Regularized estimation with variable exponential forgetting

The real-time estimation of normal regression-type models with unknown time-varying parameters is considered and discussed from the Bayesian perspective. A novel tracking technique combining the variable regularization approach with the forgetting operation is derived and elaborated into algorithmic details. The regularization of the parameter covariance is accomplished by incorporating soft equality constraints on the regression parameters into the learning procedure. The resultant procedure is designed to smooth the parameter estimate, preventing it from changing too rapidly. Moreover, the form of the constraints guarantees a minimal amount of information about the parameter estimate, which makes the estimator robust with respect to poor system excitation. The forgetting of obsolete information is provided in two different parameterization options and is performed automatically in a way that complies with the degree of the process nonstationarity. The whole concept preserves the selfreproducibility of the statistics of the normal-Wishart distribution.