Vector form EM and suboptimal joint state and parameter estimation

The expectation maximization (EM) algorithm combined with the Kalman filter (KF) can be applied iteratively to yield state estimates and ML estimates of the parameters of a linear dynamical system. In this paper new recursive forms of the accumulated second-order state moments which constitute the core of the joint state and parameter estimator are derived. The new recursions are in vector form and follow directly from the state smoothing formula as well as the properties of the Kronecker product. By loosening the optimal constraints, the new recursion forms lead to efficient suboptimal algorithms that are time-recursive. Convergence control of these recursive algorithms by exponential weighting is also considered.