Signal identification by nonlinear optimization

Deals with the use of nonlinear optimization techniques to solve the problem of signal identification. The presented idea considers cases when time series are composed of a finite number of nonlinear functions distinct in their parameter sets, and realizations of additive random error. The focus is on the sums of parameterized trigonometric functions. As the random error probability distribution is assumed unknown, the common LSQ criterion is replaced with its parameterized generalization. The obtained unconstrained nonsmooth minimization problem can be solved either directly or after a smooth reformulation to the constrained problem. The efficient nonlinear programming algorithms are utilized. The initial values for computational procedures are estimated using heuristics and suitable statistical techniques. The proposed ideas are illustrated by simple explanatory examples and accompanied by figures. Test results are shown for two optimization solvers, MS Excel Solver and advanced GAMS/MINOS. MATLAB is used for visualization.