In this paper, we study the performance of the multipath-assisted multitarget tracking using multiframe assignment
for initiating and tracking multiple targets by employing one or more transmitters and receivers. The basis
of the technique is to use the posterior Cramer-Rao lower bound (PCRLB) to quantify the optimal achievable
accuracy of target state estimation. When resolved multipath signals are present at the sensors, if proper measures
are not taken, multiple tracks will be formed for a single target. In typical radar systems, these spurious
tracks are removed from tracking, and therefore the information carried in such target return tracks are wasted.
In multipath environment, in every scan the number of sensor measurements from a target is equal to the number
of resolved signals received by different propagation modes. The data association becomes more complex as this
is in contrary to the standard data association problem whereas the total number of sensor measurements from
a target is equal to at most one. This leads to a challenging problem of fusing the direct and multipath measurements
from the same target. We showed in our evaluations that incorporating multipath information improves
the performance of the algorithm significantly in terms of estimation error. Simulation results are presented to
show the effectiveness of the proposed method.
Proc. SPIE. 6969, Signal and Data Processing of Small Targets 2008
KEYWORDS: Nonlinear filtering, Electronic filtering, Digital filtering, Detection and tracking algorithms, Monte Carlo methods, Computer simulations, Filtering (signal processing), Defense and security, Numerical analysis, Process modeling
This paper presents a novel continuous approximation approach to nonlinear/non-Gaussian Bayesian tracking.
A good representation of the probability density and likelihood functions is essential for the effectiveness of
nonlinear filtering algorithms since these functions could be multi-modal. The proposed approach uses B-spline
interpolation to represent the density and likelihood functions and tensor product approaches to extend the
filter to multidimensional case. The filter is applicable under most general circumstances since it does not make
any assumption on the form of the underlying probability density. An advantage of the proposed method is
that it retains accurate density information in a continuous low-order polynomial form and finding the target
probability in any region of the state space is straightforward. Further processing based on probability density
such as finding the higher order moments of the state estimates could also be performed with less computational
power. Simulation results are presented to demonstrate the proposed algorithm.
A passive coherent location (PCL) system exploits the ambient FM radio or television signals from powerful
local transmitters, which makes it ideal for covert tracking. In a passive radar system, also known as PCL
system, a variety of measurements can be used to estimate target states such as direction of arrival (DOA), time
difference of arrival (TDOA) or Doppler shift. Noise and the precision of DOA estimation are main issues in
a PCL system and methods such as conventional beam forming (CBF) algorithm, algebraic constant modulus
algorithm (ACMA) are widely analyzed in literature to address them. In practical systems, although it is
necessary to reduce the directional ambiguities, the placement of receivers closed to each other results in larger
bias in the estimation of DOA of signals, especially when the targets move off bore-sight. This phenomenon leads
to degradation in the performance of the tracking algorithm. In this paper, we present a method for removing
the bias in DOA to alleviate the aforementioned problem. The simulation results are presented to show the
effectiveness of the proposed algorithm with an example of tracking airborne targets.
The optimal Bayesian multi-target tracking is computationally demanding. The probability hypothesis density
(PHD) filter, which is a first moment approximation of the optimal one, is a computationally tractable alternative.
By evaluating the PHD, one can extract the number of targets as well as their individual states. Recent
sequential Monte Carlo (SMC) implementation of the PHD filter paves the way to apply the PHD filter to nonlinear non-Gaussian problems. It seems that the particle implementation of PHD filter is more dependent on current measurements, especially in the case of low observable target problems (i.e., estimates are sensitive
to missed detections and false alarms). In this paper, a PHD smoothing algorithm is proposed to improve the capability of the PHD based tracking system. By performing smoothing, which gives delayed estimates, we will get not only better estimates for target states but also better estimate for number of targets. Simulations are
performed on proposed method with a multi-target scenario. Simulation results confirm the improved performance of the proposed algorithm.
This paper presents a method for the realization of nonlinear/non-Gaussian Bayesian filtering based on spline
interpolation. Sequential Monte Carlo (SMC) approaches are widely used in nonlinear/non-Gaussian Bayesian
filtering in which the densities are approximated by taking discrete set of points in the state space. In contrast to
the SMC methods, the proposed approach uses spline polynomial interpolation to approximate the probability
densities as well as the likelihood functions. A good representation of the probability densities is an essential
issue in the success of the filtering algorithm, especially in nonlinear filtering, since the probability densities in
nonlinear filtering could be multi-modal. An advantage of the proposed approach is that it retains the accurate
density information and thus a target probability at any region in the state space can easily be obtained by
evaluating the integral of the polynomial. Further, the probability densities are represented with polynomials of
fixed order and any further processing on probability densities could be performed with less computation. This
paper uses the B-spline interpolation in order to maintain the positivity of probability density functions and
likelihood functions. Simulation results are presented to compare the performance and computational cost of the
proposed algorithm with an SMC method.
This paper presents a Sequential Monte Carlo (SMC) Probability Hypothesis Density (PHD) algorithm for decentralized state estimation from multiple platforms. The proposed algorithm addresses the problem of communicating and fusing track information from a team of multiple sensing platforms detecting and tracking multiple targets in the surveillance region. Each sensing platform makes multiple, noisy measurements of an underlying, time-varying state that describes the monitored system. The monitored system involves potentially nonlinear target dynamics described by Markovian state-space model, nonlinear measurements, and non-Gaussian process and measurement noises. Each sensing platform reports measurements to a node in the network, which performs sequential estimation of the current system state using the probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment of the full target posterior of the multi-target state. A sequential Monte Carlo method is used to implement the filter. The crucial consideration is what information needs to be transmitted over the network in order to perform online estimation of the current state of the monitored system, whilst attempting to minimize communication overhead. Simulation results demonstrate the efficiency of the proposed algorithm for a team of bearing only sensors.
Proc. SPIE. 5913, Signal and Data Processing of Small Targets 2005
KEYWORDS: Detection and tracking algorithms, Monte Carlo methods, Signal to noise ratio, Particles, Electronic filtering, Sensors, Digital filtering, Nonlinear filtering, Target detection, Algorithm development
In this paper, we present a recursive track-before-detect (TBD) algorithm based on the Probability Hypothesis Density (PHD) filter for multitarget tracking. TBD algorithms are better suited over standard target tracking methods for tracking dim targets in heavy clutter and noise. Classical target tracking, where the measurements are pre-processed at each time step before passing them to the tracking filter results in information loss, which is very damaging if the target signal-to-noise ratio is low. However, in TBD the tracking filter operates directly on the raw measurements at the expense of added computational burden. The development of a recursive TBD algorithm reduces the computational burden over conventional TBD methods, namely, Hough transform, dynamic programming, etc. The TBD is a hard nonlinear non-Gaussian problem even for single target scenarios. Recent advances in Sequential Monte Carlo (SMC) based nonlinear filtering make multitarget TBD feasible. However, the current implementations use a modeling setup to accommodate the varying number of targets where a multiple model SMC based TBD approach is used to solve the problem conditioned on the model, i.e., number of targets. The PHD filter, which propagates only the first-order statistical moment (or the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with varying number of targets. We propose a PHD filter based TBD so that there is no assumption to be made on the number of targets. Simulation results are presented to show the effectiveness of the proposed filter in tracking multiple weak targets.
Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the target number varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The Probability Hypothesis Density (PHD) filter, which propagates only the first-order statistical moment (or the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region.
With maneuvering targets, detecting and tracking the changes in the target motion model also become important, but current PHD implementations do not provide a mechanism for handling this. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-conditioned estimates in a manner similar to the one used in the Interacting Multiple Model (IMM) estimator. In this paper a multiple model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using Sequential Monte Carlo methods, is proposed. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.
Recently a general framework for sensor resource management, which has been shown to allow eﬃcient and effective utilization of a multisensor system was introduced in5. The basis of this technique is to use the Posterior Cramer-Rao Lower Bound (PCRLB) to quantify and control the optimal achievable accuracy of target state estimation. In the current paper we extend this framework by addressing the issues of imperfect sensor placement and uncertain sensor movement (e.g., sensor drift). In contrast the previous work considered only
the case where the sensor location is known exactly. The crucial consideration is then how these two forms of uncertainty affect the sensor management strategy. If unaccounted for, these uncertainties will render the output of the resource manager useless. We adjust the PCRLB to account for sensor location uncertainty, and we also allow for measurement origin uncertainty (missed target originated detections and false alarms). The work is motivated by the problem of tracking a submarine by adaptively deploying sonobuoys from a helicopter. Simulation results are presented to show the advantages of accounting for sensor location uncertainty within this focal domain of anti-submarine warfare. The same technique can be used for tracking using unattended ground sensors (UGS) or unmanned aerial vehicles (UAV).