本文關(guān)鍵詞： 卡爾曼濾波 二階 非加性噪聲 非線性系統(tǒng)　出處：《哈爾濱工業(yè)大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：卡爾曼濾波自誕生以來(lái)就有很多應(yīng)用,但典型的卡爾曼濾波只用于線性系統(tǒng)。擴(kuò)展卡爾曼濾波(Extended Kalman Filter(EKF))是解決非線性系統(tǒng)的一種方法,因?yàn)槠湔归_(kāi)點(diǎn)實(shí)時(shí)更新使其對(duì)非線性系統(tǒng)有良好的估計(jì)效果,從而EKF應(yīng)用廣泛。然而因?yàn)镋KF在線性化時(shí)是將非線性函數(shù)Taylor展開(kāi)到一階項(xiàng),忽略高階項(xiàng),所以會(huì)帶來(lái)誤差。盡管有二階擴(kuò)展卡爾曼濾波產(chǎn)生,但是文獻(xiàn)中二階擴(kuò)展卡爾曼濾波僅應(yīng)用于噪聲是仿射非線性的系統(tǒng),即系統(tǒng)關(guān)于噪聲是加性的(已有文獻(xiàn)將EKF推廣到含有非加性噪聲系統(tǒng))。事實(shí)上帶非加性噪聲尤其是乘性噪聲的非線性系統(tǒng)在實(shí)際情景中是很常見(jiàn)的,帶非加性噪聲系統(tǒng)的狀態(tài)最優(yōu)估計(jì)相應(yīng)有著重要的應(yīng)用價(jià)值。本文主要研究擴(kuò)展卡爾曼濾波問(wèn)題,給出對(duì)于一般含有非加性噪聲的非線性系統(tǒng)的二階擴(kuò)展卡爾曼濾波的遞推公式。并針對(duì)含有非加性噪聲的非線性系統(tǒng)尤其帶乘性噪聲系統(tǒng)探討推廣的EKF與改進(jìn)二階擴(kuò)展卡爾曼濾波的估計(jì)效果。第一部分主要介紹課題研究的意義背景以及研究現(xiàn)狀。第二部分給出了高斯分布的一些性質(zhì)以及最小均方誤差估計(jì)的方法,在最小均方誤差估計(jì)意義下一般非線性系統(tǒng)討論,為給出一般非加性噪聲系統(tǒng)的二階擴(kuò)展卡爾曼濾波公式做了準(zhǔn)備。第三部分給出一階擴(kuò)展卡爾曼濾波對(duì)于一般非加性噪聲系統(tǒng)的遞推公式。之后提出對(duì)于非加性噪聲系統(tǒng)的二階擴(kuò)展卡爾曼濾波公式,并給出公式推導(dǎo)證明,在此公式推導(dǎo)中應(yīng)用到高斯假設(shè)以及高斯分布的高階矩計(jì)算等眾多概率理論,已經(jīng)不單是如同EKF簡(jiǎn)單的Taylor展開(kāi)。第四部分給出仿真算例,在之后的非加性噪聲系統(tǒng)仿真實(shí)驗(yàn)中,會(huì)看到改進(jìn)的二階擴(kuò)展卡爾曼濾波要優(yōu)于推廣的EKF。
[Abstract]:Since the birth of Kalman filter, there have been many applications. But the typical Kalman filter is only used in linear systems. Extended Kalman filter is a method to solve nonlinear systems. Because its expansion point is updated in real time, it has a good estimation effect for nonlinear system, so EKF is widely used. However, because EKF expands the nonlinear function Taylor to the first order when linearization. Although the second order extended Kalman filter is produced, the second order extended Kalman filter is only applied to noise systems which are affine nonlinear. That is, the system is additive about noise (EKF has been extended to systems with non-additive noise). In fact, nonlinear systems with non-additive noise, especially multiplicative noise, are very common in actual situations. The state optimal estimation of systems with non-additive noise has important application value. In this paper, the extended Kalman filtering problem is studied. The recurrence formula of second order extended Kalman filter for nonlinear systems with general nonadditive noise is given. The generalized EKF and its modification are discussed for nonlinear systems with non-additive noise, especially for systems with multiplicative noise. The estimation effect of progressive second order extended Kalman filter. The first part mainly introduces the significance of the research background and research status. The second part gives some properties of Gao Si distribution and the method of minimum mean square error estimation. General nonlinear systems are discussed in the sense of minimum mean square error estimation. In order to give the second order extended Kalman filter formula for the general non-additive noise system, the recursive formula of the first order extended Kalman filter for the general non-additive noise system is given in the third part, and then for the non-additive system, the recursive formula for the first order extended Kalman filter is given. Second order extended Kalman filter formula for noise systems. The formula derivation proves that this formula is applied to many probability theories such as Gao Si hypothesis and the calculation of the higher-order moments of Gao Si distribution and so on. It is not just like the simple Taylor expansion of EKF. 4th gives a simulation example, in the subsequent non-additive noise system simulation experiments. It is shown that the improved second order extended Kalman filter is superior to the extended EKF.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TN713

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本文編號(hào)：1486927