The ensemble Kalman filter relies on a Gaussian approximation being a reasonably accurate representation of the filtering distribution. Reich recently introduced a Gaussian mixture ensemble transform filter which can address scenarios where the prior can be modeled using a Gaussian mixture. Reichs derivation is suitable for a scalar measurement or a vector of uncorrelated measurements. We extend the derivation to the case of vector observations with arbitrary correlations. We illustrate through numerical simulation that implementation is challenging, because the filter is prone to instability.
The use of multiple scans of data to improve ones ability to improve target tracking performance is widespread
in the tracking literature. In this paper, we introduce a novel application of a recent innovation in the SMC
literature that uses multiple scans of data to improve the stochastic approximation (and so the data association
ability) of a multiple target Sequential Monte Carlo based tracking system. Such an improvement is achieved
by resimulating sampled variates over a fixed-lag time window by artificially extending the space of the target
distribution. In doing so, the stochastic approximation is improved and so the data association ambiguity is
more readily resolved.
The probability hypothesis density (PHD) filter is a practical alternative to the optimal Bayesian multi-target filter based on
finite set statistics. It propagates only the first order moment
instead of the full multi-target posterior. Recently, a sequential
Monte Carlo (SMC) implementation of PHD filter has been used in
multi-target filtering with promising results. In this paper, we
will compare the performance of the PHD filter with that of the
multiple hypothesis tracking (MHT) that has been widely used in
multi-target filtering over the past decades. The Wasserstein
distance is used as a measure of the multi-target miss distance in
these comparisons. Furthermore, since the PHD filter does not
produce target tracks, for comparison purposes, we investigated
ways of integrating the data-association functionality into the
PHD filter. This has lead us to devise methods for integrating the
PHD filter and the MHT filter for target tracking which exploits
the advantage of both approaches.
KEYWORDS: Particles, Detection and tracking algorithms, Signal to noise ratio, Sensors, Particle filters, Tin, Digital filtering, Computer simulations, Data modeling, Target recognition
In this paper, a solution to the TENET nonlinear filtering challenge is presented. The proposed approach is based on particle filtering techniques. Particle methods have already been used in this context but our method improves over previous work in several ways: better importance sampling distribution, variance reduction through Rao-Blackwellisation etc. We demonstrate the efficiency of our algorithm through simulation.
While single model filters are sufficient for tracking targets having fixed kinematic behavior, maneuvering targets require the use of multiple models. Jump Markov linear systems whose parameters evolve with time according to a finite state-space Markov chain, have been used in these situations with great success. However, it is well-known that performing optimal estimation for JMLS involves a prohibitive computational cost exponential in the number of observations. Many approximate methods have been proposed in the literature to circumvent this including the well-known GPB and IMM algorithms. These methods are computationally cheap but at the cost of being suboptimal. Efficient off- line methods have recently been proposed based on Markov chain Monte Carlo algorithms that out-perform recent methods based on the Expectation-Maximization algorithms. However, realistic tracking systems need on-line techniques. In this paper, we propose an original on-line Monte Carlo filtering algorithm to perform optimal state estimation of JMLS. The approach taken is loosely based on the bootstrap filter which, wile begin a powerful general algorithm in its original form, does not make the most of the structure of JMLS. The proposed algorithm exploits this structure and leads to a significant performance improvement.
KEYWORDS: Monte Carlo methods, Filtering (signal processing), Target detection, Expectation maximization algorithms, Detection and tracking algorithms, Particles, Signal processing, Electronic filtering, Computer simulations, Time metrology
In this paper we consider the problem of tracking a maneuvering target in clutter. We apply an original on-line Monte Carlo filtering algorithm to perform optimal state estimation. Improved performance of the resulting algorithm over standard IMM/PDAF based filters is demonstrated.
In this paper we present simple conditions related to geometric ergodicity of Markov chains which ensure the convergence in a given sense of the simulated annealing algorithm. We prove that convergence of the algorithm occurs for a proper sequence of temperatures when a local minorization condition of the transition kernels and a drift condition are satisfied. This result may be useful in a Bayesian framework, where it is possible to take advantage of the statistical structure of the problem in order to perform efficient optimization. This is illustrated on several examples.
In this article, we address the problem of Bayesian deconvolution of point sources in nuclear imaging under the assumption of Poissonian statistics. The observed image is the result of the convolution by a known point spread function of an unknown number of point sources with unknown parameters. To detect the number of sources and estimate their parameters we follow a Bayesian approach. However, instead of using a classical low level prior model based on Markov random fields, we prose a high-level model which describes the picture as a list of its constituent objects, rather than as a list of pixels on which the data are recorded. More precisely, each source is assumed to have a circular Gaussian shape and we set a prior distribution on the number of sources, on their locations and on the amplitude and width deviation of the Gaussian shape. This high-level model has far less parameters than a Markov random field model as only s small number of sources are usually present. The Bayesian model being defined, all inference is based on the resulting posterior distribution. This distribution does not admit any closed-form analytical expression. We present here a Reversible Jump MCMC algorithm for its estimation. This algorithm is tested on both synthetic and real data.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.