"The linear prediction equations can be viewed as extremely simplified cases of the general Kalman filter theory. It would appear that if one were willing to pay a price in complexity, that some benefit should be received. Unfortunately, at the present in any case, the value of Kalman filter theroy for the processing of real speech has not been demonstrated. There are at least two serious problems. First, the computational effort is not merely slightly greater, it is actually enormous for general cases. Second, the use of a priori estimates implies a considerable knowledge of the speech signal. Kalman filter theory has been successfully used in rocket trajectory estimation and correction, for example, because the mathematics of the motion (while not the random disturbances) from start to finish are known. Direct applications to speech modeling implies, loosely speaking, that one knows a priori what the person is about to say! In spite of these problems, Kalman filter theory and sequential estimation techniques have potential for improving upon the linear prediction methods presented. Before such improvements are realized, however, it will be necessary to understand more fully the inherent properties of the speech waveforms and how they relate to the mathematics of Kalman filter theory."
Markel and Gray, Linear Prediction of Speech, Springer:New York, 1976, p. 276.