【摘要】：目標(biāo)狀態(tài)估計(jì)及其融合濾波方法作為目標(biāo)跟蹤技術(shù)的核心部分,一直以來(lái)備受人們的關(guān)注,在軍事領(lǐng)域和民用領(lǐng)域都得到了廣泛應(yīng)用,例如:情報(bào)監(jiān)控、交通管制、智能導(dǎo)航、醫(yī)學(xué)診斷等。然而,在狀態(tài)估計(jì)的實(shí)際過(guò)程中,人們總是將研究重點(diǎn)局限于原始數(shù)據(jù),并沒(méi)有使用一些已知的先驗(yàn)信息,如果我們能用先驗(yàn)信息建立約束條件,并將有效的約束應(yīng)用于濾波過(guò)程,那么我們就能提高算法的濾波精度,從而能夠使得濾波后所得到的估計(jì)值更加趨近于系統(tǒng)的真實(shí)值。因此,針對(duì)約束條件下的濾波算法的研究是非常必要的。本課題來(lái)源于國(guó)家自然科學(xué)基金項(xiàng)目“基于隨機(jī)有限集理論的多目標(biāo)跟蹤方法若干問(wèn)題研究”(NO.61201118),針對(duì)約束條件下的濾波算法進(jìn)行了分析研究,根據(jù)系統(tǒng)狀態(tài)所受到的約束條件可將約束問(wèn)題分為兩種,即線性約束濾波問(wèn)題和非線性約束濾波問(wèn)題,線性約束條件下的濾波問(wèn)題與非線性約束條件下的濾波問(wèn)題相比較更為容易解決,人們已經(jīng)提出了很多有效的解決方法處理該問(wèn)題。所以,本文著重于研究非線性約束條件下的濾波問(wèn)題,并在已有受約束濾波算法的基礎(chǔ)上給出了兩種新的濾波算法解決約束問(wèn)題。實(shí)驗(yàn)結(jié)果表明,新算法在處理約束問(wèn)題時(shí),能夠有效提高狀態(tài)估計(jì)精度,算法時(shí)間復(fù)雜度較低。本文的主要工作內(nèi)容歸納如下:(1)迭代收縮非線性狀態(tài)約束濾波非線性狀態(tài)約束濾波是實(shí)際中經(jīng)常遇到的問(wèn)題,針對(duì)該問(wèn)題,在狀態(tài)向量的高斯假定下,提出了一類迭代收縮非線性狀態(tài)約束濾波方法。該方法結(jié)合容積卡爾曼濾波、求積分卡爾曼濾波、中心差分卡爾曼濾波和不敏卡爾曼濾波思想,分別采用幾種不同的數(shù)值方法對(duì)積分進(jìn)行近似,獲得了幾種解決非線性狀態(tài)約束的實(shí)現(xiàn)算法。在實(shí)現(xiàn)過(guò)程中,為了減小基點(diǎn)誤差對(duì)于濾波結(jié)果的影響,采用迭代的方法,給非線性狀態(tài)約束函數(shù)施加一系列噪聲,從而在量測(cè)更新過(guò)程中使得經(jīng)過(guò)濾波后的方差逐步收斂,改善了濾波估計(jì)結(jié)果。實(shí)驗(yàn)結(jié)果表明,該類方法的幾種實(shí)現(xiàn)算法濾波精度較高,時(shí)間復(fù)雜度較為適中,無(wú)需求解雅可比矩陣或黑森矩陣。(2)基于序列二次規(guī)劃的非線性不等式狀態(tài)約束濾波算法針對(duì)非線性不等式狀態(tài)約束濾波問(wèn)題,提出了一種基于序列二次規(guī)劃的迭代不敏卡爾曼濾波算法。該算法在迭代不敏卡爾曼濾波的基礎(chǔ)上結(jié)合了優(yōu)化算法的思想,采用序列二次規(guī)劃優(yōu)化法求解非線性不等式約束條件下的最優(yōu)解。在實(shí)驗(yàn)驗(yàn)證中,將每一迭代問(wèn)題看做一個(gè)二次規(guī)劃子問(wèn)題,其下降方向通過(guò)求解該子問(wèn)題來(lái)確定,重復(fù)上述步驟即可獲得約束問(wèn)題的最優(yōu)解。為了保證算法具有較強(qiáng)的收斂性,利用效益函數(shù)最小化目標(biāo)函數(shù),并將其與不等式約束條件進(jìn)行權(quán)衡。此外,利用正定矩陣近似海森矩陣,以減少算法所花費(fèi)的時(shí)間。實(shí)驗(yàn)結(jié)果表明,新算法在處理非線性不等式狀態(tài)約束濾波問(wèn)題時(shí),能夠有效地提高狀態(tài)估計(jì)精度,獲得較高的濾波精度,算法時(shí)間復(fù)雜較低。
[Abstract]:Target state estimation and fusion filtering, as the core part of target tracking technology, have been paid much attention to and widely used in military and civil fields, such as intelligence monitoring, traffic control, intelligent navigation, medical diagnosis, etc. However, in the actual process of state estimation, people always have to do a lot of research. The point is limited to the original data and does not use some known prior information. If we can use prior information to establish constraints and apply the effective constraints to the filtering process, then we can improve the filtering accuracy of the algorithm, thus making the estimated value of the filter closer to the true value of the system. Therefore, the needle is more close to the true value of the system. Therefore, the needle is more close to the true value of the system. It is necessary to study the filtering algorithm under the constraint conditions. This topic comes from the research on several problems of the multi-objective tracking method based on the stochastic finite set theory (NO.61201118), which is based on the National Natural Science Foundation of China. The filtering algorithm under the constraint conditions is analyzed and studied, and the constraint conditions are based on the state of the system. The constraint problems can be divided into two kinds, namely, linear constrained filtering and nonlinear constrained filtering. The filtering problem under linear constraints is more easily solved than the filtering problem under the nonlinear constraints. Many effective solutions have been put forward to deal with the problem. So, this paper focuses on the study of the nonlinear contract. Two new filtering algorithms are given on the basis of existing constrained filtering algorithms to solve the problem of constraints. Experimental results show that the new algorithm can effectively improve the precision of state estimation and the time complexity of the algorithm is low. The main work contents of this paper are as follows: (1) iterative shrinkage Nonlinear state constraint filtering nonlinear state constraint filtering is a problem often encountered in practice. Under the Gauss assumption of state vector, a class of iterative shrinkage nonlinear state constraint filtering method is proposed. This method combines with volume Calman filter, integral Calman filter, central differential Calman filter and unsensitive. Several different numerical methods are used to approximate the integral, and several algorithms to solve the nonlinear state constraints are obtained by using several different numerical methods. In order to reduce the influence of the base point error to the filtering results, an iterative method is used to apply a series of noise to the non linear state constraint function in the process of implementation, so that the quantity of the non linear state constraint function is applied. In the process of updating, the filtered variance is gradually converged and the filter estimation results are improved. The experimental results show that the filtering accuracy is higher, the time complexity is moderate, the Jacobi matrix or the Hessen matrix is not required. (2) the nonlinear inequality state constraint filtering based on the sequence column two times programming. In this algorithm, an iterative unsensitive Calman filtering algorithm based on sequence two order programming is proposed for nonlinear inequality constraint filtering problem. The algorithm combines the idea of optimization algorithm on the basis of iterative unsensitive Calman filtering and the optimal solution of nonlinear inequality constraints is solved by sequential two programming optimization. In experimental verification, each iteration problem is considered as a two time programming subproblem. Its descent direction is determined by solving the subproblem, and the optimal solution of the constraint problem can be obtained by repeating the above steps. In order to ensure the convergence of the algorithm, the goal function is minimized by the benefit function, and the constraint conditions are entered into the inequality constraints. In addition, the positive definite matrix is used to approximate the hahson matrix to reduce the time spent in the algorithm. The experimental results show that the new algorithm can effectively improve the precision of state estimation, obtain higher filtering precision, and have a low time complexity when dealing with the nonlinear inequality state constraint filtering problem.
【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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