本文選題：容積卡爾曼濾波　切入點(diǎn)：擴(kuò)維容積卡爾曼濾波　出處：《哈爾濱工程大學(xué)》2015年博士論文

【摘要】：本文主要研究容積卡爾曼濾波(Cubature Kalman filter,CKF)及其改進(jìn)濾波,并應(yīng)用到導(dǎo)航系統(tǒng)。CKF是一種基于球面徑向容積準(zhǔn)則對(duì)狀態(tài)向量進(jìn)行采樣,獲得相同權(quán)值的容積點(diǎn),經(jīng)過(guò)非線性函數(shù)傳遞來(lái)逼近非線性高斯系統(tǒng)的狀態(tài)估計(jì)。該濾波算法實(shí)現(xiàn)簡(jiǎn)單、估計(jì)精度高,應(yīng)用前景廣闊。論文主要研究工作如下:首先,研究容積卡爾曼濾波(CKF)。根據(jù)最小方差估計(jì)準(zhǔn)則推導(dǎo)非線性濾波遞推公式,詳盡介紹CKF推導(dǎo)過(guò)程。把推導(dǎo)過(guò)程相似的無(wú)跡卡爾曼濾波(Unscented Kalman filter,UKF)和CKF進(jìn)行比較研究,二者在函數(shù)泰勒展開(kāi)式高階項(xiàng)及數(shù)值穩(wěn)定性方面存在差異。CKF能夠精確保留一階矩和二階矩信息,在三維及三維以上非線性系統(tǒng)CKF的濾波精度優(yōu)于UKF。其次,研究擴(kuò)維容積卡爾曼濾波(Augmented cubature Kalman filter,ACKF)。ACKF是一種在非線性濾波過(guò)程中獲得函數(shù)均值、方差和奇階矩等統(tǒng)計(jì)信息,并對(duì)非線性函數(shù)均值進(jìn)行泰勒展開(kāi)的濾波。通過(guò)研究發(fā)現(xiàn):在一維系統(tǒng),ACKF獲得的均值和方差更接近真實(shí)值、還能額外獲得部分奇階矩信息,使其精度比CKF更高;而二維及以上系統(tǒng),ACKF傳播的統(tǒng)計(jì)信息反而誤差更大,使其精度比CKF更差。該研究所得結(jié)論為不同維數(shù)非線性系統(tǒng)濾波方法的選取提供參考依據(jù)。再次,研究強(qiáng)跟蹤容積卡爾曼濾波(Strong tracking cubature Kalman filter,STCKF)。通常情況下,慣性器件常值漂移會(huì)被視為狀態(tài)變量的一部分而采用濾波進(jìn)行估計(jì),但是其易受運(yùn)行環(huán)境中不確定因素的影響而發(fā)生突變。CKF會(huì)因系統(tǒng)模型不確定的影響導(dǎo)致濾波穩(wěn)定性下降,而不再具有克服模型不確定的魯棒性。針對(duì)這種情況,研究在狀態(tài)預(yù)測(cè)協(xié)方差陣中引入漸消因子的STCKF算法。仿真結(jié)果表明:STCKF對(duì)突變的慣性器件常值漂移具有很強(qiáng)的跟蹤能力,具有克服非線性系統(tǒng)模型不確定的魯棒性。第四,研究自適應(yīng)容積卡爾曼濾波(Adaptive cubature Kalman filter,ADCKF)。在噪聲先驗(yàn)統(tǒng)計(jì)未知情況下,CKF濾波精度下降甚至發(fā)散。根據(jù)極大后驗(yàn)估計(jì)原理,針對(duì)慣性器件隨機(jī)噪聲統(tǒng)計(jì)在惡劣工作環(huán)境下出現(xiàn)時(shí)變性的情況,研究了一種帶噪聲統(tǒng)計(jì)估計(jì)器的ADCKF算法。仿真結(jié)果表明:ADCKF在濾波前不需要精確已知慣性器件隨機(jī)噪聲的先驗(yàn)統(tǒng)計(jì),具有應(yīng)對(duì)慣性器件隨機(jī)噪聲統(tǒng)計(jì)變化的自適應(yīng)能力。最后,研究容積卡爾曼濾波及其改進(jìn)濾波應(yīng)用于導(dǎo)航系統(tǒng)。建立以速度及姿態(tài)等誤差為基礎(chǔ)的慣性導(dǎo)航系統(tǒng)非線性誤差模型,將CKF及其改進(jìn)濾波算法應(yīng)用到慣導(dǎo)非線性系統(tǒng)。仿真結(jié)果表明:改進(jìn)濾波算法中的STCKF和ADCKF能夠解決量測(cè)方程無(wú)法精確獲知情況下的濾波估計(jì)問(wèn)題,可靠性高、實(shí)用性強(qiáng),比CKF更有優(yōu)越性,具有更好的導(dǎo)航精度。
[Abstract]:In this paper, cubital Kalman filter and its improved filtering are studied, and applied to navigation system. CKF is a kind of volume point based on spherical radial volume criterion to sample the state vector and get the same weight.The state estimation of nonlinear Gao Si system is approximated by nonlinear function transfer.The filter algorithm is simple to realize, high estimation precision and wide application prospect.The main work of this paper is as follows: firstly, the volume Kalman filter CKF is studied.According to the minimum variance estimation criterion, the nonlinear filtering recursive formula is derived, and the derivation process of CKF is introduced in detail.The unscented Kalman filter UKF, which is similar in derivation process, is compared with CKF. There are differences between them in terms of higher order terms and numerical stability of the function Taylor expansions. CKF can accurately retain the information of first and second moments.The filtering accuracy of CKF is better than that of CKF in 3D and above.Secondly, it is studied that augmented cubature Kalman filter ACKFN. ACKF is a kind of statistical information, such as function mean value, variance and odd order moment, which is obtained in nonlinear filtering process, and the nonlinear function mean value is filtered by Taylor expansion.It is found that the mean value and variance obtained by ACKF in one-dimensional system are closer to the real value, and some odd moment information can be obtained, which makes the accuracy higher than that of CKF, but the error of statistical information propagated by ACKF in two dimensional and above systems is even greater.Make its accuracy worse than CKF.The conclusion provides a reference for the selection of filtering methods for nonlinear systems with different dimensions.Thirdly, strong tracking cubature Kalman filter with strong tracking volume is studied.In general, the constant drift of the inertial device is regarded as part of the state variable and the filter is used to estimate the drift.However, it is vulnerable to the influence of uncertain factors in the operating environment, and the sudden change of CKF will lead to the degradation of filter stability due to the uncertainty of the system model, and it will no longer have the robustness to overcome the uncertainty of the model.In order to solve this problem, the STCKF algorithm which introduces fading factor into the state prediction covariance matrix is studied.The simulation results show that: STCKF has a strong tracking ability to the constant drift of the abrupt inertial device and is robust to overcome the uncertainty of the nonlinear system model.Fourthly, adaptive cubature Kalman filter (ADCKF) is studied.In the case of noise prior statistics, the accuracy of CKF filter decreases or even diverges.According to the principle of maximum posteriori estimation, a ADCKF algorithm with noise statistics estimator is studied in this paper.The simulation results show that the prior statistics of random noise of inertial devices are not required accurately before filtering, and they have adaptive ability to deal with the statistical changes of random noise of inertial devices.Finally, the volume Kalman filter and its improved filtering are studied in the navigation system.The nonlinear error model of inertial navigation system based on the error of velocity and attitude is established. The CKF and its improved filtering algorithm are applied to the nonlinear inertial navigation system.The simulation results show that the STCKF and ADCKF in the improved filtering algorithm can solve the filtering estimation problem when the measurement equation can not be accurately known. It has higher reliability, better practicability and better navigation accuracy than CKF.
【學(xué)位授予單位】：哈爾濱工程大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：TN713;TN96

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本文編號(hào)：1707973