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Filtering of second order generalized stochastic processe...
[Submitted on 25 Apr 2025 (v1), last revised 30 Jun 2026 (this v · 2025-04-26 · via math updates on arXiv.org

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Abstract:We treat the optimal linear filtering problem for a sum of two second order uncorrelated generalized stochastic processes. This is an operator equation involving covariance operators. We study both the wide-sense stationary case and the non-stationary case. In the former case the equation simplifies into a convolution equation. The solution is the Radon--Nikodym derivative between non-negative tempered Radon measures, for signal and signal plus noise respectively, in the frequency domain. In the non-stationary case we work with pseudodifferential operators with symbols in Sjöstrand modulation spaces which admits the use of its spectral invariance properties.

Submission history

From: Patrik Wahlberg [view email]
[v1] Fri, 25 Apr 2025 16:08:20 UTC (34 KB)
[v2] Tue, 30 Jun 2026 09:10:06 UTC (34 KB)