Dynamical Models for Automobile Movements

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Abstract

The Real-Time Kinematic (RTK) Global Positioning System (GPS) with Kalman filtering estimates the position and velocity of automobiles and so on by using dynamical models. If the dynamical model is not appropriate for automobile movements, the accuracy of the predicted position and velocity decreases. In this case, when the methods statistically test whether cycle slips (i.e., sudden jumps in the carrier phase observation by an integer number of cycles) occur, using the difference between observation and prediction, the inadequate dynamical models cause the mis-detections of cycle slips. To prevent these mis-detections we proposed a dynamical model in which the jerk is assumed to be a first-order Markov process (jerk model), but we did not demonstrate that this jerk model fit the automobile movements. It was therefore necessary to show that the time series data in different time intervals fit the same jerk model i.e., that the jerk model is a stationary autoregressive model. This paper describes the method that decides whether the autoregressive model is stationary. The stationarity of the jerk model is analyzed by using observation data collected with a car. Moreover, the cycle slip detection performance of the jerk model is compared with that of another model, and it is shown that the performance of the jerk model is improved.

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