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Abstract: An approach to the test of the sensor information fusion Kalman filter is proposed. It is based on the introduced statistics of mathematical expectation of the spectral norm of a normalized innovation matrix. The approach allows for simultaneous test of the mathematical expectation and the variance of innovation sequence in real time and does not require a priori information on values of the change in its statistical characteristics under faults. Using this approach, fault detection algorithm for the sensor information fusion Kalman filter is developed. [Copyright &y& Elsevier]

Let T(bjk) be a finite collection of infinite Toeplitz band matrices, let Tn(bjk) denote their (n + 1) × (n + 1) truncations, and put [This symbol cannot be presented in ASCII format] where . ·. p stands for the operator norm associated with the lp-norm 1 ≤ p < ∝ ) on Cn+1. We establish tight two-sided estimates for the difference Mp - . An. p. It is well known that if T(b) is a Hermitian Toeplitz band matrix and An = Tn(b), then M2 - . An. 2 goes to zero with polynomial speed. We show that such a slow convergence rate is, in a sense, an exceptional case, and we prove that in the generic case Mp - . An. p approaches zero with exponential speed. Our results yield good error estimates when computing the norms of certain infinite matrices via their large truncations and, conversely, when determining the norms of certain large matrices by having recourse to known norms of infinite matrices. [ABSTRACT FROM AUTHOR]