可观测度的探讨及其在捷联惯导系统可观测性分析中的应用

摘要

可观测度是为了分析线性系统中组合状态的可观测程度而提出来的,在卡尔曼滤波的滤波效果分析中得到了应用.文中先对已有的两种可观测度分析方法进行了简述,并且分析了两种方法的等价性；然后从理论上分析了此描述方法的不全面性.通过典型例子说明了理论分析的结果,给出了一种更全面的描述系统可观测组合状态可观测度的方法,并且用新的描述方式分析了捷联惯导系统的各状态可观测度.结果表明,该数值刻画方式能够定量的给出系统状态可观测的程度,是解析分析方法的很好的补充.%The degree of observability was proposed to analyze the observable degree of the combined states of linear systems. It was applied in the analysis of the efficacy of the Kalman filter. Two existed methods for calculating the degree of observability were introduced, and the equivalence of the two methods was proved. The deficiencies of the existed methods were analyzed from a theoretical perspective, and a typical example was given to verify the theoretical results. A new method to determine the degree of observability of the combined states was given which was more comprehensive than that of the existed ones. In the end, the new method was applied to the observability analysis of strapdown inertial navigation systems. The results demonstrate that the new method can quantify the observable degree of the states of the system and is a great complement to the analytic method.