在导航、定位等研究领域会用到一类具有线性、非线性混合状态的模型。其特点为量测方程仅是某些状态的非线性函数,而状态方程是线性或弱非线性方程组。这类问题可通过状态分解的Rao-Blackwellised思想求解,它是非线性状态用粒子滤波求解、非线性状态粒子给定下边缘出线性状态,用解析的方法Kalman滤波求解。文中对此进行理论研究并给出算法过程。通过对水下重力梯度辅助导航研究,发现满足此类模型条件,故应用此算法进行仿真,把它与APO-PF(人工物理优化粒子滤波)算法在相同初始误差条件进行比较研究。结果表明,该算法对于水下重力梯度组合导航更加高效。

It is to use the certain kind of model with mixed linear and nonlinear state in current navigation. Its characteristic is that measure function is a nonlinear function of some states and state equation is linear or weak nonlinear system of equations. The problem can be solved through marginal particle filter with state decomposition. The problem is solved through state decomposition of Rao-Blackwellised theory, which nonlinear state is got by particle filter. On the basis particle of nonlinear state, marginalize out linear state, which solved analytically through Kalman filter. The article provides theory study and demonstrates the flow of algorithm. With the study of underwater gravity gradient aided navigation, its condition meets on the condition of this method. So give simulation application of it, and have a comparison with APO-PF in the same large initial position error, the result indicates that the algorithm has a high efficient effect on the underwater gravity gradient navigation.