Proc. SPIE. 7698, Signal and Data Processing of Small Targets 2010
KEYWORDS: Target detection, Detection and tracking algorithms, Sensors, Digital filtering, Personal digital assistants, Surveillance, Time metrology, Electronic filtering, Algorithm development, Filtering (signal processing)
Data association is the key component in single or multiple target tracking algorithms with measurement origin.
Probabilistic Data Association (PDA), in which all validated measurements are associated probabilistically to
the predicted estimate, is a well-known method to handle the measurement origin uncertainty. In PDA, the
effect of measurement origin uncertainty is incorporated into the updated covariance by adding the spread of the
innovations term. The updated covariance may become very large after few time steps in high clutter scenarios
due to spread of the innovations term. Large covariance results in a large gate, which is used to limit the possible
measurements that could have originated from the target. Hence, the track will be lost and estimate will just
follow the prediction. Also, large gate will make the well-separated target assumption invalid, even if the targets
are well-separated. Hence, after a few time steps all the targets in the surveillance region come under the same
group, making the Joint Probabilistic Data Association (JPDA). In this paper, adaptive gating techniques are
proposed to avoid the steady increase in the updated covariance in high clutter. The effectiveness of the proposed
techniques is demonstrated on simulated data.
In this paper an efficient approach to nonlinear non-Gaussian state estimation based on spline filtering is presented.
The estimation of the conditional probability density of the unknown state can be ideally achieved
through Bayes rule. However, the associated computational requirements make it impossible to implement this
online filter in practice. In the general particle filtering problem, estimation accuracy increases with the number
of particles at the expense of increased computational load. In this paper, B-Spline interpolation is used to
represent the density of the state pdf through a low order continuous polynomial. The motivation is to reduce
the computational cost. The motion of spline control points and corresponding coefficients is achieved through
implementation of the Fokker-Planck equation, which describes the propagation of state probability density
function between measurement instants. This filter is applicable for a general state estimation problem as no
assumptions are made about the underlying probability density.
The Probability Hypothesis Density (PHD) filter is a powerful new tool in the field of multitarget tracking. Unlike
classical multi-target tracking approaches, such as Multiple Hypothesis Tracking (MHT), in each scan it provides a
complete solution to multi-target state estimation without the necessity for explicit measurement-to-track data
association. The PHD filter recursively propagates the first order moment of the multi-target posterior. This allows us to
determine the expected number of targets as well as their state estimates at each scan. However, there is no implicit
connection between the target state estimates in consecutive scans. In this paper, a new cluster-based approach is
proposed for track labeling in the Sequential Monte Carlo (SMC i.e. particle filter based) PHD filter. The method
associates a likelihood vector to each particle in the SMC estimate. This vector indicates the likelihood that the particle
estimate belongs to each of the established target tracks. This likelihood vector is propagated along with the PHD
moment and updated with the PHD function. By maintaining a set of associations from scan to scan, the new method
provides a complete PHD solution for a multi-target tracking application over time. The method is tested on both clean
and noisy multi-target tracking scenarios and the results are compared to some previously published methods.
The probability hypothesis density (PHD) filter is an estimator that approximates, on a given scenario, the
multitarget distribution through its first-order multitarget moment. This paper presents two particles labeling
algorithms for the PHD particle filter, through which the information on individual targets identity (otherwise
hidden within the first-order multitarget moment) is revealed and propagated over time. By maintaining all
particles labeled at any time, the individual target distribution estimates are obtained under the form of labeled
particle clouds, within the estimated PHD. The partitioning of the PHD into distinct clouds, through labeling,
provides over time information on confirmed tracks identity, tracks undergoing initiation or deletion at a given
time frame, and clutter regions, otherwise not available in a regular PHD (or track-labeled PHD). Both algorithms
imply particles tagging since their inception, in the measurements sampling step, and their re-tagging once they
are merged into particle clouds of already confirmed tracks, or are merged for the purpose of initializing new
tracks. Particles of a confirmed track cloud preserve their labels over time frames. Two data associations
are involved in labels management; one assignment merges measurement clouds into particle clouds of already
confirmed tracks, while the following 2D-assignment associates particle clouds corresponding to non-confirmed
tracks over two frames, for track initiation. The algorithms are presented on a scenario containing two targets
with close and crossing trajectories, with the particle labeled PHD filter tracking under measurement origin
uncertainty due to observations variance and clutter.
In this paper, a new state estimation algorithm for estimating the states of targets that are separable into
linear and nonlinear subsets with non-Gaussian observation noise distributed according to a mixture of Gaussian
functions is proposed. The approach involves modeling the collection of targets and measurements as random
finite sets and applying a new Rao-Blackwellised Approximate Conditional Mean Probability Hypothesis Density
(RB-ACM-PHD) recursion to propagate the posterior density. The RB-ACM-PHD filter jointly estimates the
time-varying number of targets and the observation sets in the presence of data association uncertainty, detection
uncertainty, noise and false alarms. The proposed algorithm approximates a mixture Gaussian distribution with a
moment-matched Gaussian in the weight update phase of the filtering recursion. A two dimensional maneuvering
target tracking example is used to evaluate the merits of the proposed algorithm. The RB-ACM-PHD filter
results in a significant reduction in computation time while maintaining filter accuracies similar to the standard
sequential Monte Carlo PHD implementation.
Probability Hypothesis Density (PHD) filter is a unified framework for multitarget tracking and provides estimates
for a number of targets as well as individual target states. Sequential Monte Carlo (SMC) implementation
of a PHD filter can be used for nonlinear non-Gaussian problems. However, the application of PHD based state
estimators for a distributed sensor network, where each tracking node runs its own PHD based state estimator,
is more challenging compared with single sensor tracking due to communication limitations. A distributed state
estimator should use the available communication resources efficiently in order to avoid the degradation of filter
performance. In this paper, a method that communicates encoded measurements between nodes efficiently while
maintaining the filter accuracy is proposed. This coding is complicated in the presence of high clutter and
instantaneous target births. This problem is mitigated using novel adaptive quantization and encoding techniques.
The performance of the algorithm is quantified using a Posterior Cramer-Rao Lower Bound (PCRLB),
which incorporates quantization errors. Simulation studies are performed to demonstrate the effectiveness of the
The Interacting Multiple Model (IMM) estimator has been proven to be effective in tracking agile targets.
Smoothing or retrodiction, which uses measurements beyond the current estimation time, provides better estimates
of target states. Various methods have been proposed for multiple model smoothing in the literature.
In this paper, a new smoothing method, which involves forward filtering followed by backward smoothing while
maintaining the fundamental spirit of the IMM, is proposed. The forward filtering is performed using the standard
IMM recursion, while the backward smoothing is performed using a novel interacting smoothing recursion.
This backward recursion mimics the IMM estimator in the backward direction, where each mode conditioned
smoother uses standard Kalman smoothing recursion. Resulting algorithm provides improved but delayed estimates
of target states. Simulation studies are performed to demonstrate the improved performance with a
maneuvering target scenario. The comparison with existing methods confirms the improved smoothing accuracy.
This improvement results from avoiding the augmented state vector used by other algorithms. In addition, the
new technique to account for model switching in smoothing is a key in improving the performance.
The joint target tracking and classification using target-to-sensor aspect-dependent Radar Cross Section (RCS)
and kinematic data for multistatic sonar network is presented in this paper. The scattered signals measured from
different orientations of a target may vary due to aspect-dependant RCS. A complex target may contain several
dozen significant scattering centers and dozens of other less significant scatterers. Because of this multiplicity
of scatterers, the net RCS pattern exhibits high variation with aspect angle. Thus, radar cross sections from
multiple aspects of a target, which are obtained via multiple sensors, will help in accurately determining the target
class. By modeling the deterministic relationship that exits between RCS and target aspect, both the target class
information and the target orientation can be estimated. Kinematic data are also very helpful in determining the
target class as it describes the target motion pattern and its orientation. The proposed algorithm exploits the
inter-dependency of target state and the target class using aspect-dependent RCS and kinematic information in
order to improve both the state estimates and classification of each target. The simulation studies demonstrate
the merits of the proposed joint target tracking and classification algorithm based on aspect-dependant RCS and
Passive sonar is widely used in practice to covertly detect maritime vessels. However, the detection of stealthy
vessels often requires active sonar. The risk of the overt nature of active sonar operation can be reduced by
using multistatic sonar techniques. Cheap sonar sensors that do not require any beamforming technique can be
exploited in a multistatic system for spacial diversity. In this paper, Gaussian mixture probability hypothesis
density (GMPHD) filter, which is a computationally cheap multitarget tracking algorithm, is used to track multiple
targets using the multistatic sonar system that provides only bistatic range and Doppler measurements.
The filtering results are further improved by extending the recently developed PHD smoothing algorithm for
GMPHD. This new backward smoothing algorithm provides delayed, but better, estimates for the target state.
Simulations are performed with the proposed method on a 2-D scenario. Simulation results present the benefits
of the proposed algorithm.
With current processing power, Multiple Hypothesis Tracking (MHT) becomes a feasible and powerful solution;
however a good hypothesis pruning method is mandatory for efficient implementation. The availability of a continuously
increasing number of tracking systems raises interest in combining information from these systems. The purpose of this
paper is to propose a method of information fusion for such trackers that use MHT locally with local information sent in
the form of sensor global hypotheses and the fusion center combining them into fused global hypotheses. The
information extracted from the best fused global hypotheses, in the form of ranking of received sensor global
hypotheses, is sent back to local trackers, for optimized pruning. Details of the method, in terms of sensor global
hypotheses generation, evaluation, pruning at local sensors, association and fusion of sensor global hypotheses at fusion
center, and usage of the information received as feedback from the fusion center are presented.
In this paper, we consider the tracking of multiple targets in the presence of clutter with poorly localized sensors in
multistatic sensor networks. In multistatic sensor networks, we have a few active sensors that emit the signals and
many passive sensors that receive the signals originated from the active sensors and reflected by the targets and
clutter. In anti-submarine warfare, sensors are typically deployed from aircraft. Optimal tracking performance
can be achieved if all the sensor locations are known. However, in general, sensor deployment accuracy is poor,
and sensors can also drift significantly over time. Hence, the location uncertainties will increase with time. If
the sensors have global position system (GPS) receiver, then their locations can be located with reasonable
accuracy. However, most of the cheap sensors do not have a GPS, and therefor, location uncertainties must
be taken in to consideration while tracking. An advantage of multistatic sensors compared to independent
monostatic sensors is that the sensors can also be tracked accurately. In this paper, we propose how to improve
the tracking performance of multiple targets by incorporating sensor uncertainties. We obtain a bound on the
tracking performance with location uncertainties being taken into consideration, and propose a technique to
select a subset of sensors (if only a few of the available sensors can be used at any measurement time) that
should be used at each time step based on the bound. Simulation results illustrating the performance of the
proposed algorithms are also presented.
Due to the availability of cheap passive sensors, it is possible to deploy a large number of them for tracking
purposes in anti-submarine warfare (ASW). However, modern submarines are quiet and difficult to track with
passive sensors alone. Multistatic sensor networks, which have few transmitters (e.g., dipping sonars) in addition
to passive receivers, have the potential to improve the tracking performance. We can improve the performance
further by moving the transmitters according to existing target states and any possible new targets. Even
though a large number of passive sensors are available, due to frequency, processing power and other physical
limitations, only a few of them can be used at any one time. Then the problems are to decide the path of the
transmitters and select a subset from the available passive sensors in order to optimize tracking performance.
In this paper, the PCRLB, which gives a lower bound on estimation uncertainty, is used as the performance
measure. We present an algorithm to decide jointly the optimal path of the movable transmitters, by considering
their operational constraints, and the optimal subset of passive sensors that should be used at each time steps for
tracking multiple, possibly time-varying, number of targets. Finding the optimal solution in real time is difficult
for large scale problems, and we propose a genetic algorithm based suboptimal solution technique. Simulation
results illustrating the performance of the proposed algorithm are also presented.