Abstract
To improve the standard point positioning (SPP) accuracy of integrated BDS (BeiDou Navigation Satellite System)/GPS (Global Positioning System) at the receiver end, a novel approach based on Long Short-Term Memory (LSTM) error correction recurrent neural network is proposed and implemented to reduce the error caused by multiple sources. On the basis of the weighted least square (WLS) method and Kalman filter, the proposed LSTM-based algorithms, named WLS–LSTM and Kalman–LSTM error correction methods, are used to predict the positioning error of the next epoch, and the prediction result is used to correct the next epoch error. Based on the measured data, the results of the weighted least square method, the Kalman filter method and the LSTM error correction method were compared and analyzed. The dynamic test was also conducted, and the experimental results in dynamic scenarios were analyzed. From the experimental results, the three-dimensional point positioning error of Kalman–LSTM error correction method is 1.038 m, while the error of weighted least square method, Kalman filter and WLS–LSTM error correction method are 3.498, 3.406 and 1.782 m, respectively. The positioning error is 3.7399 m and the corrected positioning error is 0.7493 m in a dynamic scene. The results show that the LSTM-based error correction method can improve the standard point positioning accuracy of integrated BDS/GPS significantly.
Highlights
Over the past few years, satellite navigation technology has achieved rapid development, but there are still some problems to be solved in some aspects
The positioning root mean square error of WLS in the X-axis direction is slightly lower than the Kalman filter, while the positioning root mean square error of the Kalman filter in the Y-axis and Z-axis directions is slightly lower than the weighted least square method
The root mean square error of WLS is higher and the correlation coefficient is smaller than the Kalman filter in both training set and testing set on the three axes, which illustrates that the performance on the prediction of Kalman filter is better than the prediction of WLS on three axes
Summary
Over the past few years, satellite navigation technology has achieved rapid development, but there are still some problems to be solved in some aspects. PPP is a solution to solving the position using precise ephemeris, precise satellite orbit and precision satellite clock and dual-frequency carrier phase observations [5,6] It can be divided into non-differential PPP and differential PPP according to the data processing [7,8,9]. Since the SPP solution process is a sequential data problem, the LSTM network can be used to reduce the error caused by multiple sources, including satellite clock error, ephemeris error, ionosphere and tropospheric delays, multi-path effect and the receiver error. A novel standard point positioning approach to integrate BDS/GPS (all GNSS systems would be applicable), which uses the learning method to predict the multi-source error as a whole, is proposed to reduce the multiple sources errors.
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