KEYWORDS: Signal to noise ratio, Mixtures, Clutter, Detection and tracking algorithms, Expectation maximization algorithms, Simulations, Point spread functions, Stochastic processes
The histogram-probabilistic multi-hypothesis tracker (H-PMHT) is an efficient parametric mixture fitting approach to the multi target track-before-detect (TBD) problem. It has been shown that it can give comparable performance to other methods by a fraction of the computational costs. In the original derivation of the H-PMHT, the mixing proportions are both coupled and uncorrelated over time, which may not hold true in practical scenarios involving fluctuating target amplitudes. In this paper, the mixing proportions are modeled according to a Poisson mixture measurement process. In contrast to existing approaches, a more general Markov chain prior based on the generalized inverse Gaussian (GIG) distribution is used as a prior of the Poisson mixing rates. The proposed method provides an alternative solution to the data association uncertainty in clutter, giving accurate and robust signal-to-noise ratio (SNR) estimates by utilizing the GIG Markov chain. The results are validated on simulated data.
KEYWORDS: Signal to noise ratio, Particles, Sensors, Particle filters, Point spread functions, Detection and tracking algorithms, Clouds, Target detection, Monte Carlo methods, Digital filtering
In this paper we address the problem of detecting and tracking a single dim target in unknown background noise.
Several methodologies have been developed for this problem, including track-before-detect (TBD) methods which
work directly on unthresholded sensor data. The utilization of unthresholded data is essential when signal-to-noise
ratio (SNR) is low, since the target amplitude may never be strong enough to exceed any reasonable
threshold. Several problems arise when working with unthresholded data. Blurring and non-Gaussian noise
can easily lead to very complicated likelihood expressions. The background noise also needs to be estimated.
This estimate is a random variable due to the random nature of the background noise. We propose a recursive
TBD method which estimates the background noise as part of its likelihood evaluation. The background noise
is estimated by averaging over nearby sensor cells not affected by the target. The uncertainty of this estimate
is taken into account by the likelihood evaluation, thereby yielding a more robust TBD method. The method
is implemented using sequential Monte Carlo evaluation of the optimal Bayes equations, also known as particle
filtering. Simulation results show how our method allows detection and tracking to be carried out in an uncertain
environment where current recursive TBD methods fail.
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