State Estimation in Linear Dynamical Systems By Partial Update Kalman Filtering

In this letter, we develop a partial update Kalman filtering (PUKF) algorithm to solve the state of a discrete-time linear stochastic dynamical system. In the proposed algorithm, only a subset of the state vector is updated at every iteration, which reduces its computational complexity, compared to the original KF algorithm. The required conditions for the stability of the algorithm are discussed. A closed-form expression for steady-state mean-square deviation is also derived. Numerical examples are used to validate the correctness of the provided analysis. They also reveal the PUKF algorithm exhibits a trade-off between the estimation accuracy and the computational load which is extremely profitable in practical applications.