Non-initial attitude error analysis of SINS by error closed-loop and energy-level constructing

For the optimization and algorithm design of high precision strapdown inertial navigation system (SINS), a systematic and fine attitude error analysis method is needed. To this end, a closed-loop method and an energy-level method are proposed to analyze the non-initial attitude estimation error of SINS. The closed-loop method is constructed from the basic angular velocity error equation in which angular velocity error is combined with angular velocity and rotation estimate to form a closed loop. This makes it the first time to realize the complete (theoretically unbiased) analysis of SINS rotation estimation error. The energy-level method is constructed from the energy level of angular motion which is expressed as the series expansion of rotation estimate under the defined motion such as coning and maneuvering motion. This enables us to finely analyze the error of any existing multi-sample coning algorithm based on Taylor-series method. The theoretical basis, establishment process and instructions of two methods are given in order in the paper. The detailed process of proof and reasoning of the two methods are given in Appendixes A, B, C and D. Several cases of attitude error analysis based on the proposed methods and simulation examples verify the correctness of the analysis results from the proposed method and the applicability of the proposed method, which provides a systematic analysis tool for the design of SINS and attitude algorithm.