SVD可观测度分析方法的改进及组合导航中的应用

Improvement of observable degree analysis method based on SVD and application in integrated navigation

摘要:

为解决已有的基于线性时变系统可观测性矩阵奇异值分解（SVD）的可观测度分析方法中存在的依靠外部量测信息、状态量纲比较不一致、奇异值基准不唯一的问题,提出一种改进的基于SVD理论的系统状态可观测度分析方法. 首先阐述了线性时变系统与分段式线性定常系统（PWCS）之间的关系,并介绍了PWCS可观测性分析理论,在满足该定理要求的情况下,通过PWCS的提取可观测性矩阵（SOM）替代总可观测性矩阵（TOM）可以有效降低分析计算的复杂度. 然后由系统提取可观测性矩阵SVD分解及其得到的奇异值与对应奇异向量,对系统的观测方程进行推导,根据载体不同机动情况下同一状态观测程度的纵向比较计算得到系统各状态的可观测度指标. 最后采用SINS/DVL组合导航系统进行仿真验证. 仿真结果表明, 通过该方法计算的可观测度指标与Kalman滤波状态估计误差特性相符,证明该改进方法可预见及准确描述状态的估计效果,并且依据所计算的状态可观测度进行系统自适应反馈校正,可以有效提高导航精度.

Abstract:

To solve the problems existing in the observable degree analysis method based on the SVD of the observable matrix of linear time-varying systems, such as the inconsistency of state dimensions and the nonuniqueness of singular value reference, an improved method was proposed. First, the relationship between linear time-varying system and piecewise linear constant system (PWCS) was expounded, and the PWCS observability analysis theory was introduced. Under the condition of satisfying the theorem, the complexity of the analytical calculation could be effectively reduced by the stripped observability matrix (SOM) instead of the total observability matrix (TOM). Then, the SVD of SOM and its singular value as well as the corresponding singular vector were extracted by the system. Next, the observation equation of the system was deduced, and the observability index of each state of the system was obtained according to the longitudinal comparison of the observation degree of the same state under different maneuver conditions of the carrier. Finally, the SINS/DVL integrated navigation system was used for simulation verification. Simulation results show that the observability index calculated by this method was consistent with the Kalman filter state estimation error characteristics, which proves that the improved method can predict and accurately describe the state estimation effect. Meanwhile, the system adaptive feedback correction was performed according to the calculated state observability, which could effectively improve the navigation precision.