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

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.

• S. Rozhkova
• O. Rozhkova
• A. Harlova
• V. Lasukov

• Mathematical expectation
• filtration
• anomalous noise
• memory.

[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).