Sparse parameter estimation of LTI models with <i>l<SUP align="right">p</SUP></i> sparsity using genetic algorithm

Abstract

Sparse optimisation for the identification of parametric linear model structure is equivalent to the estimation of the parameter vector. After relaxing the assumption on the order of the system, sparse optimisation techniques can be utilised to find the optimal model. This paper proposes an optimisation method to find the sparse parameter estimates. For this purpose, lp norm (0 < p < 1) penalty of parameter vector is added to the quadratic loss function which is further minimised using genetic algorithm. For the model structures other than ARX, a simulation model is realised using conditions on the quadratic simulation error. A real coded genetic algorithm is used to minimise the simulation error model. Simulation results are given for the ARX and output error model structures to show the effectiveness of the simulation error model method.