【摘要】：初始對準(zhǔn)是捷聯(lián)慣導(dǎo)(Strapdown Inertial Navigation System,SINS)的一項關(guān)鍵技術(shù)。濾波(即狀態(tài)估計)在初始對準(zhǔn)中發(fā)揮了至關(guān)重要的作用。當(dāng)誤差模型為線性時,經(jīng)典的卡爾曼濾波具有十分出色的估計效果。當(dāng)誤差模型為非線性時,采用不同的非線性濾波方法估計效果是不同的。無跡卡爾曼濾波(Unscented Kalman Filter, UKF)是一種性能十分出色的非線性濾波方法。從產(chǎn)生之日起,便在工程上得到了廣泛的應(yīng)用。自由調(diào)節(jié)參數(shù)κ的取值對于UKF的濾波精度和穩(wěn)定性是至關(guān)重要的。一直以來,傳統(tǒng)取值認(rèn)為在滿足n + κ = 3 (n為狀態(tài)變量的維數(shù)),濾波精度是最優(yōu)的。但是,隨著容積卡爾曼濾波(Cubature Kalman Filter,CKF)的產(chǎn)生,自由調(diào)節(jié)參數(shù)的傳統(tǒng)取值面臨了巨大的問題。因為從濾波方法上看,CKF濾波是UKF濾波在自由調(diào)節(jié)參數(shù)κ=0時的一種特例。在不同的維數(shù)下,兩種濾波方法的精度是不同的。因此,本文以自由調(diào)節(jié)參數(shù)為核心,主要研究了κ對于UKF濾波精度的影響。同時,針對濾波模型中會存在線性方程的情況,分別給出了兩種模型化的UKF算法。文章首先介紹了重力場的分布特性、地球形狀的兩種定義方式以及經(jīng)、緯度的有關(guān)定義。對坐標(biāo)系及坐標(biāo)變換進(jìn)行了詳細(xì)的介紹,在此基礎(chǔ)上推導(dǎo)了捷聯(lián)慣導(dǎo)系統(tǒng)的誤差方程。本文中給出了擴展與非擴展UT變換的過程,同時也給出了擴展與非擴展UKF濾波算法。對于兩種方式濾波算法的精度比較,推導(dǎo)了基于泰勒展開式的擴展與非擴展UKF的表達(dá)形式,分析了在不同維數(shù)、不同調(diào)節(jié)參數(shù)取值下兩種濾波的精度。同時,也基于均值、方差與奇次矩的形式比較了兩種濾波的精度。從而指出了在兩種調(diào)節(jié)參數(shù)取值下,如何選擇擴展或非擴展UKF會更佳的結(jié)論。同時,推導(dǎo)了 UKF的均值近似誤差的表達(dá)形式,并證明了 κ的取值與系統(tǒng)模型具有相關(guān)性。進(jìn)而提出了 κ的在線調(diào)整算法,即自調(diào)整UKF算法。整個算法第一步先根據(jù)模型初步選取κ的值,使得估計的誤差在幾個事先設(shè)定的κ下能夠達(dá)到最小。然后在每一時刻濾波時根據(jù)量測量的一步預(yù)測信息在第一步的κ取值附近進(jìn)行在線調(diào)整,使得濾波估計達(dá)到最優(yōu)。在線調(diào)整算法相比固定參數(shù)的UKF,雖然計算量有所增加,但是估計精度會得到提高。若狀態(tài)方程或量測方程有一個是線性時,那么UKF算法就會得到簡化,從而推導(dǎo)了兩種模型化的UKF。本文對兩種模型化UKF算法的計算量進(jìn)行了定量的分析。相比傳統(tǒng)UKF算法,兩種模型化的算法在保證精度不會降低的同時,算法的計算量都會得到減小。最后,本文根據(jù)SINS誤差模型的特點,將自調(diào)整UKF和模型化UKF應(yīng)用到初始對準(zhǔn)中,分別解決傳統(tǒng)UKF估計精度低和計算量大的問題。仿真結(jié)果表明了兩種非線性濾波算法的有效性,為實際工程應(yīng)用提供了有力的理論保證。
[Abstract]:Initial alignment is a key technology of sins (Strapdown Inertial Navigation System,SINS. Filtering (state estimation) plays an important role in initial alignment. When the error model is linear, the classical Kalman filter has a very good estimation effect. When the error model is nonlinear, the estimation effect of different nonlinear filtering methods is different. Unscented Kalman filter (Unscented Kalman Filter, UKF) is an excellent nonlinear filtering method. Since its birth, it has been widely used in engineering. It is very important for the filtering accuracy and stability of UKF to adjust the parameter 魏 freely. Traditionally, it is considered that the filtering accuracy is optimal when n 魏 = 3 (n is the dimension of the state variable). However, with the production of volumetric Kalman filter (Cubature Kalman Filter,CKF), the traditional value of freely adjusted parameters is faced with great problems. Because from the view of filtering method, CKF filter is a special case of UKF filter when the parameter 魏 = 0. Under different dimensions, the accuracy of the two filtering methods is different. Therefore, the effect of 魏 on the accuracy of UKF filtering is mainly studied with the freely adjusted parameters as the core. At the same time, two modelled UKF algorithms are given to solve the problem of linear equations in the filter model. In this paper, the distribution characteristics of gravity field, two definitions of earth shape, and the definitions of longitude and latitude are introduced. The coordinate system and coordinate transformation are introduced in detail, and the error equation of strapdown inertial navigation system is derived. In this paper, the process of extended and non-extended UT transform is given, and the extended and non-extended UKF filtering algorithms are also given. For the comparison of the accuracy of the two filtering algorithms, the expressions of extended and non-extended UKF based on Taylor expansion are derived, and the accuracy of the two filtering methods under different dimensions and different adjusting parameters are analyzed. At the same time, the accuracy of the two filtering methods is compared based on the mean, variance and odd moment. It is pointed out that it is better to choose extended or non-extended UKF under two adjusting parameters. At the same time, the expression of the mean approximation error of UKF is deduced, and the correlation between the value of 魏 and the system model is proved. Furthermore, an online adjustment algorithm of 魏, self-tuning UKF algorithm, is proposed. The first step of the whole algorithm is to select the value of 魏 according to the model, so that the error of estimation can be minimized under several pre-set 魏. Then the filter is adjusted online according to the one-step prediction information of the measurement at every time, which makes the filter estimate to be optimal. Compared with the UKF, with fixed parameters, the estimation accuracy of the online adjustment algorithm will be improved. If one of the equations of state or measurement is linear, the UKF algorithm is simplified and two modelled UKF. are derived. In this paper, the computational complexity of two modeling UKF algorithms is analyzed quantitatively. Compared with the traditional UKF algorithm, the computational complexity of the two modeling algorithms will be reduced at the same time as the accuracy will not be reduced. Finally, according to the characteristics of SINS error model, self-adjusting UKF and modelled UKF are applied to initial alignment to solve the problems of low accuracy and large computational complexity of traditional UKF estimation, respectively. The simulation results show the effectiveness of the two nonlinear filtering algorithms and provide a strong theoretical guarantee for practical engineering applications.
【學(xué)位授予單位】：哈爾濱工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TN713;TN96

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