine how to separate their input measurements into subsets
corresponding to the observations of individual targets. These observation sets form the tracks of the system, and the
process of determining these sets is known as data association. Real-time constraints frequently force the use of only the
maximum likelihood choice for data association (over some time window), although alternative data association choices
may have been considered in the process of choosing the most likely.
This paper presents a Tracker Adjunct Processing (TAP) system that captures and manages the uncertainty encountered
in making data association decisions. The TAP combines input observation data and the data association alternatives
considered by the tracker into a dynamic Bayesian network (DBN). The network efficiently represents the combined
alternative tracking hypotheses. Bayesian network evidence propagation methods are used to update the network in light of
new evidence, which may consist of new observations, new alternative data associations, newly received late observations,
hypothetical connections, or other flexible queries. The maximum likelihood tracking hypothesis can then be redetermined,
which may result in changes to the best tracking hypothesis. The recommended changes can then be communicated back
to the associated tracking system, which can then update its tracks. In this manner, the TAP's interpretation makes the firm,
fixed (formerly maximum likelihood) decisions of the tracker "softer," i.e., less absolute. The TAP can also assess (and
reassess) track purity regions by ambiguity level.
We illustrate the working of the TAP with several examples, one in particular showing the incorporation of critical, late
or infrequent data. These data are critical in the sense that they are very valuable in resolving ambiguities in tracking and
combat identification; thus, the motivation to use these data is high even though there are complexities in applying it. Some
data may be late because of significant network delays, while other data may be infrequently reported because they come
from "specialized" sensors that provide updates only every once in a while.
In non-monopulse mechanically scanned surveillance radars, each
target can be detected multiple times as the beam is scanned across
the target. To prevent redundant reports of the object, a centroid
processing algorithm is used to associate and fuse multiple
detections, called primitives, into a single object measurement. At
the 2001 SPIE conference,<sup>1</sup> Part I of this paper was
presented wherein a new recursive least squares algorithm was
derived that produces a single range-bearing centroid estimate. In
this Part II paper, the problem is revisited to address one
important aspect not previously considered. We develop a new
algorithm component that will parse merged measurements that result
from the presence of closely-spaced targets. The technique uses
tracker feedback to identify the number of constituents in which to
decompose the identified merged measurement. The algorithm has two
components: one is a decomposition group formation algorithm, and
the second is the expectation-maximization based centroid
decomposition algorithm. Simulation results are presented that show
the algorithm improves tracker completeness as well as measurement
accuracy in scenarios with closely spaced objects.
The MHT/MFA approach to tracking has been shown to have significant advantages compared to single frame methods.
This is especially the case for dense scenarios where there are many targets and/or significant clutter. However, the data
association problem for such scenarios can become computationally prohibitive. To make the problem manageable, one
needs effective complexity reduction methods to reduce the number of possible associations that the data association algorithm
must consider. At the 2005 SPIE conference, Part I of this paper<sup>1</sup> was presented wherein a number of "gating
algorithms" used for complexity reduction were derived. These included bin gates, coarse pair and triple gates, and multiframe
gates. In this Part II paper, we provide new results that include additional gating methods, describe a hierarchical
framework for the integration of gates, and show simulation results that demonstrate a greater than 95% effectiveness at
removing clutter from the tracking problem.
Advanced tracking algorithms such as multiple frame assignment (MFA) and multiple hypothesis tracking (MHT) require the formation of a "frame of data" to input measurements into the tracking system. A "frame" is a collection of measurements in which a target should appear at most once. For some sensor types, the frame definition is straightforward: all measurements in "one scan" of the antenna across the surveillance area compose a frame of data. However, for electronically scanned array (ESA) radar, the beam pointing is agile and the radar may point the beam in a sequence of overlapping positions. If the data from the sequence of dwells are merged into one frame, duplicate measurements may result from targets in the overlap regions. But restricting each frame to be one dwell has negative consequences because it causes an incomplete representation of closely-spaced targets within each frame. This paper presents a new algorithm for the formation of frames of data for ESA radar systems. The algorithm uses a series of gating tests to determine which radar dwells may be merged together. For overlapping beams, a selection technique is developed that minimizes the number of redundant measurements that appear in any given frame. A summary of tracking performance results attained when using the algorithm is provided.
Most approaches to data association in target tracking use a likelihood-ratio based score for measurement-to-track and track-to-track matching. The classical approach uses a likelihood ratio based on <i>kinematic</i> data. Feature-aided tracking uses <i>non-kinematic</i> data to produce an "auxiliary score" that augments the kinematic score. This paper develops a nonkinematic likelihood ratio score based on statistical models for the signal-to-noise (SNR) and radar cross section (RCS) for use in narrowband radar tracking. The formulation requires an estimate of the target mean RCS, and a key challenge is the tracking of the mean RCS through significant "jumps" due to aspect dependencies. A novel multiple model approach is used track through the RCS jumps. Three solution are developed: one based on an α-filter, a second based on the median filter, and the third based on an IMM filter with a median pre-filter. Simulation results are presented that show the effectiveness of the multiple model approach for tracking through RCS transitions due to aspect-angle changes.
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.
Proc. SPIE. 5204, Signal and Data Processing of Small Targets 2003
KEYWORDS: Signal to noise ratio, Infrared sensors, Point spread functions, Detection and tracking algorithms, Sensors, Particles, Image resolution, Monte Carlo methods, Optical resolution, Expectation maximization algorithms
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 <i>k</i>-best assignments and solving a number of $n$-dimensional assignment problems over <i>n</i> frames to find a decomposition among several pixel-cluster decomposition hypotheses that best represents a frame of data based on the information from <i>n</i>
frames of data.
Batch <i>maximum likelihood</i> (ML) and <i>maximum a posteriori</i> (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.
Proc. SPIE. 5204, Signal and Data Processing of Small Targets 2003
KEYWORDS: Target detection, Radar, Signal to noise ratio, Switches, Detection and tracking algorithms, Computer simulations, Data processing, Signal processing, Algorithm development, Radar signal processing
Electronically scanned narrowband radar systems detect non-extended targets in one or two range cells depending on whether the object straddles the range cell boundary. For two detections, the range estimate may be refined using a fusion process. However, for scenarios with multiple closely spaced objects ambiguity exists in how many objects are present and how the range cells should be paired to produce the refined estimates. In this paper, we present a new algorithm that first segments the primitive radar measurements, and second fuses paired measurements to produce object reports used by a tracking system. The segmentation algorithm is developed by forming a hypothesis partition model for a set of consecutive range cells with detections, and then evaluating the joint likelihood function for each feasible partition of the cells into pairs or singletons. Simulation results that demonstrate the utility of the algorithm are provided using a modern missile tracking simulation environment.
Proc. SPIE. 4728, Signal and Data Processing of Small Targets 2002
KEYWORDS: Target detection, Radar, Signal to noise ratio, Detection and tracking algorithms, Scattering, Data processing, Missiles, Algorithm development, Expectation maximization algorithms, Data fusion
This paper develops a new algorithm for high range resolution (HRR) radar centroid processing for scenarios where there are closely spaced objects. For range distributed targets with multiple discrete scatterers, HRR radars will receive detections across multiple range bins. When the resolution is very high, and the target has significant extent, then it is likely that the detections will not occur in adjacent bins. For target tracking purposes, the multiple detections must be grouped and fused to create a single object report and a range centroid estimate is computed since the detections are range distributed. With discrete scatterer separated by multiple range bins, then when closely spaced objects are present there is uncertainty about which detections should be grouped together for fusion. This paper applies the EM algorithm to form a recursive measurement fusion algorithm that segments the data into object clusters while simultaneously forming a range centroid estimate with refined bearing and elevation estimates.
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.
In non-monopulse mechanically scanned surveillance radars, each target can be detected multiple times as the beam is scanned across the target. To prevent redundant reports of the object, a centroid processing algorithm is used to associate and cluster the multiple detections, called primitives, into a single object measurement. This paper reviews several techniques for centroid processing, and presents a new center of mass algorithm that is implemented with the recursive least squares algorithm. The new algorithm has a unique gating process to enable the primitive measurement association. Simulation results of the new algorithm are reported. Multiple object merged measurement handling issues within the centroid processing context are discussed.
Proc. SPIE. 4048, Signal and Data Processing of Small Targets 2000
KEYWORDS: Target detection, Radar, Signal to noise ratio, Detection and tracking algorithms, Monte Carlo methods, Electronic filtering, Algorithm development, Performance modeling, Systems modeling, Data fusion
In a previous paper, the authors proposed a new general and systematic electronic counter-countermeasure (ECCM) technique called the Decomposition and Fusion (D&F) approach. This ECCM is implemented within the multiple target-tracking framework for protection against range- gate-pull-off (RGPO) and range false target ECM techniques. The original formulation left open the specific multiple target tracking framework. In this paper, we develop a specific implementation of the D&F technique and evaluate it within the Benchmark 2 Problem environment. Simulation results are presented showing the track-loss rejection capabilities and the track accuracy performance of the D&F technique.
Range deception, such as range-gate-pull-off (RGPO) is a common electronic countermeasure (ECM) technique used to defeat or degrade tracking radars. Although a variety of heuristic approaches/tricks have been proposed to mitigate the impact of this type of ECM on the target tracking algorithms, none of them involve a systematic means to reject the countermeasure signals. This paper presents a general and systematic approach, called Decomposition and Fusion (DF) approach, for target tracking in the presence of range deception ECM and clutter. It is effective against RGPO, range-gate-pull-in, and range false target ECM techniques for a radar system where the deception measurements have virtually the same angles as the target measurement. This DF approach has four fundamental components: (a) decomposing the validated measurements by determination of range deception measurements using hypothesis testing; (b) running one or more tracking filters using the detected range deception measurements only; (c) running a conventional tracking-in-clutter filter using the remaining measurements; (d) fusing the tracking filters by a probabilistically weighted sum of their estimates. Several algorithms within the DF approach are discussed.
Proc. SPIE. 3068, Signal Processing, Sensor Fusion, and Target Recognition VI
KEYWORDS: Radar, Signal to noise ratio, Statistical analysis, Data modeling, Receivers, Personal digital assistants, Monte Carlo methods, Electronic filtering, Filtering (signal processing), Pulse filters
This paper develops the pulse train probabilistic data association filter (PT-PDAF) for use in pulse train analysis and deinterleaving applications. The approach is based on a state-space formulation of the pulse train evolution model. The PDA approach overcomes real-world problems of false and missing pulses which cause the basic Kalman filter to break down. Simulations are developed to show that the PT-PDAF approach is superior to a nearest neighbor filter. An augmented PDA approach which incorporates available pulse parameter measurements such an angle of arrival into the PDA algorithms is shown to further improve the filter performance.
Star-tracking systems, optical communication systems, and infrared tracking systems are examples in which the measurement and correction of alignment errors between the optical source and receiver must be made. In this paper, we develop a new position estimator that retains curacy even under poor SNR conditions. This estimator is derived using an estimation theoretic approach to the problem of tracking a quasi-stationary object given photoevent data in a continuously distributed detector. We derive a maximum likelihood position estimator via application of the expectation-maximization (EM) algorithm. Simulation results are given to show that under low SNR conditions, the estimator performance is superior to that of the commonly used centroid estimator.