Eric Wan, Alex Nelson
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, maximum(cid:173) likelihood and Kalman frameworks are discussed which involve the dual process of estimating both the model parameters and the un(cid:173) derlying state of the system. We review several established meth(cid:173) ods in the linear case, and propose severa! extensions utilizing dual Kalman filters (DKF) and forward-backward (FB) filters that are applicable to neural networks. Methods are compared on several simulations of noisy time series. We also include an example of nonlinear noise reduction in speech.