Estimation and Compensation of Heading Misalignment Angle for Train SINS/GNSS Integrated Navigation System Based on Observability Analysis  
[PERSON]  
1 School of Instrumentation Science and Optoelectronic Engineering, Beihang University, Beijing 100191, China; [EMAIL_ADDRESS]  
[PERSON]  
2 School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China  
Inertial navigation systems (INS) measure a train's speed and directional changes using inertial sensors and calculate its current position based on its initial position using dead reckoning [16; 17; 18]. Its advantages include independence from external signals, good real-time performance, reliability even in signal-obstructed environments, and the ability to obtain comprehensive navigation information, including speed, position, and attitude [19; 20; 21]. However, due to the working principle of dead reckoning, INS is susceptible to cumulative errors, which gradually increase over time and require correction through other means [22]. The SINS/GNSS integrated navigation system, consisting of INS and GNSS, leverages information fusion to obtain real-time navigation data for the train, including attitude, speed, and position. By overcoming the issue of INS error divergence over time, this system has the potential to become the new mainstream equipment for train speed and location measurement [23; 24; 25]. However, based on an observability analysis, it is inferred that, during a uniform straight-line motion, the heading misalignment angle of the train SINS/GNSS integrated navigation system is unobservable, leading to a significant problem of large heading misalignment angles that ultimately causes a low precision in train speed and position estimation [26; 27]. The errors in inertial navigation solution are also strongly correlated with the dynamic characteristics of the moving platform [28]. For a train, which is constrained to a one-dimensional motion on the track, its motion trajectory can be decomposed into straight lines and curves, with its motion on the track mainly divided into acceleration and deceleration phases and uniform motion phases [29]. Therefore, the errors in inertial navigation solution can be analyzed through the decomposition and combination of the train's motion trajectory and dynamic modes. Using an observability analysis, it is found that the heading misalignment angle during the most dominant motion mode of the train, i.e., uniform straight-line motion, is unobservable when aided by position and velocity information [30; 31]. When entering a satellite signal blockage scenario, the accumulated heading misalignment angle will have a cubic impact on the train's position accuracy and a quadratic impact on the train's speed accuracy with respect to the navigation time [32]. The estimation of attitude is closely related to the maneuvering mode of the moving platform, especially the estimation of the heading angle. By analyzing the train's motion modes, it is observed that pitch and roll angles are strongly observable, and thus, the roll and heading angles can be accurately estimated throughout the entire train route [33]. However, the heading angle is unobservable during the train's uniform straight-line motion, which severely affects the accuracy of position and speed estimation when satellite signals are lost. To solve this problem, this paper proposes an estimation and compensation method for the train SINS/GNSS integrated navigation system based on an observability analysis. As the train's motion is constrained to the track, the velocity heading angle will be highly accurate under high-speed conditions. This paper primarily utilizes this valuable information to estimate the zenith gyro zero bias, thereby achieving the precise estimation of the heading misalignment angle. Depending on the different track segments of the train's movement, the observability of the heading angle continuously changes.