A genetic algorithm approach to the spectral estimation of time series with noise and missed observations

This study considers the problem of estimating the autoregressive moving average (ARMA) power spectral density when measurements are corrupted by noise and by missed observations. The missed observations model is based on a probabilistic structure. Unlike conventional cases of missed observation in parameter estimation problems, the variance of noise is unavailable, that is the time points of missed observations are unknown, and the probability of missing data needs to be estimated. In this situation, spectral estimation is more difficult to solve and becomes a highly nonlinear optimization problem with many local minima. In this paper, we use the genetic algorithm (GA) method to achieve a global optimal solution with a fast convergence rate for this spectral estimation problem. From the simulation results, we have determined that the performance is significantly improved if the probability of data loss is considered in the spectral estimation problem.