A new method of seamless land navigation for GPS/INS integrated system
Highlights
► We establish a INS/GPS/integrated navigation based on neural network and wavelet. ► Neural network can make the system work seamlessly during GPS outages. ► Wavelets can de-noise the errors of the signal which are the outputs of the NN. ► By re-training NN with WMRA, system accuracies have been improved. ► The method proposed can improve the approximation closer to the actual model.
Introduction
Vehicle navigation technology has attracted increasing attention in recent years. Many navigation systems use a global positioning system (GPS) to obtain precise velocity and position information. GPS receivers must track four satellites in order to achieve good performance; however, such conditions cannot be met in many circumstances. For example, weak GPS signals may reduce system accuracies of vehicles in an urban canyon. The strapdown inertial navigation system (SINS) is an autonomous system, which includes three accelerometers and three gyroscopes that measure the linear acceleration and angular rate of the motion of vehicles, respectively. However, system errors may increase with time because of noise, dependent random noise, bias instability error, and random-walk error.
To mitigate the shortcomings of using a single navigation system, SINS is usually integrated with GPS or other sensors. GPS can improve the performance of SINS and prevent the increase of errors through its long-term and stable precision characteristics. SINS also possesses excellent short-term precision, which can aid in solving GPS-related problems, such as cycle slips and clock errors. The Kalman filter (KF) is used in information fusion algorithm under the conditions that the dynamic model of the system error, the stochastic model of the transducer error, and prior knowledge about standard data deviation are exactly known. Although KF is used generally as a standard algorithm for an integrated navigation system, the following issues have to be considered: (1) acquiring an accurate stochastic model; (2) obtaining all alternate transducers that can provide an accurate system model and prior knowledge of the measurement errors that are very important factors in achieving system precision; and (3) system precision is generally depends on INS quality during long-term outages of GPS signals.
Due to the disadvantages of KF, many researchers have studied other feasible solutions that focus on artificial intelligence (AI) technology. Chiang et al. [1], [2] introduced the velocity–position error (V–δP) and heading angle–position error (φ–δP) modules that set velocities and heading angle as the input and position errors as the output. However, the authors only assessed positioning precision without correcting the attitudes and velocities of the vehicle; moreover, that paper did not attempt to prevent the effect of noise on the training accuracy of the neural network (NN). Sharaf et al. [3] introduced a position–position error (P–δP) module using radial basis function (RBF) structures. Although the author introduced wavelet-based de-noising to reduce the effect of noise on the system, using all the data of SINS and GPS to train RBF increased the computational burden and influenced the real-time performance. Furthermore, the module only corrected the position error, whereas the precision of other parameters have not been evaluated. El_Shafie et al. [4] and Ahjebory et al. [5] introduced an adaptive neuro-fuzzy inference system (ANFIS) to assist the P–δP module in a mobile multi-sensor system. Sharaf et al. [6] combined SINS and GPS data based on ANFIS; however, the high noise and instability of micro-electo-mechanical system (MEMS) sensors affected the system precision. Semeniuk and Noureldin [7] proposed an AI-based segmented forward predictor method. This method provided forecast errors using RBF NN to combine position and velocity segment information from SINS and GPS.
The current paper aims to introduce a method of wavelet-based NN (WBNN) [8] to provide attitude and position information during GPS outages. Back-propagation NN (BPNN) and wavelet multi-resolution analysis (WMRA) are applied to a SINS/GPS/magnetometer integrated navigation system. BPNN can predict observation values for KF, and WMRA can enhance the approximation of NN to the actual model.
Section snippets
Wavelet de-noising
Recently, wavelet analysis has become a widely used method in various fields of signal processing. It has the advantage of possessing localization properties in time and frequency domains [9], [10]. In the 1990s, it was applied in all areas of geodesy, such as gravity field approximation, filtering and prediction, deformation monitoring, numerical computing, and data interpretation [11]. The wavelet analysis with threshold is the first technology used in the domain of wavelet de-noising and can
System structures
Based on the above mentioned theory, the AI method based on wavelet de-noising technology was applied to the SINS/GPS/magnetometer integrated system. The method can continuously provide attitude and position information of vehicles even during GPS outages. Fig. 1a shows the system structure when GPS works well, that is, when SINS provides attitude, velocity and position information; GPS provides velocity and position information; and the magnetometer provides the heading angle. These data are
Error modelling
The psi-angle position, velocity, and attitude errors are given below.
Psi-angle error is given by:where ϕn = [ϕEϕNϕU]T is the orientation error of the calculated platform represented in the local East–North-Upward ENU coordinate frame; represents the rotation projections of the Earth onto the ENU axes; ωe = 7.292115 × 10−5 rad/s represents the angular velocity of the rotation of the Earth; represents the angular
Test setup
To evaluate the performance of the intelligent navigation system, several tests were conducted by the advanced navigation system research group of Southeast University (Nanjing, China). These tests were conducted on a land vehicle platform equipped with different SINS/GPS integrated systems. These systems consisted of a navigation grade INS PHINS of IXSEA Corporation, a fiber optical gyro (FOG)–INS designed by Southeast University, a magnetometer, and a TRIUMPH-1 GPS receiver of JAVAD
Conclusions
The present article proposed an SINS/GPS/magnetometer integrated method under unfavorable GPS conditions by incorporating artificial neural networks and wavelet de-noising technology. The performance of this technique was evaluated based on field tests in urban areas, whereby the arcmin level attitude accuracies and position accuracy within a few meters were obtained.
The proposed method, known as the intelligent navigator, utilizes GPS position, velocity, and heading angle of the magnetometer
Acknowledgments
This work was supported in part by the National Natural Science Foundation (60904088), the Foundation of Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology of the Ministry of Education (201008), and the Electronic Information System Integration Laboratory Fund of Shanxi Province (201101Y19), Key Projection Guidance Fund of Southeast University Research Basic Operating Expenses (3222001102).
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