Nonlinear Bayesian Estimator for Parameter Learning: A Fixed-Point Characterization

arXiv stat.ML1mo4 min read

arXiv:2606.10111v2 Announce Type: replace-cross Abstract: This paper presents a nonlinear parameter estimator for Wiener-type state-space models obtained as a fixed-point architecture that couples two affine minimum mean-squared error (MMSE) estimators: one for the unknown parameters and one for latent variables. The architecture retains the functional structure of the optimal affine MMSE parameter estimator while incorporating Dynamic Basis Statistics (DBS) estimates that summarize nonlinear basis-function evaluations. Two DBS construction strategies are developed, leading to two nonlinear es

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Nonlinear Bayesian Estimator for Parameter Learning: A Fixed-Point Characterization

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