Method for joint estimation for states and parameters concerning non-linear systems with time-correlated measurement noise

A dimensionality-reduction-augmented non-linear state-space representation has been proposed to reduce the optimisation space for maximum-likelihood estimation. Based on the above representation, an expectation-maximisation algorithm has been derived to realise joint estimation of states and parameters. During the expectation step, the system state was estimated via the use of a fifth-order cubature Kalman filter and Rauch-Tung-Striebel smoother based on the state-augmented method. During the maximisation step, unknown parameters within iterations were estimated using the Newton method. Subsequently, two joint-estimation methods - one containing all measurements and the other involving a sliding window - were developed to estimate the invariants and step parameters, respectively. An example concerning manoeuvring-target tracking has been discussed to demonstrate the performance of proposed algorithms.