Selective Finite Memory Structure Filtering Using the Chi-Square Test Statistic for Temporarily Uncertain Systems

Abstract

In this paper, a finite memory structure (FMS) filtering with two kinds of measurement windows is proposed using the chi-square test statistic to cover nominal systems as well as temporarily uncertain systems. First, the simple matrix form for the FMS filter is developed from the conditional density of the current state given finite past measurements. Then, one of the two FMS filters, the primary FMS filter or the secondary FMS filter, with different measurement windows is operated selectively according to the presence or absence of uncertainty, to obtain a valid estimate. The primary FMS filter is selected for the nominal system and the secondary FMS filter is selected for the temporarily uncertain system, respectively. A declaration rule is defined to indicate the presence or absence of uncertainty, operate the suitable one from two filters, and then obtain the valid filtered estimate. A test variable for the declaration rule is developed using a chi-square test statistic from the estimation error and compared to a precomputed threshold. In order to verify the proposed selective FMS filtering and compare with the existing FMS filter and the infinite memory structure (IMS) filter, computer simulations are performed for a selection of dynamic systems including a F404 gas turbine aircraft engine and an electric motor. Simulation results confirm that the proposed selective FMS filtering works well for nominal systems as well as temporarily uncertain systems. In addition, the proposed selective FMS filtering is shown to be remarkably better than the IMS filtering for the temporarily uncertain system.

Recursive Optimal Finite Impulse Response Filter and Its Application to Adaptive Estimation

“…Finally, it can be shown that the finite horizon Kalman filter with estimated initial conditions is equivalent to the conventional optimal FIR filter (32) by applying the estimated initial state (16) and error covariance (19) to the finite horizon Kalman filter (38) as per the following theorem.…”

“…Theorem 2. The optimal FIR filter (32) can be obtained by replacying x k−N and P k−N in the finite Kalman filter (38) with the estimated initial conditions ( 16) and (19), respectively.…”

“…These could originate the divergence problem in the Kalman filter [1][2][3]. In order to prevent divergence problems, finite impulse response (FIR) filters have been used as an alternative to the Kalman filter [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Since FIR filters estimate the states by using finite measurements on the most recent time interval, these filters are known to be more robust against modeling uncertainties and numerical errors that cause of divergence problem in Kalman filter.…”

“…Furthermore, the ROFIR filter provides the best linear unbiased estimate (BLUE) of the state on the finite estimation horizon. In addition, since AFIR filters in previous studies were designed in batch form, they were mostly focused on how to adjust the horizon length [17][18][19]. To the author's best knowledge, there are no results on the adaptive FIR (AFIR) filters which consider noise statistics, thus, we propose a new adaptive FIR filtering algorithm by employing a sequential noise statistics estimation technique as an application of the proposed ROFIR filter.…”

Statistical Analysis of Current Financial Instrument Quotes in the Conditions of Market Chaos

“…Based on the studies presented above, it can be concluded that the nature of the considered series of observations is deeply inconsistent with the known limitations of statis- Thus, the quality of recovery of the system component in data model ( 1) is determined by the compromise between the values of statistical and dynamic estimation errors. Furthermore, the shift in the balance between them depends either on the filter coefficient α (for a filter of type ( 2)) or on the size of the filter memory [22]. In the conditions of chaotic dynamics described by model ( 1), the choice of this parameter also has no analytically sound recommendations and is based on empirical fitting to the results of retrospective analysis on previous observation segments that serve as a dataset.…”