Statistical Analysis of Positioning Errors in Long-Endurance Dual-Axis Rotary Modulation Inertial Navigation System

Abstract

To address the uncertainty in the statistical distribution model of positioning error for the accuracy test of long-endurance inertial navigation systems, a probability distribution model adheres to the statistical rule of the radial positioning error of inertial navigation systems. The probability distribution density function (PDF), cumulative density function (CDF), and characteristic numbers (mean, standard deviation, root-mean-square) of the radial positioning error are derived based on the static-base positioning error of the long-range inertial navigation systems. Methods are provided for estimating the parameters of the probability distribution of the radial positioning errors. The theoretical derivation results demonstrate that the radial positioning error follows the Hoyt distribution. The distribution parameters and the number of features grow linearly with time, while the mean and standard deviation converge to 60% and 80% of the root-mean-square, respectively. Through a large-sample Monte Carlo simulation, the experimental results were consistent with the theoretical derivation results. These results indicate that the theoretical derivation results can be used to optimize the design of the long-endurance rotary modulation inertial navigation system’s accuracy test.