2019
DOI: 10.3390/app9204257
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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… Show more

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Cited by 6 publications
(15 citation statements)
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“…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.…”
Section: Lemma 1 ([21]mentioning
confidence: 99%
See 3 more Smart Citations
“…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.…”
Section: Lemma 1 ([21]mentioning
confidence: 99%
“…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.…”
Section: Lemma 1 ([21]mentioning
confidence: 99%
See 2 more Smart Citations
“…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.…”
mentioning
confidence: 99%