On using the adaptive delay filter in sparse identification and extensions to sparse deconvolution and sinusoid detection

The drawbacks of using the adaptive delay filter for plant identification are discussed. These drawbacks are due to regression and gain estimation errors and the filter´s limitations under colored excitation hypotheses. After proposing simple solutions for both drawbacks, the authors show how the limitations can be solved by using different known techniques, such as dynamic programming or by applying adaptively thresholded gradient-type algorithms. The direct use of the latter algorithms is also presented as an alternative. Some simulation results illustrate the behaviour of the proposed modifications and extensions