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 estimator frameworks. The dual basis-parameter estimator combines an affine basis estimator with the affine parameter estimator, whereas the dual state-parameter estimator first computes affine state estimates and their covariances, then maps these state-estimate statistics through a Gaussian DBS operator to obtain DBS estimates. Both dual estimators admit fixed-point characterizations that alternate between estimating each component using the updated prior of the other, obtained from that component's plug-in estimate statistics from the previous iteration. The efficacy of the proposed methods is examined via extensive Monte Carlo experiments, showing that the dual basis-parameter estimator attains parameter mean-squared errors comparable to those of the purely affine parameter estimator, while the dual state-parameter estimator achieves the lowest parameter mean-squared error, outperforming both the dual basis-parameter and purely affine parameter estimators, as well as sequential Monte Carlo variants of classical Particle Gibbs and Expectation-Maximization schemes.

翻译：本文提出一种用于Wiener型状态空间模型的非线性参数估计器，其架构基于不动点原理，耦合了两个仿射最小均方误差（MMSE）估计器：一个用于未知参数，另一个用于潜变量。该架构保留了最优仿射MMSE参数估计器的功能结构，同时引入动态基统计量（DBS）估计，以汇总非线性基函数评估结果。本文发展了两种DBS构造策略，从而衍生出两种非线性估计器框架。双基-参数估计器将仿射基估计器与仿射参数估计器相结合，而双状态-参数估计器则先计算仿射状态估计及其协方差，再通过高斯DBS算子将这些状态估计统计量映射为DBS估计值。两种双估计器均具有不动点特性，通过交替使用各分量的更新先验（该先验由前一次迭代中该分量的插值估计统计量获得）进行估计。通过大量蒙特卡洛实验验证所提方法的有效性，结果表明：双基-参数估计器参数均方误差与纯仿射参数估计器相当，而双状态-参数估计器实现了最低的参数均方误差，其性能优于双基-参数估计器、纯仿射参数估计器以及经典粒子吉布斯与期望最大化方法的序贯蒙特卡洛变体。