LAUSR

In optimal input design input sequences are typically generated without paying attention to the correlations between the regressors of the model to be estimated. In fact, in many cases high correlations are beneficial. This is in contrast to the requirements in sparse estimation. Mutual coherence is the maximum of these correlations, and in case the parameter vector is known to be sparse, we need a low mutual coherence in order to estimate it accurately. This contribution proposes adding a constraint on the mutual coherence to the optimal input design problem to improve the accuracy of estimated sparse models. The proposed method can be combined with any sparse estimation algorithm to estimate the parameters of a model. However, we focus in particular on the bound on the mutual coherence required for Orthogonal Matching Pursuit (OMP), a well-known algorithm in sparse estimation. Furthermore, we analyze the effect of the proposed method on the required input power. Finally, we evaluate, in a numerical study, the performance of the proposed method compared to state-of-the-art algorithms for input design.