本文選題：卡爾曼濾波 + 混合階　； 參考：《西南大學(xué)》2017年碩士論文

【摘要】：目標(biāo)跟蹤在現(xiàn)代科技生活中的應(yīng)用日益普遍,從國(guó)家軍事方面的航空登月軌道預(yù)測(cè)追蹤到現(xiàn)實(shí)生活中的車(chē)輛軌跡追蹤。從定義上看,目標(biāo)追蹤可簡(jiǎn)單理解為對(duì)目標(biāo)運(yùn)動(dòng)軌跡的估計(jì)問(wèn)題。如何解決這些問(wèn)題,實(shí)時(shí)、準(zhǔn)確地對(duì)目標(biāo)進(jìn)行跟蹤是技術(shù)上的難點(diǎn)。多年來(lái),人類對(duì)于目標(biāo)跟蹤的方法理論和實(shí)踐的研究從未止步。作為目標(biāo)跟蹤的一個(gè)重要實(shí)現(xiàn)方法,貝葉斯濾波算法的研究是個(gè)熱點(diǎn)也是難點(diǎn)。其中,以卡爾曼濾波算法最為典型,在實(shí)現(xiàn)過(guò)程中,該濾波算法需要將未知參數(shù)當(dāng)作隨機(jī)變量來(lái)處理,進(jìn)而使用先驗(yàn)概率和當(dāng)前觀測(cè)到的數(shù)據(jù)信息來(lái)計(jì)算后驗(yàn)概率,協(xié)調(diào)了先驗(yàn)信息和當(dāng)前數(shù)據(jù)信息的應(yīng)用。此外,在線性系統(tǒng)下,卡爾曼濾波算法可以在最小均方誤差條件下,通過(guò)先驗(yàn)概率與后驗(yàn)概率的遞歸運(yùn)算給出信號(hào)的最優(yōu)估計(jì),是一種應(yīng)用相當(dāng)廣泛的濾波算法。但是在實(shí)際中,我們所遇到的系統(tǒng)大都是非線性的,這種常規(guī)的線性卡爾曼濾波算法只能局限于線性系統(tǒng)模型的應(yīng)用中。非線性濾波算法也因此得到了更多的關(guān)注并逐漸被人們提出。近年來(lái),被廣泛應(yīng)用的非線性濾波算法主要有無(wú)跡卡爾曼濾波算法、容積卡爾曼濾波算法以及球面單純形容積卡爾曼濾波算法等等。這類濾波算法大都是在高斯假設(shè)的前提下,結(jié)合貝葉斯濾波理論,通過(guò)對(duì)概率密度函數(shù)進(jìn)行近似處理,再利用數(shù)值積分理論進(jìn)行近似計(jì)算,從而得到一系列采樣點(diǎn)以及相應(yīng)的權(quán)重�？紤]到這些復(fù)雜多變的噪聲以及其他一些不確定性因素,人們需要去尋找魯棒性能好且能適應(yīng)復(fù)雜非線性環(huán)境的非線性卡爾曼濾波算法來(lái)改善估計(jì)性能。此外,科技的日益進(jìn)步對(duì)算法提出的要求也越來(lái)越高,這就意味著對(duì)濾波器的研究不能僅限于新型算法的設(shè)計(jì),而必須意識(shí)到算法性能在其應(yīng)用上的重要性,而衡量不同濾波器性能好壞的一個(gè)重要指標(biāo)就是狀態(tài)的估計(jì)精度。據(jù)此,本文在對(duì)已有的研究進(jìn)行了解之后,主要圍繞如下幾個(gè)方面進(jìn)行了研究工作:(1)對(duì)采樣準(zhǔn)則的改進(jìn)。這種改進(jìn)主要針對(duì)容積準(zhǔn)則,傳統(tǒng)的容積卡爾曼濾波算法是基于相同階數(shù)的球面-徑向容積準(zhǔn)則推導(dǎo)而來(lái)的,而本文則是將混合階的思想應(yīng)用在球面-徑向容積準(zhǔn)則上,提出了一種新型的基于混合階的容積卡爾曼濾波器,并通過(guò)MATLAB仿真對(duì)所提算法與傳統(tǒng)算法在時(shí)間復(fù)雜度和精度上進(jìn)行了綜合比較,驗(yàn)證了該算法在工程實(shí)踐中的應(yīng)用價(jià)值。(2)研究了增廣算法在復(fù)雜環(huán)境應(yīng)用中表現(xiàn)的魯棒性。本文將一類基于確定性采樣的增廣非線性卡爾曼濾波算法應(yīng)用于目標(biāo)跟蹤模型中,通過(guò)設(shè)置狀態(tài)的突變干擾和時(shí)變干擾來(lái)驗(yàn)證該增廣非線性卡爾曼濾波算法在復(fù)雜環(huán)境中能表現(xiàn)出較好的魯棒性能,證明了其在目標(biāo)實(shí)時(shí)跟蹤中的實(shí)用性和有效性。(3)對(duì)混合階算法進(jìn)行了精度分析。在傳統(tǒng)的球面單純形-徑向容積卡爾曼濾波算法的基礎(chǔ)上,同樣將混合階的思想應(yīng)用在球面單純形-徑向容積準(zhǔn)則中,并利用基于泰勒展開(kāi)式的精度分析方法對(duì)所提的混合階球面單純形-徑向容積卡爾曼濾波算法進(jìn)行了均值和協(xié)方差的分析,仿真分析驗(yàn)證了該算法能夠有效地提高濾波精度。
[Abstract]:The application of target tracking is becoming more and more common in modern scientific and technological life. The tracking of vehicle trajectory in real life is traced from the orbit of the air landing orbit of the national military. In terms of definition, the target tracking can be simply understood as the estimation of the trajectory of the target. How to solve these problems in real time and accurately track the target It is a technical difficulty. For many years, the research on the theory and practice of target tracking has never stopped. As an important realization method of target tracking, the research of Bias filtering algorithm is a hot and difficult point. Among them, the Calman filtering algorithm is the most typical. In the process of implementation, the filtering algorithm needs to be unknown parameter. The number is treated as a random variable, and then the posterior probability is calculated using the prior probability and the data information observed at present, and the application of the prior information and the current data information is coordinated. In addition, under the linear system, the Calman filtering algorithm can be given by the recursive operation of the prior probability and the posterior probability under the minimum mean square error condition. The optimal estimation of the output signal is a fairly wide range of filtering algorithms. However, in practice, most of the systems we have encountered are nonlinear. This conventional linear Calman filtering algorithm can only be limited to the application of linear system model. The nonlinear filtering algorithm has also received more attention and is gradually proposed by people. In recent years, the widely used nonlinear filtering algorithms mainly include the Untraced Calman filter algorithm, the volume Calman filter algorithm and the spherical simplex volume Calman filter algorithm and so on. Most of these filtering algorithms are based on the hypothesis of Gauss and approximated the probability density function by combining the Bayesian filtering theory. A series of sampling points and corresponding weights are obtained by using the numerical integration theory to obtain a series of sampling points and corresponding weights. Considering these complex and changeable noises and other uncertain factors, people need to find the nonlinear Calman filtering algorithm with good robust performance and can adapt to the complex nonlinear environment to improve the estimation performance. In addition, the increasing progress of science and technology is becoming more and more demanding for the algorithm, which means that the research of the filter can not be limited to the design of the new algorithm, but must realize the importance of the performance of the algorithm in its application, and the estimation accuracy of the state is an important index to measure the performance of the different filters. After understanding the existing research, we mainly focus on the following aspects: (1) improving the sampling criteria. This improvement is mainly aimed at the volume criterion. The traditional volume Calman filtering algorithm is derived from the spherical radial volume criterion of the same order, and this paper applies the thought of the mixed order. A new type of volume Calman filter based on mixed order is proposed on the spherical radial volume criterion. The time complexity and accuracy of the proposed algorithm are compared with the traditional algorithm by MATLAB simulation. The application value of the algorithm in engineering practice is verified. (2) the application of augmented algorithm in complex environment is studied. In this paper, an augmented nonlinear Calman filtering algorithm based on deterministic sampling is applied to the target tracking model. By setting the state mutation interference and time-varying interference, it is proved that the augmented nonlinear Calman filter algorithm can show good robust performance in the complex environment, and it is proved that it is in the target. The practicability and effectiveness of the real-time tracking. (3) the precision analysis of the mixed order algorithm is carried out. On the basis of the traditional spherical simplex radial volume Calman filtering algorithm, the idea of mixed order is also applied to the spherical simplex radial volume criterion, and the precision analysis method based on the Taylor expansion formula is used for the mixture. The mean and covariance are analyzed by the uniform spherical simplex radial volume Calman filter algorithm. The simulation results show that the algorithm can improve the filtering accuracy effectively.
【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
【分類號(hào)】：TN713

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