导航随机微分模型的三次样条插值求解探索

Cubic spline interpolation for solving navigation stochastic differential model

中文关键词  三次样条  插值函数  贝叶斯估计  导航随机微分模型

英文关键词  cubic spline  interpolation function  Bayesian estimation  navigation stochastic differential model

中文摘要

      提出一种用三次样条插值逼近导航系统状态概率密度函数的方法. 导航随机微分模型的弱解由前向Kolmogorov方程表示, 其解析解很难求得. 本文通过三次样条插值函数来逼近其解可得到状态的先验概率密度函数, 再由Bayes公式得到状态的后验概率密度函数, 解决了构造三次样条插值条件的难点问题, 并以水下潜器组合导航系统为背景, 与粒子滤波方法进行性能对比分析, 仿真结果验证了三次样条插值逼近导航随机微分模型解析解的可行性.

英文摘要

      We propose applying cubic spline function to approximate the probability density function of the state of a navigation system. The weak solution of navigation stochastic differential model is described by the Kolmogorov’s forward equation which is difficult to be solved. This article approaches its solution through cubic spline interpolation functions to obtain a prior probability density function of the state, and then a posterior probability density function is gained through the Bayes formula. Thus, the most difficult problem in forming cubic spline interpolation is solved. By taking the underwater vehicle integrated navigation system as the background and performing the comparison analysis with the particle filter, the feasibility of solving navigation stochastic differential model by using the cubic spline interpolation is confirmed through simulation experiment.