Structure-Induced Complex Kalman Filter for Decentralized Sequential Bayesian Estimation

The letter considers a multi-sensor state estimation problem configured in a decentralized architecture where local complex statistics are communicated to the central processing unit for fusion instead of the raw observations. Naive adaptation of the augmented complex statistics to develop a decentralized state estimation algorithm results in increased local computations, and introduces extensive communication overhead, making it practically unattractive. The letter proposes a structure-induced complex Kalman filter framework with reduced communication overhead. In order to further reduce the local computations, the letter proposes a non-circularity criterion which allows each node to examine the non-circularity of its local observations. A local sensor node disregards its extra second-order statistical information when the non-circularity coefficient is small. In cases where the local observations are highly non-circular, an intuitively pleasing circularization approach is proposed to avoid computation and communication of the pseudo-covariance matrices. Simulation results indicate that the proposed structured-induced complex Kalman filter (SCKF) provides significant performance improvements over its traditional counterparts.