Automatic Bayesian Range Estimation for Passive Bistatic Radar using Slice Sampling via Histograms

Abstract

Estimating the range for a Passive Bistatic Radar (PBR) is a critical problem for the signal processing research community. An efficient solution to this problem, in terms of time-complexity and estimation accuracy, has been proposed recently. This solution implemented maximum likelihood estimator (MLE), a classical technique, using the Markov chain Monte Carlo (MCMC) method to maximize the likelihood function. Specifically, the hybrid Metropolis-Hastings (MH) MCMC method was used. In our study, we adopt the Bayesian framework to solve this problem in which the parameters of interest are considered random variables instead of unknown deterministic constants as in classical approaches. The Bayesian model accounts for the inherent randomness of the PBR system. It also incorporates prior knowledge about the parameter to be estimated into the estimator. This improves the estimation accuracy. Bayesian techniques are comparatively less computationally expensive for high-dimensional and multi-modal problems like PBR. To compute the global maximum of the target probability distribution function (pdf), we have chosen three MCMC methods, namely, MH, hybrid MH, and slice sampling. Out of these three, the slice sampling technique is simpler to implement and can adapt to the characteristics of the target pdf, making it suitable for automated use and software development. It can also be concluded from our experiments that slice sampling, in conjunction with the histogram method, can be slightly faster than MH and hybrid MH sampling methods for a particular case, as shown in the comparative table in Section V of this manuscript.