Maximum a posteriori estimation of time-varying ARMA processes from noisy observations

The estimation of the parameters of discrete-time autoregressive moving-average (ARMS) processes observed in white noise is considered. A class of time-varying ARMA processes in which the parameter process is the output of a known linear system driven by white Gaussian noise is examined. The maximum a posteriori (MAP) estimator is defined for the trajectory of the parameter's random process. A two-step estimate-and-maximize (EM)-based (E-step and M-step) iterative algorithm is derived. The posterior probability of the parameters is increased in each iteration, and convergence to stationary points of the posterior probability is guaranteed. Each iteration involves two linear systems and is easily implemented. It is shown that similar results can be obtained for a wide class of parameter estimation problems.>