Batch Optimal FIR Smoothing: Increasing State Informativity in Nonwhite Measurement Noise Environments

Strictly nonwhite measurement noise (NMN) is observed in many industrial processes. Therefore, effective smoothing is often required to extract useful information about the process state with maximum accuracy. This article proposes a batch
$q$
-lag optimal finite impulse response (OFIR) smoother, operating under NMN with full block covariance matrices. It is shown that the OFIR smoother significantly outperforms the Rauch–Tung–Striebel (RTS) smoother and the unbiased FIR (UFIR) smoother. Testing is provided based on object tracking. The results are validated by a practical example of a three degree-of-freedom helicopter system, which confirms that OFIR smoothing provides better noise reduction than UFIR smoothing, RTS smoothing, and modified RTS smoothing using state augmentation and measurement differencing.