High-resolution frequency estimation via a weighted forward and backward autoregressive modelling

A new method for generating the AR process parameters useful for spectral estimation is introduced. The method is based on weighted averaging of forward and backward models with weights proportional to the corresponding average energies of the linear prediction errors. It is demonstrated that improvements in resolution may be so obtained relative to equally weighted forward-backward schemes. It is also shown that this method results in asymptotically consistent estimates for stationary data and in the nonstationary case bounds the influence of the poorer of the forward-backward models. Finally, it is demonstrated that the new technique permits recursive implementation with computational complexity proportional to the AR process order squared.