Spectral estimation based on AR-model excited by t-distribution process

A new spectral estimation method is proposed. Since in the least square L₂ method the obtained estimates are very much affected by the large signal portions, in the proposed method a loss function which assigns large weighting factor for the small residual portions and vice versa is used. The loss function is based on an assumption that the residual signal has an identical and independent t-distribution t(α) with α degrees of freedom to achieve accurate and efficient (low standard deviation) estimates. When α=∞, the conventional L₂ method is obtained. In the calculation, the loss function is modified in a way similar to the autocorrelation method, so that the proposed method can be seen as a generalization of the autocorrelation method. The optimal solution is selected by the Newton-Raphson method. The simulation results show that only a few iterations are needed to reach a stationary point, the stationary point is always a local minimum, and the obtained predictor is stable