Maximum likelihood recursive state estimation: An incomplete-information based approach

This paper revisits classical work of Rauch et al. (1965) and develops a novel statistical method for maximum likelihood (ML) recursive state estimation in general state–space models. The new method is based on statistical estimation theory for incomplete information, which has been well developed primarily for ML parameter estimation (Dempster et al., 1977). Distributional identities for the posterior score function and information matrix of state are established. Using these identities, a fast convergent EM-gradient algorithm is proposed, extending the Lange (1995) algorithm for ML recursive state estimation. It revisits and provides an improvement to the EM-algorithm of Ramadan and Bitmead (2022). An explicit form of the information matrix is developed to provide empirical estimates of the standard errors. Sequential Monte Carlo method is used for the valuation of the score function, information and posterior covariance matrices. Some numerical examples are discussed to exemplify the main results.