3种确定性采样非线性滤波算法的复杂度分析

张召友, 郝燕玲, 吴旭

(哈尔滨工程大学 自动化学院, 150001 哈尔滨)



摘要:

为考察非线性卡尔曼滤波在SINS／GPS组合导航中的实时性问题,对无迹卡尔曼滤波(UKF)、中心差分卡尔曼滤波(CDKF)和容积卡尔曼滤波(CKF)3种常用确定性采样非线性算法的实现复杂度进行了理论分析,并总结了实时性选择的依据．根据确定性采样卡尔曼滤波的统一迭代步骤,以等效浮点操作数作为评价准则对3种算法进行了复杂度分析,导出了精确计算复杂度的表达式,并进一步对三者之间的差异进行了推导．将上述算法应用于SINS／GPS紧耦合导航中,并进行了蒙特卡罗仿真.结果表明:3种算法的精度一致,UKF复杂度最高,在状态维数高于量测维数的系统中CKF复杂度最低,但在高维量测系统中CDKF可望获得最小的硬件开销．

关键词:  确定性采样  非线性  卡尔曼滤波  复杂度  组合导航

DOI：10.11918/j.issn.0367-6234.2013.12.020

分类号:

基金项目:国家自然科学基金资助项目(60834005).



Complexity analysis of three deterministic sampling nonlinear filtering algorithms

ZHANG Zhaoyou, HAO Yanling, WU Xu

(College of Automation, Harbin Engineering University, 150001 Harbin,China)

Abstract:

To study the real time problem of nonlinear Kalman filter in SINS／GPS integrated navigation system, the complexity of three usual deterministic sampling nonlinear Kalman filters (UKF, CDKF and CKF) is analyzed and a selection basis is summarized. Numbers of floating-point operations (flops) of the three algorithms are counted according to unified filtering steps, so the accurate expressions of computing complexity are gotten. And a further derivation of the complexity differences among three algorithms is carried out. The aforementioned algorithms are applied in SINS／GPS tightly coupled navigation. Monte Carlo simulation results indicate that three algorithms have similar precision, UKF has the biggest complexity and the complexity of CKF is lower than that of CDKF when the dimension of system states is larger than measurement, and CDKF can get the lowest complexity in some high-dimensional measurement systems.

Key words:  deterministic sampling  nonlinear  Kalman filter  complexity  integrated navigation