The Design And Applications Of Unscented Kalman Filter Based On Support Vector Regression

With the development of science and technology, the application of engineering becomes more and more complex. In order to guarantee the precision of the engineering construction, a large number of filtering technology is used in the process of design and implementation. Filtering technology is still developing as the scope of the engineering application more and more widely. And it’s been widely used in target tracking, satellite navigation, space orientation, image processing, engineering control and other engineering fields. In response to a variety of complex data application environment, the filtering technology is used in combination with many the new theories and the new methods which can extend filtering applications, optimize the filter structure, and improve the filtering performance. Such as the Wiener filter and Kalman filter only used in linear system, but now there are many filter as extended Kalman filter,particle filter,Unscented Kalman filter and differential filter etc also can be used in complex nonlinear system. These new types of filters play an important role in all kinds of engineering application.Kalman filter is a linear system by the theory of optimal estimation theory to get a kind of state space method in time domain. Consists of a set of recursive filtering algorithm, the algorithm has a small amount of calculation, the characteristics of small storage capacity, simple structure, easy to realize ideal for using computer to calculate. But Kalman filter conditions are calculated by using Bayesian recursive relationship state probability density functions, obtained from the probability density function is detailed information of system state estimation method is only applicable to linear system. But the practical engineering application cases always are non-linear. In order to solve the problem that applications of filter used in nonlinear system, to estimation the state of nonlinear random system accurately. Many people carried out extensive and in-depth research. The approximate method can only be used in the nonlinear model. The nonlinear estimation accuracy is depends on the degree of approximation method was applied to real data. There are many filters used in nonlinear system, the most commonly used are Extended Kalman filter (EKF), Particle filter (PF) and Unscented Kalman filter (UKF). The UKF is the best one of them. Compared with the EKF, UKF does not need to truncated high-order item and calculate the Jacobi matrix, so practicability and precision should be significantly better than EKF. Compared with PF, the uncertainty of sampling of UKF is better than random sampling strategy of PF, which doesn’t appear particle degradation phenomenon, with the higher approximation effect and stability.Because of the excellent performance, UKF can be applied to many engineering fields to solve nonlinear filtering problem. But there are some problems have to solve. In order to make the model has better generalization and robustness, majority filtering model is set up parameters control to adjust filter characteristics, to satisfy different condition. UKF the deterministic sampling, producing a set of weights with Sigma point, through the different weights of Sigma point by the state equation and observation equation transformed statistics as estimated values. There is a scaling factor which used determines the scope of the sampling points and weights need to define. Scaling factor for unscented transformation has a great influence on the effect of the nonlinear approximation. By mathematical method and experiments, we get the conclusion that if the scaling factor is bad, the Sigma point distribution deviates from the true value, resulting in a decline in approximation effect is poorer filtering precision. In extreme circumstances can make the filter divergence. So the scaling factor is an important parameter which needs to set up carefully. In conventional methods the factor is a fixed value which set based on the system dimension, and the effect is not good. Although the scaling techniques is added in the improved algorithm, which can eliminate the unscented transform when sampling the nonlocal effect to ensure that the covariance matrix is qualitative, and increase the flexibility of parameter choice. But the scaling technology is failed to solve random divergence of UKF, and introduces two new parameters, which increases the difficulty of parameter adjustment system.In view of the scaling factor is a matter of choice, need to study new scale parameter selection method. There is only a small study of scaling factor optimization selection, so in this paper, we propose a new method to select the scaling factor by the Differential Evolution algorithm (DE). In recent years, DE is applied to many kinds of optimization problems especially on the problem in view of the various system parameters optimization selection has obtained the very good application results. This paper proposed two models to use DE choosing scaling factors. They are the part way and the whole way. The part way treats the period of filtering and get one scaling factor for the period of filtering. The whole way is use DE in every moment of the filtering process. The former one is simple and quick;the latter one can significantly improve the filtering accuracy. Apply two kinds of methods to different dimensions of experiment in the system. Experimental results show that the application of differential evolution to choose parameters of the filter precision is higher than the practical fixed scaling factor of the filter value, especially in the high latitude is more obvious. And, more importantly, DE makes scaling factor can be adjusted according to current state filtering, avoids the Sigma point distribution deviates from the situation, solve the filtering random divergence problem.So we get the conclusion:scaling factor should be adjusted according to current state filtering can achieve better filtering effect in UKF. But DE is the posteriori type optimization method, which need a group without error theoretical values as a standard to guide scaling factor to the optimal solution. But in real-time environment, there isn’t a standard, it can’t be optimized in posteriori way. So we need to use other method to real-time adjust the scaling factor.Support vector regression(SVR) is support vector machine (SVM) is used to solve regression problem form of promotion.SVR has the advantage that can be close to all kinds of complicated nonlinear continuous function with any degree of accuracy and is suitable for dealing with small samples, nonlinear and high dimension problems. Only need to specify the input data and output data, select the appropriate model parameters can be set up mapping relationship of the two set up regression model. So this paper proposed adjust scaling factor by SVR. The results which get from DE is sample data, build the model of scaling factor by SVR. Through the experiment analysis of radial basis kernel function is chosen as the final regression model of kernel function, based on the current the covariance of filtering to choose the scaling factor.We found that SVR cannot get multiple variable regressions at the same time. This limits its application scope, so we proposed the Multi-dimensional output vector regression (MSVR). Firstly the paper introduced the three solutions;they are MSVR based on hyper sphere loss function, MSVR based on collaborative kriging, MSVR based on virtualization vector. By contrast with the experimental analysis concluded that the MSVR based on hyper sphere loss function is the best method. In this method only modify the definition of loss function, use super ball instead of a hypercube as the sensitive areas not directly solve the penalties different problems. The loss functions of hyper sphere in regression with the fitting error of each component to the overall performance optimization but also has stronger noise resistance and robustness. Least changes throughout the whole process, without introducing a new parameter, main parameters and conventional one-dimensional output SVR is consistent, the most convenient to use. MSVR based on collaborative kriging express multidimensional interpolation statistical estimates of the results of the relationship between the outputs. In the process of approximate need to choose the right fitting variorums model, the variorums’model selection effect as of the end result of uncertainty. It need to calculated the cross covariance, when the different dimension variable of covariance as the kernel function. The whole process is too complicated and the system parameters is more, need to coordinate the two sets of system parameter application increased the difficulty, has affected the model regression precision. The MSVR based on virtualization vector extend the feature space by binary representation;keep the form of integrity by virtualization vector. But after enlarge dimensional vector calculation process is complicated;the system dimension is higher when the efficiency is low. Kernel function is needed to introduce one to adjust the degree of similarity between different dimensions of the output variable coefficient function. But the coefficient increased the uncertainty of systemAfter solve the multi-dimensional output after regression problems, we can use the support vector regression machine fitting model is set up in some complex system. The mathematical model of system can be estimated by SVR, to estimate the states of the system data and reduce the error by filter. The model of UKF based on MSVR is used in time series analysis problem. Due to the complexity and uncertainty of the time series data itself, characterized by strong non-stationary series, nonlinear, non-Gaussian characteristics. The traditional methods in modeling are difficult to reach ideal forecast effect with the problem of One-sidedness, the timeliness. Using the proposed model to analyze time series data, applied to the abnormal monitoring data and the forecast problem of the stock. The fitting model was established based on historical records, to effectively estimate and forecast system data. In abnormal data monitoring applications, the state of sewage disposal data model is set up, test and identify abnormal data in the record. In stock market prediction, the state model of stock index model is established, and the1day or5days in the future to predict the stock index. Experiments show that under the premise of accurate state space model is established, can better estimate of the time series data and prediction effect.