Time‐variant linear optimal finite impulse response estimator for discrete state‐space models

Abstract

A general p-shift linear optimal finite impulse response (FIR) estimator is proposed for filtering (p D 0), p-lag smoothing (p < 0), and p-step prediction (p > 0) of discrete time-varying state-space models. An optimal solution is found in the batch form with the mean square initial state function self-determined by solving the discrete algebraic Riccati equation. An unbiased batch solution is shown to be independent on noise and initial conditions. The mean square errors in both the optimal and unbiased estimates have been determined along with the noise power gain and estimate error bound. The following important inferences have been made on the basis of numerical simulation. Unlike the time-invariant Kalman filter, the relevant optimal FIR one is very less sensitive to noise, especially when N 1. Both time varying, the optimal FIR and Kalman estimates trace along almost the same trajectories with similar errors and sensitivities to noise. Overall, the optimal FIR estimator demonstrates better robustness than the Kalman one against faults in the noise description.

Fast bias‐constrained optimal FIR filtering for time‐invariant state space models

“…In the minimum MSE sense, the OFIR was derived in [11] for the purposes of system identification [32,33] (both w n and v n are filtered out) and in [23] as a regular filter (only v n is filtered out). In turn, the UFIR filter shown in [24] satisfies only the unbiasedness constraint:…”

“…In [22], Han, Kwon, and Kim have suggested a relevant algorithm for deterministic time-invariant control systems, and Shmaliy derived an iterative algorithm [11] for the p-shift time-invariant unbiased FIR (UFIR) estimator. The latter was further extended in [23] to time-variant models. A distinctive advantage of the iterative UFIR algorithm [24] is that it completely ignores the noise statistics and the initial error statistics, thus, leading to many applications in diverse areas [25][26][27].…”

Improving state estimates over finite data using optimal FIR filtering with embedded unbiasedness

“…The KF, UFIR and OFIR filters are employed as benchmarks when necessary. Similar examples can also be found in in [7,8,13]. The two-state harmonic model can be specified by B = [ Fig.…”

“…Here, the unbiasedness was checked a posteriori and the solution thus belongs to CU. Soon after, the UFIR filter [6] was extended to time-variant systems [7,8]. For nonlinear models, an extended UFIR filter was proposed in [9] and unified forms for FIR filtering and smoothing were discussed in [10].…”

A finite memory structure filtering for indoor positioning in wireless sensor networks with measurement delay

“…The valid duration of the model might as well be limited to the recently finite time, which is the basic theory of the finite memory structure (FMS) filters. [8][9][10][11][12][13] In addition, due to the IMS, the Kalman filter can tend to accumulate the filtering error as time goes. Thus, the Kalman filter has known to be sensitive and show even divergence phenomenon for temporary modeling uncertainties and round-off errors.…”