Dual Kalman Filtering Methods for Nonlinear Prediction, Smoothing and Estimation

Prediction, estimation, and smoothing are fundamental to signal processing. To perform these interrelated tasks given noisy data, we form a time series model of the process that generates the data. Taking noise in the system explicitly into account, maximumlikelihood and Kalman frameworks are discussed which involve the dual process of estimating both the model parameters and the underlying state of the system. We review several established methods in the linear case, and propose severa!