# Maximum Likelihood Recursive State Estimation using the Expectation Maximization Algorithm

arXiv: https://arxiv.org/abs/2103.10475 · HTML: https://mlsanity.com/paper/2103.10475/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2021.

## Built on by (most cited first, 2 of 2)

- [Maximum likelihood recursive state estimation in state-space models: A new approach based on statistical analysis of incomplete data](https://mlsanity.com/paper/2211.04631/) (2022)
- [Maximum likelihood smoothing estimation in state-space models: An incomplete-information based approach](https://mlsanity.com/paper/2303.16364/) (2023)

## Abstract (arXiv)

A Maximum Likelihood recursive state estimator is derived for non-linear and non-Gaussian state-space models. The estimator combines a particle filter to generate the conditional density and the Expectation Maximization algorithm to compute the maximum likelihood state estimate iteratively. Algorithms for maximum likelihood state filtering, prediction and smoothing are presented. The convergence properties of these algorithms, which are inherited from the Expectation Maximization algorithm, are proven and examined in two examples. It is shown that, with randomized reinitialization, which is feasible because of the algorithm simplicity, these methods are able to converge to the Maximum Likelihood Estimate (MLE) of multimodal, truncated and skewed densities, as well as those of disjoint support.