Analysis of Filtering in Stochastic Systems on Continuous-Time Memory Observations in the Presence of Anomalous Noises

Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov

Abstract:

For optimal unbiased filter as mean-square and in the case of functioning anomalous noises in the observation memory channel, we have proved insensitivity of filter to inaccurate knowledge of the anomalous noise intensity matrix and its equivalence to truncated filter plotted only by non anomalous components of an observation vector.

Keywords: Mathematical expectation, filtration, anomalous noise, memory.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100527

References:

[1] S.V Rozhkova, O. V. Rozhkova. Filtering in stochastic systems with continuous time over observations with memory in the presence of anomalous noises. Раrt 1: Synthesis, J. Adv. Mat. Res. (2014) in press. (in Russian).
[2] R.Griffin, E Sage, The sensitivity analysis of discrete algorithms for filtering and smoothing. Rocketry and astronautics. 10 (1969) pp 85-93 (in Russian).
[3] N.S. Demin, O.V. Rozhkova, S.V. Rozhkova. Generalized moving extrapolation of stochastic processes of jointly continuous and discrete observations with memory, Izvestiya RAS. Theory and Control Systems 4 (2000) pp. 39-51 (in Russian).
[4] F.R.Gantmakher, Theory of Matrices, Nauka, Moscow, 1978 (in Russian).
[5] A Albert, Regression, pseudoinverse and recursive estimation, Nauka, Moscow, 1977 (in Russian).
[6] K.A. Abgaryan, Matrix and asymptotic methods in the theory of linear systems, Nauka, Moscow, 1973 (in Russian).