An ARMA modeling method and its application in Kalman filtering

An ARMA modeling method is proposed to compensate for the random errors of the inertial sensor's output. In the method, the length of samples for modeling was determined by combining runs test method for ensuring the stationarity of the samples with coefficients of variation of sample variances firstly. Then, the random error of the inertial sensor is processed as the colored noise governed by an ARMA model and superimposes by a white noise. The ARMA model parameters are derived by filtering the samples. In the following, the colored noises governed by the ARMA(6, 4) model are simulated to study the effect of the model accuracy on the Kalman filtering performance by comparing the Kalman filtering results of the derived ARMA(6, 4) model with the ones of an approximated AR(2) model. Finally, the model reduction method based on the observability degree analysis is proposed to improve the real time performance of the modeling method with an acceptable accuracy degradation in applications. The modeling method is applied to process the random noise of an accelerometer. The standard deviations of the Kalman filtering residuals of the high-order model and the reduced order model are just 1/66 and 1/28 of one of the unprocessed noise respectively, proving the effectiveness of the modeling method.