Multi-sensor information fusion white noise filter weighted by scalars based on Kalman predictor

A unified multi-sensor optimal information fusion criterion weighted by scalars is presented in the linear minimum variance sense. The criterion considers the correlation among local estimation errors, only requires the computation of scalar weights, and avoids the computation of matrix weights so that the computational burden can obviously be reduced. Based on this fusion criterion and Kalman predictor, an optimal information fusion filter for the input white noise, which can be applied to seismic data processing in oil exploration, is given for discrete time-varying linear stochastic control systems measured by multiple sensors with correlated noises. It has a two-layer fusion structure. The first fusion layer has a netted parallel structure to determine the first-step prediction error cross-covariance for the state and the filtering error cross-covariance for the input white noise between any two sensors at each time step. The second fusion layer is the fusion center to determine the optimal scalar weights and obtain the optimal fusion filter for the input white noise. Two simulation examples for Bernoulli-Gaussian white noise filter show the effectiveness.