Identification of linear time varying systems using basis pursuit

System identification involves creating mathematical models of systems using measurements of their inputs and outputs. Linear time-varying systems form an important sub-class of models that require the use of specialized system identification techniques. One such approach involves expanding the time-varying parameters onto a set of temporal basis functions and then estimating the resulting expansion coefficients. This, however, requires the estimation of a large number of parameters and often results in extreme noise sensitivity. In this paper a novel algorithm for identifying time-varying systems is presented. It combines a temporal expansion with a term selection step that uses the "Least Absolute Shrinkage and Selection Operator", or Lasso. The Lasso term selection technique constructs a model structure with a nearly minimal number of non-zero terms, and hence with relatively low estimation variances. The algorithm is demonstrated by using it to detect changes in the dynamic stiffness of the human elbow immediately following the onset of a broadband perturbation.