本文選題：高斯和濾波 + 非高斯分布��； 參考：《西安工程大學(xué)》2015年碩士論文

【摘要】：高斯和濾波理論主要用于處理系統(tǒng)噪聲為非高斯分布、或非線性系統(tǒng)模型的后驗(yàn)概率密度不能用單個(gè)高斯分布來(lái)近似的情況。目前,航空航天、電子信息和目標(biāo)跟蹤等領(lǐng)域都廣泛和充分的應(yīng)用了高斯和理論。針對(duì)各種特定條件下的系統(tǒng),學(xué)者們結(jié)合高斯和思想,推導(dǎo)出了相應(yīng)特定環(huán)境下的濾波算法:例如適用于線性系統(tǒng)的高斯和卡爾曼濾波算法、能夠處理弱非線性系統(tǒng)的高斯和擴(kuò)展卡爾曼濾波算法、能夠解決強(qiáng)非線性系統(tǒng)的高斯和粒子濾波算法等。但是目前的研究成果還有兩個(gè)方面的不足沒(méi)有得到完全徹底的解決:一方面是由于算法本身的缺陷使得濾波效果不夠好,另一方面是某些條件下的濾波問(wèn)題還沒(méi)有相應(yīng)的算法能夠處理。因此本課題在現(xiàn)有算法的基礎(chǔ)上作進(jìn)一步的改進(jìn)和研究,提出濾波精度更高和能夠處理其他不同條件下的高斯和濾波算法。本課題完成的研究?jī)?nèi)容包括:(1)欠觀測(cè)條件下的高斯和增量卡爾曼濾波算法由于環(huán)境和設(shè)備的影響,濾波過(guò)程中常常帶有未知的量測(cè)系統(tǒng)誤差,欠觀測(cè)條件下的增量卡爾曼濾波算法能夠在很大程度上去除這種誤差,很好地進(jìn)行狀態(tài)跟蹤。然而,當(dāng)系統(tǒng)過(guò)程噪聲以及系統(tǒng)量測(cè)噪聲是非高斯分布的情況下,這種方法不能直接使用。針對(duì)該問(wèn)題,本課題結(jié)合高斯和的理論思想,提出一種欠觀測(cè)條件下的高斯和增量卡爾曼濾波算法。該算法將初始狀態(tài)、系統(tǒng)過(guò)程噪聲以及系統(tǒng)量測(cè)噪聲都用高斯和的方式來(lái)近似,接著按照增量卡爾曼濾波的思想對(duì)每個(gè)高斯項(xiàng)做預(yù)測(cè)以及更新,最后以累加和的形式近似的表示出系統(tǒng)的狀態(tài)估計(jì)值。仿真結(jié)果表明:該算法在非高斯噪聲分布的情況下,既能成功地消除量測(cè)系統(tǒng)誤差,又能有效地提高濾波估計(jì)的準(zhǔn)確度和可靠性。(2)基于弦線去導(dǎo)的高斯和迭代擴(kuò)展卡爾曼濾波算法當(dāng)系統(tǒng)為強(qiáng)非線性高斯分布系統(tǒng),且量測(cè)方程的非線性函數(shù)比較復(fù)雜,Jacobian矩陣的求解比較困難時(shí),通過(guò)采用弦線法去導(dǎo)并結(jié)合IEKF算法進(jìn)行狀態(tài)估計(jì),但是當(dāng)系統(tǒng)的非線性較強(qiáng)且滿足非高斯分布時(shí),這種算法不再適用。針對(duì)該問(wèn)題,本課題提出基于弦線去導(dǎo)的高斯和迭代擴(kuò)展卡爾曼濾波算法。該算法使用高斯和濾波理論來(lái)處理非高斯分布的情況,同時(shí)采用割線法,即求解兩點(diǎn)間的割線斜率代替Jacobian矩陣,這樣避免了不易求解Jacobian矩陣帶來(lái)的困擾。仿真實(shí)驗(yàn)證明:該算法能夠提高濾波精度,能有效地進(jìn)行狀態(tài)估計(jì)和狀態(tài)跟蹤。(3)有色噪聲條件下的高斯和卡爾曼濾波算法標(biāo)準(zhǔn)卡爾曼濾波算法要求系統(tǒng)的過(guò)程噪聲以及系統(tǒng)的量測(cè)噪聲的均值都是零而且要是高斯白噪聲。然而在實(shí)際應(yīng)用的過(guò)程中,經(jīng)常會(huì)遇到噪聲是非高斯分布的有色噪聲,因此不能直接應(yīng)用卡爾曼濾波算法。針對(duì)該問(wèn)題,我們結(jié)合處理有色噪聲的濾波思想以及高斯和濾波理論,提出了有色噪聲條件下的高斯和卡爾曼濾波算法。首先,分別采用狀態(tài)擴(kuò)維以及量測(cè)擴(kuò)維的方法對(duì)系統(tǒng)的過(guò)程噪聲和系統(tǒng)的量測(cè)噪聲進(jìn)行白化處理。然后,根據(jù)高斯和濾波思想,用多個(gè)高斯項(xiàng)的疊加來(lái)近似非高斯分布,實(shí)現(xiàn)對(duì)系統(tǒng)的狀態(tài)估計(jì)。仿真實(shí)驗(yàn)?zāi)軌蜃C明,本文提出的新算法能夠消除有色噪聲的影響,有效地追蹤目標(biāo)狀態(tài)。
[Abstract]:Gauss and filter theory are mainly used to deal with the condition that the system noise is non Gauss distribution, or the posterior probability density of the nonlinear system model can not be approximated by a single Gauss distribution. At present, the aerospace, electronic information and target tracking are widely and fully applied to Gauss and theory. In combination with Gauss and thought, scholars have derived a corresponding filtering algorithm in a specific environment, such as Gauss and Calman filtering algorithms suitable for linear systems, which can handle Gauss and extended Calman filtering algorithms for weak nonlinear systems, and can solve the Gauss and particle filtering algorithms of strong nonlinear systems. There are two deficiencies in the results are not completely solved: on the one hand, because of the defects of the algorithm itself, the filtering effect is not good enough, on the other hand, the filtering problem under certain conditions has no corresponding algorithm to deal with. The wave precision is higher and can deal with the Gauss and filtering algorithms under different conditions. The research contents of this topic include: (1) the Gauss and incremental Calman filtering algorithms under under observed conditions often have unknown measurement system error and incremental Calman filter under the condition of under observation due to the influence of environment and equipment. This method can not be used directly when the noise of the system process and the measurement noise of the system are non Gauss distribution. In view of the problem, this paper proposes a kind of Gauss and increment under the condition of under observation. The Calman filtering algorithm, which approximates the initial state, the system process noise and the system measurement noise in the way of Gauss and the method, then predicts and updates each Gauss term according to the thought of incremental Calman filtering. Finally, the state estimation of the system is approximated in the form of accumulative sum. The simulation results show that: In the case of non Gauss noise distribution, the algorithm can not only successfully eliminate the measurement system error, but also effectively improve the accuracy and reliability of the filter estimation. (2) the Gauss and iterative extended Calman filtering algorithm based on the string to guide the system is strongly nonlinear Gauss distribution system, and the nonlinear function of the measurement equation is complex, Jac When the solution of Obian matrix is difficult, the algorithm is used to estimate the state by using string method and IEKF algorithm. But when the system has strong nonlinearity and satisfies the non Gauss distribution, this algorithm is no longer applicable. In this problem, we propose the Gauss and iterative extended Calman filtering algorithm based on the chord line to guide. The algorithm is used. Gauss and filter theory are used to deal with the non Gauss distribution. At the same time, the secant method is used to solve the secant slope between two points instead of the Jacobian matrix. This avoids the difficulty of solving the problems caused by the Jacobian matrix. The simulation experiment proves that the algorithm can improve the filtering precision and can effectively carry out state estimation and state tracking. (3) colored noise. The standard Calman filtering algorithm for Gauss and Calman filtering algorithms under sound conditions requires that the process noise of the system and the mean of the measurement noise of the system are zero and if Gauss is white noise. However, in the actual application process, the noise is often encountered in the non Gauss distribution of the colored noise, so it can not be directly applied to the Calman filter. In view of this problem, we combine the filtering idea of colored noise and the Gauss and filter theory, and propose a Gauss and Calman filtering algorithm under the colored noise condition. First, the process noise of the system and the measurement noise of the system are whitened with the method of state expansion and measurement expansion. According to Gauss and filter thought, the state estimation of the system is realized by using the superposition of multiple Gauss terms to approximate the state of the system. The simulation experiment can prove that the new algorithm proposed in this paper can eliminate the influence of colored noise and effectively track the state of the target.
【學(xué)位授予單位】：西安工程大學(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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