Chapter 3

General Concepts of Bayesian Estimation

The process of estimation begins with an experiment that provides a set of observable outcomes, usually some form of data. Examples of observable data can include a time-sampled succession of bearings and/or ranges to a target or successive samples of a stock price for sales throughout a day of trading. Based on the observable data, one would like to estimate some characteristic parameters that may be unobservable directly. For example, with bearings-only observations one would like to estimate the target location and velocity as a function of time. In the case of stock price data, one would like to estimate the volatility of the stock.

This book concentrates on estimation methods that include models of the temporal dynamics of the variables to be estimated as well as models of the relationship between the observable data and the unobservable variables to be estimated. In particular, discussions will be limited to recursive estimation methods for discretely sampled data. Thus, it is always assumed that the parameters to be estimated follow a known recursive dynamic process and that there is a known analytical link between the observed data and the parameters to be estimated.

In addition, Bayesian estimation assumes that both the parameters to be estimated and the observed data are stochastic entities. The analytical link (a transformation) between the observed data and the parameters to be estimated provide a unifying framework ...

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