A new measurement noise estimation method for autoregressive and moving average modeling

In the existing autoregressive and moving average (ARMA) modeling methods, only the higher-order measurement autocovariances are used to form the Yule-Walker equations, so that the estimation accuracy of measurement noise variance deteriorates due to the unemployment of low-order measurement autocovariances. Moreover, if the AR order p is not greater than the MA order q, the measurement noise variance cannot be estimated in the existing methods. To deal with this problem, we propose a method for estimating the measurement noise variance independently. In this method, the ARMA model is first approximated by a higher-order AR model; then, the Yule-Walker equations of measurement autocovariances are formed with orders starting from one. Because of the full use of statistical information, the estimation accuracy of the measurement noise variance is improved. This not only lays the foundation for improving the accuracy in estimating AR and MA parameters, but also solves the problem occurred when the AR order p is not greater than the MA order q. Simulation and experiment results validated the effectiveness of the method.