# Maximum likelihood recursive state estimation in state-space models: A new approach based on statistical analysis of incomplete data

arXiv: https://arxiv.org/abs/2211.04631 · HTML: https://mlsanity.com/paper/2211.04631/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 54 references that are in the map.
- First posted on arXiv 9 Nov 2022.

## Builds on (most cited first, 2 of 2)

- [Maximum Likelihood Recursive State Estimation using the Expectation Maximization Algorithm](https://mlsanity.com/paper/2103.10475/) (2021)
- [Some results on maximum likelihood from incomplete data: finite sample properties and improved M-estimator for resampling](https://mlsanity.com/paper/2108.01243/) (2021)

## Built on by (most cited first, 1 of 1)

- [Maximum likelihood smoothing estimation in state-space models: An incomplete-information based approach](https://mlsanity.com/paper/2303.16364/) (2023)

## Abstract (arXiv)

This paper revisits the work of Rauch et al. (1965) and develops a novel method for recursive maximum likelihood particle filtering for general state-space models. The new method is based on statistical analysis of incomplete observations of the systems. Score function and conditional observed information of the incomplete observations/data are introduced and their distributional properties are discussed. Some identities concerning the score function and information matrices of the incomplete data are derived. Maximum likelihood estimation of state-vector is presented in terms of the score function and observed information matrices. In particular, to deal with nonlinear state-space, a sequential Monte Carlo method is developed. It is given recursively by an EM-gradient-particle filtering which extends the work of Lange (1995) for state estimation. To derive covariance matrix of state-estimation errors, an explicit form of observed information matrix is proposed. It extends Louis (1982) general formula for the same matrix to state-vector estimation. Under (Neumann) boundary conditions of state transition probability distribution, the inverse of this matrix coincides with the Cramer-Rao lower bound on the covariance matrix of estimation errors of unbiased state-estimator. In the case of linear models, the method shows that the Kalman filter is a fully efficient state estimator whose covariance matrix of estimation error coincides with the Cramer-Rao lower bound. Some numerical examples are discussed to exemplify the main results.