Gradient Descent Optimization-Based SINS Self-Alignment Method and Error Analysis

In this paper, the self-alignment for stationary strapdown inertial navigation system (SINS) is formulated as an optimization problem, and two gradient descent optimization-based SINS self-alignment methods (GD1 and GD2) are proposed. The highlight lies in that two quaternion-based objective functions are firstly formulated to solve the stationary SINS self-alignment problem. Different from conventional initial alignment methods, we firstly construct a quaternion-based objective function for stationary SINS using gravity, Earth rate and local latitude information in GD1, and employs gradient descent method to achieve the minimum of the objective function. Secondly, we further improve the quaternion-based objective function in GD2 by using the measurements from IMU to represent the Earth rate instead of using the local latitude directly. Thus, GD2 method is more competent for SINS self-alignment when the local latitude information is not available. In addition, we also analyze the bias errors of accelerometer and gyroscope and the quaternion normality error for GD1 and GD2 method respectively. Moreover, based on the analysis results, a scale factor is also introduced to reduce the alignment errors of GD1 caused by gyroscope biases. Simulation and static experiment are implemented to test the performances of GD1 and GD2 method, and the results verify the accuracy and speed of the proposed methods.