Nonlinear estimation and modeling of noisy time series by dual Kalman filtering methods

Numerous applications require either the estimation or prediction of a noisy time-series. Examples include speech enhancement, economic forecasting, and geophysical modeling. A noisy time-series can be described in terms of a probabilistic model, which accounts for both the deterministic and stochastic components of the dynamics. Such a model can be used with a Kalman filter (or extended Kalman filter) to estimate and predict the time-series from noisy measurements. When the model is unknown, it must be estimated as well; dual estimation refers to the problem of estimating both the time-series, and its underlying probabilistic model, from noisy data. The majority of dual estimation techniques in the literature are for signals described by linear models, and many are restricted to off-line application domains. Using a probabilistic approach to dual estimation, this work unifies many of the approaches in the literature within a common theoretical and algorithmic framework, and extends their capabilities to include sequential dual estimation of both linear and nonlinear signals. The dual Kalman filtering method is developed as a method for minimizing a variety of dual estimation cost functions, and is shown to be an effective general method for estimating the signal, model parameters, and noise variances in both on-line and off-line environments.