Fusion of estimates from multiple Kalman filters

Abstract

The objective of data fusion is to combine elements of raw data from different sources into a single set of meaningful information. In recent years, there has been increased recognition by the command, control, communication and intelligence community of the need to perform track-to-track fusion. This interest has been caused by the availability of sensors based on the characteristics of the optical, infrared, and electromagnetic spectrums for tracking targets with Kalman filter associated with each sensor. When we talk about filtering problem, there must be a system, generally dynamic, of which measurements are available. The system may operate in discrete or continuous time, with the underlying equations either difference equations or differential equations. And it is implicit that the system and sensors under consideration are noisy. In this dissertation, we present new filter using combining N (arbitrary number) filters linearly based on observation vector partition methods in Kalman filter and extended Kalman filter. And we also present method to overcome the dependency problem between sensor``s noises when combining multiple filters. In the classical statement of filtering problem the best estimate of the state is chosen according to the minimum of the mean square error (MSE). In this thesis, after we decompose Kalman filter (or extended Kalman filter) into N local filters by observation vector partition method, we combine N filters in minimum of MSE sense. When we combine multiple filters it is important to derive the equation of cross-covariance between each filter``s estimation error. So we derive the equation of cross-covariance based on well-known equation for covariance matrix of state vector in continuous filter and also generalize to discrete filter. To overcome dependency between sensor``s noise, the Cholesky decomposition method is used to find linear transformation of the observation vector whose sensor``s noises will be uncorrelated. The pro...