An Efficient Method for Estimation of Autoregressive Signals Subject to Colored Noise

The problem of unbiased estimation of autoregressive (AR) signals subject to colored noise is investigated. The previously proposed improved least-squares method for colored noise (called ILS-CN) is revisited. This leads to derivation of a new system of bilinear equations with respect to the AR parameters and the colored observation noise autocovariances. It is shown that separate estimations of the AR parameters and the autocovariance vector of the colored observation noise can be made by using the separable least-squares method to solve the derived system of bilinear equations. The new estimation method is superior to the previous ILS-CN method in that there is no need to alternate estimations between the AR parameters and the colored observation noise autocovariances; and it can enhance the accuracy of the AR parameter estimates by forming an overdetermined system of bilinear equations. Computer simulations verify the theoretical predictions.