Noise Power Gain for Discrete-Time FIR Estimators

The noise power gain (NPG) matrix is specialized in state space for transversal finite impulse response (FIR) estimators intended for filtering, prediction, and smoothing of discrete time-variant K-state models with M states measured. A computationally efficient iterative algorithm for NPG associated with unbiased estimation is provided along. Based on a numerical example, we show that the estimates are well bounded with the error bound (EB) specified in the three-sigma sense by the main components of the NPG matrix and measurement noise variance. In turn, the cross-components in the NPG matrix represent interactions in the estimator channels. It is concluded that EB can serve as an efficient measure of errors in optimal and suboptimal FIR and Kalman structures.