一維離散數(shù)據(jù)的卡爾曼濾波模型的參數(shù)估計及自適應濾波算法的改進
發(fā)布時間：2019-03-07 14:40
【摘要】：本文綜述了卡爾曼濾波的研究背景和現(xiàn)狀,詳細研究了線性卡爾曼濾波及非線性卡爾曼濾波,分析了它們的優(yōu)缺點,討論了它們的應用范圍。首先,基于一維離散狀態(tài)數(shù)據(jù)和觀測數(shù)據(jù),分別提出了狀態(tài)方程的參數(shù)估計法(SPL法)和觀測方程的參數(shù)估計法(OSL法)。第一種方法,先求出與當前狀態(tài)數(shù)據(jù)相關的下一時刻狀態(tài)數(shù)據(jù)的概率分布,再利用最小二乘法估計出狀態(tài)方程中的參數(shù),最后得出狀態(tài)方程；第二種方法,在等分狀態(tài)數(shù)據(jù)和和觀測數(shù)據(jù)的基礎上,在每個區(qū)間內(nèi)用最小二乘法估計觀測矩陣,構造出狀態(tài)變量和觀測矩陣之間的函數(shù)關系式,最終得到觀測方程。其次,對簡化的Sage-Husa自適應濾波算法進行了兩點改進。第一點,用觀測噪聲Rk-1代替觀測噪聲Rk,計算出卡爾曼增益Kk,解決了原算法中的死循環(huán)問題；第二點,在原算法的基礎上增加了兩步,即先利用前面求得的觀測噪聲Rk重新計算卡爾曼增益Kk,再利用新的卡爾曼增益Kk重新計算估計值xk。接著,針對單時滯系統(tǒng),給出了具體的卡爾曼濾波算法,并且在狀態(tài)過程和觀測過程均為平穩(wěn)的情況下,提出了一種估計觀測延遲時間的方法。最后,實證分析了本文提出的上述方法,估計出狀態(tài)方程和觀測方程的相應參數(shù)以及觀測延遲時間,并利用本文提出的評價函數(shù)R(s)驗證了這些方法的有效性。
[Abstract]:In this paper, the research background and present situation of Kalman filter are summarized, linear Kalman filter and nonlinear Kalman filter are studied in detail, their advantages and disadvantages are analyzed, and their application scope is discussed. Firstly, based on one-dimensional discrete state data and observation data, the parameter estimation method of equation of state (SPL method) and the parameter estimation method of observation equation (OSL method) are proposed respectively. In the first method, the probability distribution of the next state data related to the current state data is obtained first, then the parameters in the state equation are estimated by the least square method, and finally the state equation is obtained. In the second method, on the basis of the equal state data and the sum observation data, the observation matrix is estimated by the least square method in each interval, and the function relation between the state variable and the observation matrix is constructed, and finally the observation equation is obtained. Secondly, two improvements are made to the simplified Sage-Husa adaptive filtering algorithm. Firstly, the Kalman gain Kk, is calculated by using observation noise Rk-1 instead of observation noise Rk, to solve the dead loop problem in the original algorithm. Second, two steps are added on the basis of the original algorithm, that is, the Kalman gain Kk, is recalculated by the observation noise Rk obtained before and the estimated xk. is recalculated by the new Kalman gain Kk. Then, for the single time-delay system, a specific Kalman filter algorithm is given, and a method to estimate the observation delay time is proposed under the condition that both the state process and the observation process are stationary. Finally, the above-mentioned methods are empirically analyzed, the corresponding parameters of the state equation and observation equation and the observation delay time are estimated, and the effectiveness of these methods is verified by using the evaluation function R (s) proposed in this paper.
【學位授予單位】：南京理工大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TN713
本文編號：2436202
[Abstract]:In this paper, the research background and present situation of Kalman filter are summarized, linear Kalman filter and nonlinear Kalman filter are studied in detail, their advantages and disadvantages are analyzed, and their application scope is discussed. Firstly, based on one-dimensional discrete state data and observation data, the parameter estimation method of equation of state (SPL method) and the parameter estimation method of observation equation (OSL method) are proposed respectively. In the first method, the probability distribution of the next state data related to the current state data is obtained first, then the parameters in the state equation are estimated by the least square method, and finally the state equation is obtained. In the second method, on the basis of the equal state data and the sum observation data, the observation matrix is estimated by the least square method in each interval, and the function relation between the state variable and the observation matrix is constructed, and finally the observation equation is obtained. Secondly, two improvements are made to the simplified Sage-Husa adaptive filtering algorithm. Firstly, the Kalman gain Kk, is calculated by using observation noise Rk-1 instead of observation noise Rk, to solve the dead loop problem in the original algorithm. Second, two steps are added on the basis of the original algorithm, that is, the Kalman gain Kk, is recalculated by the observation noise Rk obtained before and the estimated xk. is recalculated by the new Kalman gain Kk. Then, for the single time-delay system, a specific Kalman filter algorithm is given, and a method to estimate the observation delay time is proposed under the condition that both the state process and the observation process are stationary. Finally, the above-mentioned methods are empirically analyzed, the corresponding parameters of the state equation and observation equation and the observation delay time are estimated, and the effectiveness of these methods is verified by using the evaluation function R (s) proposed in this paper.
【學位授予單位】：南京理工大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TN713
【參考文獻】
相關期刊論文 前5條
1 徐天河,楊元喜;改進的Sage自適應濾波方法[J];測繪科學;2000年03期
2 楊元喜;;動態(tài)Kalman濾波模型誤差的影響[J];測繪科學;2006年01期
3 趙留彥;;中國通脹預期的卡爾曼濾波估計[J];經(jīng)濟學(季刊);2005年03期
4 劉曉輝;陳小平;;基于擴展卡爾曼濾波的主動視覺跟蹤技術[J];計算機輔助工程;2007年02期
5 耿延睿;李大字;郭文榮;;衰減因子自適應估計卡爾曼濾波比較研究[J];控制工程;2006年S2期
相關碩士學位論文 前1條
1 蘇云鵬;基于卡爾曼類濾波方法的利率期限結構模型估計研究[D];天津大學;2007年
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