本文選題：容積卡爾曼濾波器　切入點(diǎn)：單純型　出處：《西南大學(xué)》2017年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：本文基于非線性系統(tǒng),提出了新的非線性卡爾曼濾波器。R.E.Kalman在1960年,提出了著名的卡爾曼濾波器算法,它是一種以最小二乘法為基礎(chǔ)的遞推最優(yōu)估計(jì)算法,能夠處理多維度且非平穩(wěn)的隨機(jī)信號(hào)。這種算法有著結(jié)構(gòu)簡(jiǎn)單易于實(shí)現(xiàn)的優(yōu)點(diǎn),因此在工程界大受歡迎,很快得到廣泛應(yīng)用。但是它有一定的應(yīng)用局限,即只適合于線性系統(tǒng),然而大多數(shù)實(shí)際物理系統(tǒng)是非線性的,因此,針對(duì)卡爾曼濾波器的這一局限,科學(xué)家提出了一種能夠應(yīng)用于非線性系統(tǒng)的卡爾曼濾波器,即擴(kuò)展卡爾曼濾波器(extended Kalman filter,EKF)。EKF是將非線性系統(tǒng)線性化,存在著精度不高,易于發(fā)散的問(wèn)題,并且只適用于那些時(shí)域更新時(shí)近乎是線性的系統(tǒng)。而后提出的無(wú)先導(dǎo)卡爾曼濾波器(unscented Kalman filter,UKF)算法結(jié)合了無(wú)先導(dǎo)變換(unscented transformation,UT)和卡爾曼濾波器(Kalman Filter,KF)算法的思想。UKF和EKF的計(jì)算復(fù)雜度相當(dāng),但是相比較之下,UKF的精度更高,省略了計(jì)算系統(tǒng)的雅克比(Jacobi)矩陣和漢森(Hession)矩陣的步驟,不要求系統(tǒng)的非線性程度,其適用范圍更廣。近年來(lái),非線性卡爾曼濾波器主要朝著高效地近似高斯概率密度函數(shù)的方向發(fā)展,由此設(shè)計(jì)出數(shù)值精度更高、性能更好的非線性卡爾曼濾波器。文中的新的非線性卡爾曼濾波器設(shè)計(jì)方法主要有三種,其中之一就是源于這一思想。非線性卡爾曼濾波器算法可以由貝葉斯濾波理論統(tǒng)一描述,基于其設(shè)計(jì)的關(guān)鍵是計(jì)算高斯概率密度函數(shù)加權(quán)的多維非線性函數(shù)的積分。數(shù)值積分方法中,最具代表性的方法是一類(lèi)容積準(zhǔn)則,便提出了容積卡爾曼濾波器(cubature Kalman filter,CKF)。然而容積卡爾曼濾波器也存在著一些缺點(diǎn),其精度只能達(dá)到三階。由此,本文提出新型設(shè)計(jì)的非線性卡爾曼濾波器。新的非線性卡爾曼濾波器設(shè)計(jì)方法之二是利用Huber M估計(jì)算法實(shí)現(xiàn)狀態(tài)的量測(cè)更新,其提出思想,基于采用統(tǒng)計(jì)線性回歸模型近似非線性量測(cè)模型,結(jié)合基于高階球面-徑向容積準(zhǔn)則的狀態(tài)預(yù)測(cè)模塊,構(gòu)成基于Huber的高階容積卡爾曼濾波器,應(yīng)用于跟蹤模型構(gòu)成跟蹤算法。能夠有效改善其濾波精度和魯棒性。方法之三是在方法二的基礎(chǔ)上,將q微分引入到Huber方法中,以UKF為例,構(gòu)成基于q微分的Huber無(wú)先導(dǎo)卡爾曼濾波器。本文在深入理解的基礎(chǔ)上,并設(shè)計(jì)出新的濾波器。首先,從卡爾曼濾波理論的基本原理入手,以常用的估計(jì)準(zhǔn)則為起點(diǎn),介紹了最小二乘估計(jì)、線性最小方差估計(jì)等估計(jì)準(zhǔn)則、貝葉斯濾波理論,以及新的改進(jìn)方法。其次,用Matlab對(duì)新算法進(jìn)行仿真驗(yàn)證,實(shí)現(xiàn)了新的非線性卡爾曼濾波器設(shè)計(jì)。最后,進(jìn)行了總結(jié)歸納,并對(duì)下一步需要做的工作進(jìn)行了展望。
[Abstract]:In this paper, a new nonlinear Kalman filter .R.E. Kalman is proposed based on nonlinear systems. In 1960, a famous Kalman filter algorithm is proposed, which is a recursive optimal estimation algorithm based on the least square method. This algorithm has the advantage of simple structure and easy to implement, so it has been widely used in engineering field. However, it has some limitations, that is, it is only suitable for linear systems. However, most practical physical systems are nonlinear. Therefore, in view of this limitation of Kalman filter, a kind of Kalman filter which can be applied to nonlinear system is proposed. That is, extended Kalman filter is linearized by extended Kalman filter. EKF has the problem of low precision and easy divergence. The unscented Kalman filter and the unscented Kalman filter (UKF) algorithm, which combines the unscented transformation (UTT) algorithm and the Kalman filter KF (Kalman filter filter KF) algorithm, have the same computational complexity as the EKF algorithm, which is only applicable to those systems where the time domain update is almost linear, and the proposed unscented Kalman filter algorithm combines the unscented transformation with the unscented transform UTU (unscented transform UTU) and the Kalman filter filter KF (KF). But by comparison, the UKF has higher precision, omitting the steps of Jacobi matrix and Hansen Hessionation matrix of the computing system, which does not require the degree of nonlinearity of the system, and its application scope is wider in recent years. The nonlinear Kalman filter mainly develops towards the direction of efficiently approximating Gao Si's probability density function, so the numerical accuracy is higher. Nonlinear Kalman filter with better performance. There are three main methods for designing nonlinear Kalman filter in this paper. The nonlinear Kalman filter algorithm can be described by Bayesian filtering theory. The key of its design is to calculate the integral of the multi-dimensional nonlinear function weighted by Gao Si's probability density function. In the numerical integration method, the most representative method is a kind of volumetric criterion. The volume Kalman filter (cubature Kalman filter) is proposed. However, the volume Kalman filter has some disadvantages, and its precision can only reach the third order. In this paper, a new nonlinear Kalman filter is proposed. The second method is to use Huber M estimation algorithm to realize the state update. Based on the approximate nonlinear measurement model based on statistical linear regression model and the state prediction module based on higher-order spherical and radial volumetric criteria, a high-order volumetric Kalman filter based on Huber is constructed. It can improve the filtering accuracy and robustness effectively. The third method is to introduce Q differential into the Huber method based on the second method and take UKF as an example. In this paper, a new filter is designed on the basis of deep understanding. Firstly, starting with the basic principle of Kalman filter theory, the paper starts with the common estimation criterion. The least square estimation, linear minimum variance estimation, Bayesian filtering theory and new improved method are introduced. Secondly, the new algorithm is simulated by Matlab, and a new nonlinear Kalman filter is designed. Summarized and summarized, and the need to do the next work is prospected.
【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TN713

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本文編號(hào)：1602851