State-space recursive least-squares with adaptive memory

State-space recursive least-squares (SSRLS) enhances the tracking ability of the standard recursive least-squares (RLS) by incorporating the underlying model of the environment. Its overall performance, however, depends on model uncertainty, presence of external disturbances, time-varying nature of the observed signal or nonstationary behavior of the observation noise. It turns out that the forgetting factor plays an important role in this context. However, depending on the problem, it may be difficult or even impossible to have a prior estimate of the best value of forgetting factor. As a logical approach to such situations, SSRLS with adaptive memory (SSRLSWAM) is developed in this paper. This in turn has been achieved by stochastic gradient tuning of the forgetting factor. An approximation based on steady-state SSRLS is also derived. The resultant filter alleviates the computational burden of the full-fledged algorithm. An example of tracking a noisy chirp demonstrates the overall capability and power of the new algorithm. It is expected that this new filter will be able to track and estimate time-varying signals that are difficult to handle with the available tools.