A Modified Recursive Least Squares Algorithm with Forgetting and Bounded Covariance
Adam L. Bruce, Dennis S. Bernstein · 2019
Recursive least squares (RLS) is widely used in identification and estimation. An unfortunate weakness of RLS is the divergence of its covariance matrix in cases where the data are not sufficiently persistent. To solve this problem, [1] introduced the exponential forgetting and resetting algorithm (EFRA), whose covariance update equation is modified so that the covariance matrix remains bounded. Unfortunately, EFRA does not include RLS as a special or limiting case, and cannot easily approximate RLS estimates. In this paper, we derive a modified RLS variant of EFRA that includes RLS without forgetting as a limiting case, and that can closely approximate RLS with forgetting. An additional advantage of MRLS relative to EFRA is greater ease in choosing parameters to set the covariance bounds.