Abstract
This paper deals with the problem of state estimation for the vector-tracking loop of a software-defined Global Positioning System (GPS) receiver. For a nonlinear system that has the model error and white Gaussian noise, a noise statistics estimator is used to estimate the model error, and based on this, a modified iterated extended Kalman filter (IEKF) named adaptive iterated Kalman filter (AIEKF) is proposed. A vector-tracking GPS receiver utilizing AIEKF is implemented to evaluate the performance of the proposed method. Through road tests, it is shown that the proposed method has an obvious accuracy advantage over the IEKF and Adaptive Extended Kalman filter (AEKF) in position determination. The results show that the proposed method is effective to reduce the root-mean-square error (RMSE) of position (including longitude, latitude and altitude). Comparing with EKF, the position RMSE values of AIEKF are reduced by about 45.1%, 40.9% and 54.6% in the east, north and up directions, respectively. Comparing with IEKF, the position RMSE values of AIEKF are reduced by about 25.7%, 19.3% and 35.7% in the east, north and up directions, respectively. Compared with AEKF, the position RMSE values of AIEKF are reduced by about 21.6%, 15.5% and 30.7% in the east, north and up directions, respectively.
Highlights
Traditional Global Positioning System (GPS) receivers utilize scalar tracking loops (STL) to track the received GPS signals
In order to overcome these problems, the noise statistics estimator is employed in the iterated extended Kalman filter (IEKF)
As mentioned in the previous section, the GPS receiver position error, velocity error, receiver clock bias and clock drift terms consist of the adaptive iterated Kalman filter (AIEKF) state vector, while the code phase and carrier frequency discriminator outputs are the measurement of AIEKF
Summary
Traditional Global Positioning System (GPS) receivers utilize scalar tracking loops (STL) to track the received GPS signals. In order to overcome this problem, unscented Kalman filter (UKF) [12] and iterated EKF (IEKF) [13] are proposed. The UKF employs a deterministic sampling technique known as the unscented transform to pick a minimal set of sample points (so called sigma points) around the mean These sigma points are propagated through the non-linear functions, from which the mean and covariance of the estimate are recovered [14]. In order to overcome this problem, the IEKF is proposed to reduce the bias and the estimation error by increasing only a few simple iterative operations [9,10,11]. The AIEKF which combines the advantages of the Adaptive EKF (AEKF) [9] and the IEKF is proposed for the VTL GPS receiver.
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