本文選題：慣性導(dǎo)航系統(tǒng) + 卡爾曼濾波　； 參考：《北京理工大學(xué)》2014年博士論文

【摘要】：在慣性導(dǎo)航系統(tǒng)中，由于載體運動無法預(yù)知、慣性器件測量精度變化等因素的影響，引起導(dǎo)航系統(tǒng)誤差模型存在結(jié)構(gòu)不確定，同時由于隨機噪聲的統(tǒng)計特性難以精確獲知等問題，使得標準的卡爾曼濾波算法無法解決這類系統(tǒng)的狀態(tài)估計問題。采用自適應(yīng)卡爾曼濾波算法可以解決未知噪聲統(tǒng)計特性參數(shù)的在線估計問題，但其穩(wěn)定性分析十分困難，理論上尚未完全解決。 論文針對慣性導(dǎo)航系統(tǒng)中線性模型存在結(jié)構(gòu)不確定性、噪聲統(tǒng)計特性未知條件下的濾波估計問題開展研究，主要創(chuàng)新點如下： (1)針對模型存在結(jié)構(gòu)不確定的濾波估計問題，引入有限模型自適應(yīng)控制思想，建立了有限模型卡爾曼濾波算法框架。提出了一種基于極小化矢量距離準則的有限模型卡爾曼濾波算法，通過二階多項式函數(shù)擬合系統(tǒng)量測信息在特定時間窗內(nèi)的動態(tài)過程，構(gòu)建了系統(tǒng)模型切換目標函數(shù)，提高了算法的魯棒性。 (2)針對導(dǎo)航系統(tǒng)中模型存在過程(或觀測)噪聲統(tǒng)計特性未知時的狀態(tài)估計問題，提出了利用量測序列來進行未知參數(shù)在線辨識的方法，構(gòu)建了存在未知過程(或觀測)噪聲協(xié)方差矩陣的卡爾曼濾波算法。以數(shù)理統(tǒng)計理論和代數(shù)黎卡提方程為分析工具，證明了所提出算法的噪聲協(xié)方差矩陣估計收斂于真值，且狀態(tài)估計與標準的卡爾曼濾波算法的收斂性一致。 (3)提出采用二階隨機游走模型描述未知系統(tǒng)動態(tài)過程，針對該模型中存在噪聲統(tǒng)計特性未知時的濾波估計問題，提出噪聲協(xié)方差矩陣未知的卡爾曼濾波算法。證明了所提出算法的噪聲協(xié)方差矩陣估計收斂于真實值，且狀態(tài)估計與標準卡爾曼濾波算法的收斂性一致。 (4)利用提出的有限模型卡爾曼濾波算法和噪聲協(xié)方差矩陣未知的卡爾曼濾波算法，解決了慣性導(dǎo)航系統(tǒng)實際應(yīng)用中由于環(huán)境擾動導(dǎo)致慣性器件漂移變大等問題，有效抑制了隨機誤差對測量精度的影響，提高了輸出信號的平穩(wěn)性和可靠性。利用提出的觀測噪聲協(xié)方差矩陣未知的卡爾曼濾波算法，，解決了慣導(dǎo)系統(tǒng)初始對準過程中觀測噪聲協(xié)方差矩陣未知時的誤差狀態(tài)估計問題，降低了濾波算法對觀測信息隨機誤差統(tǒng)計特性的要求，提高了算法的魯棒性和實用性。
[Abstract]:In the inertial navigation system, the structure of the navigation system error model is uncertain because of the unpredictable motion of the carrier and the change of the measuring accuracy of the inertial device.At the same time, it is difficult to accurately know the statistical characteristics of random noise, so the standard Kalman filtering algorithm can not solve the state estimation problem of this kind of system.Adaptive Kalman filter algorithm can be used to solve the problem of on-line estimation of unknown noise statistical characteristic parameters, but its stability analysis is very difficult and has not been completely solved theoretically.In this paper, the filtering estimation problem of linear model in inertial navigation system under the condition of uncertain structure and unknown noise statistical characteristics is studied. The main innovations are as follows:1) aiming at the problem of filter estimation with uncertain structure, a framework of finite model Kalman filter algorithm is established by introducing the idea of finite model adaptive control.A finite model Kalman filter algorithm based on minimization vector distance criterion is proposed. The system model switching objective function is constructed by fitting the dynamic process of system measurement information in a specific time window by second order polynomial function.The robustness of the algorithm is improved.In order to solve the problem of state estimation when the statistical characteristics of process (or observation) noise are unknown in navigation system, a method of on-line identification of unknown parameters using measurement sequence is proposed.A Kalman filter algorithm with unknown process (or observation) noise covariance matrix is constructed.Using mathematical statistics theory and algebraic Riccati equation as analytical tools, it is proved that the estimation of noise covariance matrix of the proposed algorithm converges to the true value, and the convergence of the state estimation is consistent with that of the standard Kalman filtering algorithm.(3) A second-order random walk model is proposed to describe the dynamic process of unknown systems. A Kalman filtering algorithm with unknown noise covariance matrix is proposed for the filtering estimation of unknown noise statistical characteristics in the model.It is proved that the estimation of the noise covariance matrix of the proposed algorithm converges to the real value, and the convergence of the state estimation is consistent with that of the standard Kalman filtering algorithm.4) using the proposed finite model Kalman filter algorithm and the Kalman filter algorithm with unknown noise covariance matrix, the problem of inertial device drift in inertial navigation system caused by environmental disturbance is solved.The influence of random error on measurement accuracy is effectively restrained, and the stability and reliability of output signal are improved.Using the proposed Kalman filtering algorithm with unknown observation noise covariance matrix, the problem of error state estimation in the initial alignment of inertial navigation system is solved when the observation noise covariance matrix is unknown.The requirements of the filtering algorithm for the statistical characteristics of random error of observation information are reduced, and the robustness and practicability of the algorithm are improved.
【學(xué)位授予單位】：北京理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TN966;TN713

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