By James V. Candy
New Bayesian procedure is helping you resolve tricky difficulties in sign processing very easily. sign processing relies in this basic conceptthe extraction of serious details from noisy, doubtful facts. so much options depend on underlying Gaussian assumptions for an answer, yet what occurs while those assumptions are inaccurate? Bayesian recommendations sidestep this obstacle via supplying a totally different technique which may simply comprise non-Gaussian and nonlinear approaches besides the entire traditional tools at present on hand. this article allows readers to completely take advantage of the various a. Read more...
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Extra info for Bayesian signal processing: classical, modern, and particle filtering methods
This concept of estimating the underlying distribution and using it to extract a signal estimate provides the foundation of Bayesian signal processing developed in this text. Let us investigate this idea in more detail. We start with the previous problem of trying to estimate the random parameter, X, from noisy data Y = y. Then the associated conditional distribution Pr(X|Y = y) is called the posterior distribution because the estimate is conditioned “after (post) the measurements” have been acquired.
Maximum likelihood produces the “best” estimate as the value which maximizes the probability of the measurements given that the parameter value is “most likely” true. In the estimation problem, the measurement data are given along with the underlying structure of the probability density function (as in the Bayesian case), but the parameters of the density are unknown and must be determined from the measurements; therefore, the maximum likelihood estimate can be considered heuristically as that value of the parameter that best “explains” the measured data giving the most likely estimation.
We show the coupling between model-based signal processing (MBSP) incorporating the a priori knowledge of the underlying processes and the Bayesian framework for specifying the distribution required to develop the processors. The idea of the sampling approach evolving from Monte Carlo (MC) and Markov chain Monte Carlo (MCMC) methods is introduced as a powerful methodology for simulating the behavior of complex dynamic processes and extracting the embedded information required. The main idea is to present the proper perspective for the subsequent chapters and construct a solid foundation for solving signal processing problems.