Two-stage signal reconstruction under unknown parameters and missing data

This paper considers the signal reconstruction problem under unknown parameters and nature missing data. The solution is divided into two stages. At the first stage, the parameter estimation of autoregressive moving average (ARMA) model with nature missing data is studied. In the second stage, a robust Kalman filter to reconstruct the input signal is developed. The missing data model is based on a probabilistic structure with unknown. In this situation, the estimation becomes a highly nonlinear optimization problem with many local minima. In this paper, we combine the global search method of genetic algorithm and simulated annealing (GA/SA) to achieve a global optimal solution with fast convergent rate. After the system parameters are exactly estimated in the first stage, the problem of reconstructing the missing signal can be handled elegantly using the proposed robust Kalman filter in the second stage.