Comparison of state and information based sensor fusion

In this paper, state and information space estimation methods used in both linear and nonlinear systems are compared. General recursive estimation and in particular the Kalman filter is discussed and a Bayesian approach to probabilistic information fusion is outlined. The notion and measures of information are defined. This leads to the derivation of the algebraic equivalent of the Kalman filter, the linear information filter. The characteristics of this filter and the advantages of information space estimation are discussed. Examples are then implemented in software to illustrate the algebraic equivalence of the Kalman and Information filters. The benefits of information space are also explored in these case studies. State estimation for systems with nonlinearities is considered and the extended Kalman filter treated. Linear information space is then extended to nonlinear information space by deriving the extended information filter. This establishes all the necessary mathematical tools required to exhaustive information space estimation. The advantages of the extended information filter over the extended Kalman filter are presented and demonstrated. This extended information filter constitute an original and significant contribution to estimation theory made in this paper. Examples of systems involving both nonlinear state evolution and nonlinear observations are simulated. Thus, the algebraic equivalence of the two filters is illustrated and the benefits of nonlinear information space manifested.