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1、 7.3918%,30.912%和7.3677%,34.082%之间，便于以后在工程中的应用。同时，对演化 Kalman 滤波在 INS/GPS 组合导航系统的应用进行了初探。 本文的主要创新之处在于: 1) 提出一种新的基于正交设计的差分演化算法; 2) 指出了 演化函数优化与演化 Kalman 滤波之间的关系; 3) 提出了演化 Kalman 滤波的理论框架, 并 把三个不同的演化算法应用到演化 Kalman 滤波中测试其性能; 4) 对基于演化 Kalman 滤波 的 INS/GPS 组合导航系统的原理进行了初探，提出了相应的原理框架。 本文的主要章节安排如下: 第一章主要介绍了演化算法
2、与优化计算的一些背景知识，并介绍了演化算法的一些特 性；同时，简要介绍了 Kalman 滤波理论的背景及其在组合导航中的应用。 第二章主要介绍Kalman滤波器的理论基础， 基本方程及其一些改进的Kalman滤波器。 同时，介绍 Kalman 在组合导航中的一些应用。 第三章重点介绍了差分演化算法的基本原理，同时把正交设计的思想引入到差分演化 算法中， 对差分演化算法进行改进， 并把改进差分演化算法应用到函数优化问题的求解中。 第四章指出了演化 Kalman 滤波与演化函数优化之间的联系， 并提出演化 Kalman 滤波 器的基本设计思路；给出本文中应用到的演化 Kalman 滤波器的详细设计
3、方法；把郭涛算 法、基本差分演化算法和改进的差分演化算法应用于演化 Kalman 滤波器中，并把此演化 Kalman 滤波器应用到一个具体实例中，测试算法的性能。同时，对演化 Kalman 滤波在 INS/GPS 组合导航系统的应用进行了初探。 第五章为本文总结部分，对本文的工作进行了总结，并对未来工作提出了一些设想。 关键词：演化算法；Kalman 滤波；差分演化算法；正交设计；组合导航 RESEARCH ON EVOLUTIONARY KALMAN FILTER AND ITS APPLICATION Master Candidate：Wenyin Gong Supervisor：Prof
4、. Zhihua Cai ABSTRACT Evolutionary algorithms (EAs) are search methods that take their inspiration from natural selection and survival of the fittest in the biological world, which have many characteristics such as self-organization, self-adaptive, robustness, universality, the thought simply, easy
5、to implement, the effective and efficient application and so on. It suits massively parallel because it is a generic population-based metaheuristic optimization algorithm. Evolutionary algorithm has been widely applied in the different scientific domain and engineering optimization, in which evoluti
6、onary optimization is one direction. The Kalman filter is a real-time recursion algorithm, which realizes by the computer. It processes the object with the random signal. And it uses the statistical property of the system noise and the observation noise to process the signal. Kalman filter applies t
7、he system observation as the input of the filter and the estimation (system state or parameter) as the output. Between the input and the output of the filter it processes the signal according to the system equation and the observation equation. Not only it may carry on the process to the steady uni-
8、dimensional stochastic process, also it can estimate the non-steady, the multi-dimensional stochastic process, therefore its application is very widespread. The Kalman filter is widely used in stochastic optimum control, breakdown diagnosis and so on, in which INS/GPS navigation system design is a s
9、uccess application of it. In this thesis, firstly, I briefly introduce the background of the Evolutionary Algorithm (EA) and Kalman filter. Secondly, a novel Differential Evolution algorithm (DE) based on the orthogonal design method is proposed in order to make DE more robust and faster. Moreover,
10、ODE can make the Evolutionary Kalman Filter (EvoKF) more effective and efficient. The ODE combines the conventional DE (CDE), which is simple and efficient, with the orthogonal design, which can exploit the optimum offspring. The ODE has some features. 1) It uses a robust crossover based on orthogon
11、al design and an optimal offspring is generated with the constrained statistical optimal method. 2) To decrease the number of the orthogonal design and make the algorithm converge faster, decision variable fraction strategy is applied here. 3) It uses simple diversity rules to handle the constraints
12、 and maintain the diversity of the population; 4) A multi-parent hybrid adaptive-crossover-mutation operator based on the non-convex theory is proposed, which can enhance the non-convex search ability. 5) The ODE simplifies the scaling factor F of the CDE, which can reduce the parameters of the algo
13、rithm and make it easy to use for engineers. We execute the proposed algorithm to solve 12 benchmark functions with low or high dimensions and very large numbers of local minima. Through comparison with some state-of-the-art evolutionary algorithms, the experimental results demonstrate that the perf
14、ormance of the ODE outperforms other evolutionary algorithms in terms of the quality of the final solution and the stability; and its computational cost (measured by the average number of fitness function evaluations) is lower than the cost required by the other techniques compared. Thirdly, in Chap
15、ter 4, the basic principle of the evolutionary Kalman filter (EvoKF) is proposed. To estimate the performance of the EvoKF, we employ the Guos algorithm (GT) and the conventional Differential Evolution (CDE) algorithm in the EvoKF after I point out the relationship between function optimization and
16、EvoKF. Simulations indicate that the three proposed EvoKF (DEKF, GTKF, and ODEKF) can improve the performance compared on the conventional Kalman filter both in exact estimation value and in non-exact estimation value. Meanwhile, I propose the principle of the EvoKF to apply in INS/GPS elementarily. The main innovations of this thesis are: 1) A novel DE algorithm based on the orthogonal design method is proposed. 2) I point out the rela
