Research On Evolutionary Kalman Filter And Its Application

Evolutionary algorithms (EAs) are search methods that take their inspiration from naturalselection and survival of the fittest in the biological world, which have many characteristics suchas self-organization, self-adaptive, robustness, universality, the thought simply, easy toimplement, the effective and efficient application and so on. It suits massively parallel because itis a generic population-based metaheuristic optimization algorithm. Evolutionary algorithm hasbeen widely applied in the different scientific domain and engineering optimization, in whichevolutionary optimization is one direction.The Katman filter is a real-time recursion algorithm, which realizes by the computer. Itprocesses the object with the random signal. And it uses the statistical property of the systemnoise and the observation noise to process the signal. Kalman filter applies the systemobservation 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 systemequation and the observation equation. Not only it may carry on the process to the steadyuni-dimensional stochastic process, also it can estimate the non-steady, the multi-dimensionalstochastic process, therefore its application is very widespread. The Kalman filter is widely usedin stochastic optimum control, breakdown diagnosis and so on, in which INS/GPS navigationsystem design is a success 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 theorthogonal design method is proposed in order to make DE more robust and faster, Moreover,ODE can make the Evolutionary Kalman Filter (EvoKF) more effective and efficient. The ODEcombines 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 robustcrossover based on orthogonal design and an optimal offspring is generated with the constrainedstatistical 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 simplediversity rules to handle the constraints and maintain the diversity of the population. 4) Amulti-parent hybrid adaptive-crossover-mutation operator based on the non-convex theory isproposed, which can enhance the non-convex search ability. 5) The ODE simplifies the scalingfactor F of the CDE, which can reduce the parameters of the algorithm and make it easy to usefor engineers. We execute the proposed algorithm to solve 12 benchmark functions with low orhigh dimensions and very large numbers of local minima. Through comparison with somestate-of-the-art evolutionary algorithms, the experimental results demonstrate that theperformance of the ODE outperforms other evolutionary algorithms in terms of the quality of thefinal solution and the stability; and its computational cost(measured by the average number offitness function evaluations) is lower than the cost required by the other techniques compared.Thirdly, in Chapter 4, the basic principle of the evolutionary Kalman filter (EvoKF) is proposed.To estimate the performance of the EvoKF, we employ the Guo's algorithm (GT) and theconventional Differential Evolution (CDE) algorithm in the EvoKF after I point out therelationship between function optimization and EvoKF. Simulations indicate that the threeproposed EvoKF (DEKF, GTKF, and ODEKF) can improve the performance compared on theconventional 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 orthogonaldesign method is proposed. 2) I point out the relationship between function optimization andEvoKF. 3) I propose the basic principle of EvoKF and test its performance using threealgorithms. And 4) I propose the principle of the EvoKF to apply in INS/GPS.The main chapters are as follows:Chapter 1, we mainly introduced the background knowledge of the evolutionary algorithm andthe optimization computation, and introduced some characteristics of the evolutionary algorithm.At the same time, we briefly introduced the background of the Kalman filter theory and itsapplication in INS/GPS navigation system.Chapter 2, the theory of the Kalman filter, its basic equations and some improved Kalmanfilters were introduced. Meanwhile, we introduced the application of the Kalman filter inINS/GPS navigation system.Chapter 3, we introduced the basic theory of the conventional Differential Evolution. Also, weproposed a novel Differential Evolution based on the orthogonal design method (ODE) to makeDifferential Evolution faster and more robust. To test the performance of ODE, we tested it on anumber of benchmark function optimization problems.Chapter 4, we proposed the principle of the evolutionary Kalman filter (EvoKF) and pointedout the relationship between EvoKF and the evolutionary function optimization. Also weintroduced the design method of the EvoKF in detail, including how to design the fitnessfunction, how to encode and decode the individual, and how to deal with the constraints.Thereafter, we use the GT, CDE and ODE in the EvoKF with a simulation example to test theperformance of the EvoKF. Meanwhile, we proposed the evolutionary INS/GPS navigation system based on the EvoKF proposed above.Chapter 5, we summarized the main work of this thesis and described our future work.