Low-Complexity Approximation to the Kalman Filter Using the Dichotomous Coordinate Descent Algorithm

The Kalman Filter is known to be the optimal solution to tracking and data prediction tasks under linear Gaussian models. However, depending on the application, the Kalman filter is very costly to implement, since $\mathcal {O}(M^{2.376})$ operations are required for each time update. On the other hand, the RLS algorithm (for which $\mathcal {O}(M)$ versions are available) is known to be equivalent to the Kalman filter for a certain model for the evolution of the unknown weight vector. This article seeks to extend the class of models for which RLS-like $\mathcal {O}(M)$ algorithms exist, proposing new low complexity versions of the Kalman Filter which use the Dichotomous Coordinate Descent (DCD) technique.