State-space recursive least-squares with adaptive memory

State-space recursive least-squares (SSRLS) is optimal a linear estimator for deterministic signals. The performance of SSRLS however, depends on model uncertainty, time-varying nature of the observed signal or nonstationary behavior of the observation noise. We incorporate stochastic gradient tuning of the forgetting factor to develop SSRLS with adaptive memory. This new algorithm addresses the limitations faced by standard SSRLS. An approximation of the actual filter, which alleviates the computational burden, is also derived. An example of tracking a noisy chirp signifies and demonstrates the overall capability and power of the new algorithm. It is expected that this new filter is able to track and estimate time-varying signals that are difficult to deal with the available tools.