Optimal Sequential Fusion Kalman Filter for Multi-Sensor Linear Systems with Noise Cross-Correlated

For the state estimation problem of multi-sensor linear systems with noise cross-correlated, where process noise correlates with measurement noise and measurement noises are mutually correlated, researchers have long attempted to design a sequential fusion Kalman filter that is strictly equivalent to the centralized fusion Kalman filter. To the best of our knowledge, this problem has remained unsolved. To this end, this paper designs a truly globally optimal sequential fusion filter suitable for such systems. First, an innovative method is proposed to indirectly decorrelate process noise from all measurement noise, addressing the challenge of their direct decorrelation. Then, the measurement equations are equivalently rewritten based on the Gram-Schmidt orthogonalization principle so that mutual independence among the noises is achieved. Next, a sequential fusion Kalman filter is established based on the rewritten measurement equation. Finally, the equivalence between filters is rigorously proven theoretically. To demonstrate the effectiveness of the proposed algorithms, the problem of tracking a target moving with constant velocity is considered.