跳变约束下马尔可夫切换非线性系统滤波

Nonlinear filtering for Markov switched systems under jump constraints

针对系统状态演化多模不确定性和状态约束多样性,本文提出了跳变约束下马尔可夫切换非线性系统的交互式多假设估计方法.定义了包含跳变马尔可夫参数可能取值的假设集,根据最优贝叶斯滤波,推导出状态与假设的后验概率递推更新.基于统计线性回归线性化非线性函数,利用伪量测法,将线性化的约束扩维到真实量测中,给出了非线性系统滤波的近似解析最优解.最终给出所提算法的稀疏网格积分近似最优估计实现.在交叉道路机动目标跟踪仿真场景中,所提算法的滤波精度优于基于泰勒展开的交互式多模型算法,基于统计线性回归的交互式多模型算法,以及基于泰勒展开的非线性系统约束滤波算法.

For multi-mode uncertainty of system state evolution and diversity of state constraints,an interactive multihypothesis estimation method for Markov switched systems with jump constraints is proposed.The hypothesis set containing the possible values of the jump Markov parameter is defined.According to the optimal Bayesian filtering,the recursive update of the posterior probability of the state and hypothesis is derived.Based on statistical linear regression,the pseudo measurement method is used to extend the linearized constraint to the real measurement,and the approximate analytical optimal solution of the nonlinear system filtering is given.Finally,an approximate optimal estimation of the sparse grid integral algorithm is presented.In the simulation scenario of crossing road maneuvering target tracking,the filtering accuracy of the proposed algorithm is better than that of the interactive multi-model algorithm based on Taylor expansion,the interactive multi-model algorithm based on statistical linear regression,and the constrained filtering algorithm for nonlinear systems based on Taylor expansion.