A new error bound for MIMO discrete-time state-space transversal estimators

We address an exact noise power gain (NPG) matrix for the p-shift linear time-variant transversal finite impulse response (FIR) estimator intended for filtering (p = 0), p-step prediction (p>0), and p-lag smoothing (p<;0) of discrete-time K-state space system models with M states measured. We also propose a new error bound (EB) formed in the three-sigma sense with the NPG and measurement noise variance. A fast iterative algorithm for NPG and EB of the p-shift unbiased FIR estimator is provided along. It is demonstrated that the unbiased FIR and Kalman estimates well range within a gap between EB and -EB.