SINS/GNSS Integrated Navigation Based on Left Equivariant Error Model in Inertial Frame

Abstract

Reliable and continuous vehicle positioning in urban canyons remains a critical challenge for intelligent transportation systems. To address this issue, this article presents a left equivariant error model for strapdown inertial navigation system and global navigation satellite system (SINS/GNSS) integrated navigation in the inertial frame. Unlike the imperfect invariant extended Kalman filter and its variant, the proposed method copes with the biases states in a more natural way. Also, different from the current equivariant filter based SINS/GNSS integrated navigation, the linearized measurement matrices of this method are independent of the system’s position. This method allows the initial alignment stage and integrated navigation stage to be combined into one stage, enabling faster and more accurate navigation results in challenging urban settings. Firstly, we introduce the two-frame group and associated group actions on the state space and input space of the biased INS from the perspective of left equivariant filter. Secondly, we derive the left equivariant error dynamics in inertial frame and the measurement models for both loosely coupled (LC) SINS/GNSS and tightly coupled (TC) SINS/GNSS, respectively. Thirdly, we conduct the simulation and field test to evaluate the practical performance of the proposed method. Experimental results demonstrate that the proposed method achieves superior transient response in urban canyon environments compared to conventional approaches, enabling reliable one-step alignment and continuous positioning for intelligent vehicles operating in complex traffic scenarios.