Multilevel mixture Kalman filter
The authors consider the model \[ x_t= F_{\lambda t} x_{t-1}+ G_{\lambda_t} u_t,\qquad y_t= H_{\lambda_t}x_t+ K_{\lambda_t} v_t, \] where \(u_t\) and \(v_t\) are the state and observation noise respectively, and \(\lambda_t\) is a sequence of random indicator variables which form a Markov chain. The matrices \(F_{\lambda_t}\), \(G_{\lambda_t}\), \(H_{\lambda_t}\), and \(K_{\lambda_t}\) are known given \(\lambda_t\). The authors apply a mixture Kalman filter which generates Monte Carlo samples only in the indicator space and uses a mixture of Gaussian distributions to approximate the target conditional distribution. The complexity of the filter is quite high if the dimension of the indicator sampling space is high. In the case of the hierarchical structure of the indicator space, the authors address this difficulty by constructing a new filter, namely, the multilevel mixture Kalman filter.
scientific article; zbMATH DE number 2163857