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.