A NEW ROBUST TWO DIMENSIONAL SPECTRAL ESTIMATION BASED ON AN AR MODEL EXCITED BY A t DISTRIBUTION PROCESS AND ITS QR-DECOMPOSITION RECURSIVE ALGORITHM

Abstract

In this paper a novel robust two dimensional spectral estimation based on an AR model is proposed. The robustness of the method is obtained by assuming that the output or the residual signals are independently and identically distributed (IID) t-processes with small; α degrees of freedom. By doing so, the effect of large amplitude residuals is reduced. To reduce the calculation burden, the optimal solution is recursively calculated by incorporating the QR-decomposition method. The optimal solution is updated each time the number of input samples grows. Simulation results show that when the excitation is Gaussian, the obtained estimate by using large and small α are comparable. On the other hand, when the excitation is impulsive, the obtained estimate after 100 by 100 pixels iterations by using small α ; i.e. α = 3; is more accurate than that obtained by using α = ∞ which is applied in the conventional least square approach. The plots of the mean square error (MSE) show that by using small α we can achieve smaller MSE's than that by using large α.