Adaptive Sequential MCMC for Combined State and Parameter Estimation

TL;DR

This paper introduces an adaptive sequential MCMC method for joint state and parameter estimation in linear state space models, utilizing a self-tuning approach and Gaussian mixture representations for efficient online inference.

Contribution

It presents a novel adaptive MCMC algorithm that combines self-tuning, delayed acceptance, and Gaussian mixture modeling for real-time state and parameter estimation.

Findings

Effective in irregular GPS time series data

Maintains high acceptance rates in online mode

Accelerates sampling with sliding window approach

Abstract

In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean and covariance structure informs the proposed mechanism and is also used in a delayed-acceptance algorithm. Information on the resulting state of the system is given by a Gaussian mixture. In on-line mode, the algorithm is adaptive and uses a sliding window approach to accelerate sampling speed and to maintain appropriate acceptance rates. We apply the algorithm to joined state and parameter estimation in the case of irregularly sampled GPS time series data.