發(fā)布時(shí)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(xì)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(diǎn),討論了它們的應(yīng)用范圍。首先,基于一維離散狀態(tài)數(shù)據(jù)和觀測(cè)數(shù)據(jù),分別提出了狀態(tài)方程的參數(shù)估計(jì)法(SPL法)和觀測(cè)方程的參數(shù)估計(jì)法(OSL法)。第一種方法,先求出與當(dāng)前狀態(tài)數(shù)據(jù)相關(guān)的下一時(shí)刻狀態(tài)數(shù)據(jù)的概率分布,再利用最小二乘法估計(jì)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(cè)數(shù)據(jù)的基礎(chǔ)上,在每個(gè)區(qū)間內(nèi)用最小二乘法估計(jì)觀測(cè)矩陣,構(gòu)造出狀態(tài)變量和觀測(cè)矩陣之間的函數(shù)關(guān)系式,最終得到觀測(cè)方程。其次,對(duì)簡化的Sage-Husa自適應(yīng)濾波算法進(jìn)行了兩點(diǎn)改進(jìn)。第一點(diǎn),用觀測(cè)噪聲Rk-1代替觀測(cè)噪聲Rk,計(jì)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(diǎn),在原算法的基礎(chǔ)上增加了兩步,即先利用前面求得的觀測(cè)噪聲Rk重新計(jì)算卡爾曼增益Kk,再利用新的卡爾曼增益Kk重新計(jì)算估計(jì)值xk。接著,針對(duì)單時(shí)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(cè)過程均為平穩(wěn)的情況下,提出了一種估計(jì)觀測(cè)延遲時(shí)間的方法。最后,實(shí)證分析了本文提出的上述方法,估計(jì)出狀態(tài)方程和觀測(cè)方程的相應(yīng)參數(shù)以及觀測(cè)延遲時(shí)間,并利用本文提出的評(píng)價(jià)函數(shù)R(s)驗(yàn)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(xué)位授予單位】：南京理工大學(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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本文編號(hào)：2436202