New Nonlinear Parameter Estimator for State-Space Models Using Dual Bayesian Affine Architecture
Researchers have proposed a nonlinear parameter estimator for Wiener-type state-space models built from two coupled affine minimum mean-squared error estimators in a fixed-point architecture. The method introduces Dynamic Basis Statistics to capture nonlinear structure while preserving the tractability of affine estimation. Monte Carlo experiments show the dual state-parameter variant achieves lower parameter mean-squared error than classical Particle Gibbs and Expectation-Maximization approaches.
A preprint submitted to arXiv on June 8, 2026 introduces a nonlinear estimator framework for Wiener-type state-space models, designed to improve parameter learning by coupling two affine minimum mean-squared error estimators in a fixed-point loop. The key innovation is the concept of Dynamic Basis Statistics, which summarize nonlinear basis-function evaluations and feed into the affine estimation structure without abandoning its analytical tractability. Two distinct estimator variants are presented: the dual basis-parameter estimator, which pairs an affine basis estimator with an affine parameter estimator, and the dual state-parameter estimator, which first computes affine state estimates and then maps their statistics through a Gaussian DBS operator. Both variants iterate by alternately updating each component using plug-in statistics from the other's previous estimate. Extensive Monte Carlo experiments across 32 pages and 9 figures demonstrate that the dual state-parameter estimator achieves the best parameter mean-squared error, surpassing not only the dual basis-parameter estimator but also sequential Monte Carlo-based Particle Gibbs and Expectation-Maximization benchmarks.
What's missing
As a preprint, this work has not yet undergone peer review. The experiments are limited to Monte Carlo simulations; real-world empirical validation on practical datasets is absent. The scope is restricted to Wiener-type state-space models, and generalizability to other model classes remains an open question.
What different sources said
- arXiv cs.LGCenter
Nonlinear Estimator: Dual Bayesian Affine Estimators for Parameter Learning
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