變分非線性濾波方法研究及其在水下潛器組合導(dǎo)航中的應(yīng)用
發(fā)布時(shí)間：2018-07-25 20:38
【摘要】：基于貝葉斯估計(jì)原理的濾波器具有算法實(shí)現(xiàn)簡單、濾波精度高、收斂性好等優(yōu)點(diǎn),正逐漸成為當(dāng)前及未來非線性估計(jì)理論研究熱點(diǎn)和重點(diǎn)之一。本文圍繞水下潛器組合導(dǎo)航系統(tǒng)對狀態(tài)估計(jì)器的應(yīng)用需求,系統(tǒng)開展變分非線性濾波方法研究,論文的主要研究工作歸納如下:針對水下潛器組合導(dǎo)航的特點(diǎn),建立其狀態(tài)估計(jì)模型,并通過前向科爾莫格洛夫方程給出模型求解的弱解方程(即隨機(jī)微分模型)。由此提出利用變分解法探索濾波器設(shè)計(jì)的思路。針對低維狀態(tài)空間,嘗試采用三次樣條插值和雙二次插值方法逼近一維系統(tǒng)和二維系統(tǒng)的狀態(tài)概率解,并給出了理論推導(dǎo)和算法流程,分析了算法的計(jì)算復(fù)雜度與收斂速度。仿真實(shí)驗(yàn)采用非線性系統(tǒng)模型評價(jià)插值方法的性能,實(shí)驗(yàn)結(jié)果顯示插值穩(wěn)定性好,插值結(jié)果與目標(biāo)曲線吻合度高,即插值方法可以很好的跟蹤系統(tǒng)狀態(tài)的變化,且與粒子濾波算法相比估計(jì)精度高,仿真結(jié)果驗(yàn)證了插值方法在低維狀態(tài)空間中逼近隨機(jī)微分模型概率解的可行性。針對高維狀態(tài)空間系統(tǒng),提出一種基于有限元遞推估計(jì)的非線性濾波方法(Finite Element Method based Filter,FEMF),利用區(qū)域剖分和分片插值思想,理論推導(dǎo)出在函數(shù)空間中逼近導(dǎo)航狀態(tài)概率解的過程,并對算法的收斂性、收斂速度和計(jì)算復(fù)雜度進(jìn)行了數(shù)學(xué)分析。通過與擴(kuò)展卡爾曼濾波、無跡卡爾曼濾波、粒子濾波算法的對比分析實(shí)驗(yàn),表明有限元方法可以提高濾波估計(jì)精度。通過仿真驗(yàn)證該方法較粒子濾波算法具有更好的性能。針對FEMF方法實(shí)時(shí)性不高的問題,提出一種基于Yau-Yau Method與有限元相結(jié)合的混合濾波算法。該算法利用Yau-Yau Method估計(jì)形函數(shù)構(gòu)造模型中的估值點(diǎn),再用有限元估計(jì)系統(tǒng)狀態(tài)概率解,有效地提高了算法的運(yùn)行效率。該方法與FEMF方法相比極大地降低了算法計(jì)算量,并且編程實(shí)現(xiàn)較有限元方法簡單。采用非線性非高斯系統(tǒng)模型進(jìn)行仿真實(shí)驗(yàn),仿真結(jié)果顯示YY-FEMF方法更適合處理目標(biāo)跟蹤等對實(shí)時(shí)性及精度要求較高場合下的非線性非高斯?fàn)顟B(tài)估計(jì)問題。針對FEMF方法對插值函數(shù)的光滑性限制,提出一種基于Hermit基函數(shù)的投影濾波算法。該算法可以建立一個(gè)在整個(gè)連續(xù)空間具有高階微分導(dǎo)數(shù)性質(zhì)的插值函數(shù),且在求解過程中不涉及矩陣和積分運(yùn)算,極大地減少了計(jì)算量,提高濾波算法的實(shí)時(shí)性,并且從理論上分析了算法的收斂性。仿真實(shí)驗(yàn)中采用兩個(gè)非線性模型,給出投影濾波與擴(kuò)展卡爾曼濾波、無跡卡爾曼濾波、粒子濾波算法對比分析實(shí)驗(yàn)結(jié)果,表明算法有效地提高了濾波估計(jì)性能。論文最后選擇慣性/地形、慣性/地磁兩種應(yīng)用于水下潛器的新興組合導(dǎo)航模式進(jìn)行濾波算法性能評估,仿真結(jié)果表明本文提出的方法均具有較好的輸出精度和應(yīng)用效果。
[Abstract]:The filter based on Bayesian estimation principle has the advantages of simple algorithm, high filtering accuracy and good convergence. It is becoming one of the hot and important points in the research of nonlinear estimation theory at present and in the future. In this paper, the research of variational nonlinear filtering method is carried out around the application demand of underwater vehicle integrated navigation system. The main research work of this paper is summarized as follows: aiming at the characteristics of underwater vehicle integrated navigation system, The state estimation model is established, and the weak solution equation (i.e. stochastic differential model) is given through the forward Kolmoglof equation. Therefore, the idea of using variable decomposition method to explore filter design is put forward. For low dimensional state space, cubic spline interpolation and biquadratic interpolation are used to approximate the state probabilistic solutions of one-dimensional and two-dimensional systems. The theoretical derivation and algorithm flow are given, and the computational complexity and convergence rate of the algorithm are analyzed. In the simulation experiment, nonlinear system model is used to evaluate the performance of the interpolation method. The experimental results show that the interpolation method has good stability and high consistency with the target curve, that is, the interpolation method can track the change of the system state. Compared with the particle filter algorithm, the estimation accuracy is higher. The simulation results show that the interpolation method is feasible to approximate the probabilistic solution of the stochastic differential model in the low-dimensional state space. For high dimensional state space system, a nonlinear filtering method (Finite Element Method based filter based on finite element recursive estimation (Finite Element Method based filter FEMF) is proposed. The process of approaching the probabilistic solution of navigation state in function space is derived theoretically by using the idea of region partition and piecewise interpolation. The convergence, convergence speed and computational complexity of the algorithm are analyzed. By comparing with extended Kalman filter, unscented Kalman filter and particle filter, it is shown that the finite element method can improve the estimation accuracy of the filter. Simulation results show that this method has better performance than particle filter algorithm. A hybrid filtering algorithm based on Yau-Yau Method and finite element method is proposed to solve the problem of low real-time performance of FEMF method. The algorithm uses Yau-Yau Method to estimate the estimated points in the model and finite element method to estimate the probabilistic solution of the system state. The efficiency of the algorithm is improved effectively. Compared with the FEMF method, this method greatly reduces the computational complexity of the algorithm, and the programming is simpler than the finite element method. The simulation results show that the YY-FEMF method is more suitable to deal with the nonlinear non-Gao Si state estimation problems with higher real-time and precision requirements such as target tracking by using the nonlinear non-Gao Si system model. A projection filtering algorithm based on Hermit basis function is proposed to limit the smoothness of interpolation function by FEMF method. This algorithm can establish an interpolation function with the property of high-order differential derivative in the whole continuous space, and the matrix and integral operation are not involved in the solution process, which greatly reduces the computational complexity and improves the real-time performance of the filtering algorithm. The convergence of the algorithm is analyzed theoretically. In the simulation experiment, two nonlinear models are used, the projection filter and the extended Kalman filter, the unscented Kalman filter and the particle filter algorithm are compared and the experimental results show that the algorithm can improve the performance of the filter estimation effectively. Finally, two new integrated navigation modes, inertial / topographic, inertial / geomagnetic, are selected to evaluate the performance of the filtering algorithm. The simulation results show that the proposed methods have good output accuracy and application effect.
【學(xué)位授予單位】：哈爾濱工程大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：U666.1;TN713;TN967.2
[Abstract]:The filter based on Bayesian estimation principle has the advantages of simple algorithm, high filtering accuracy and good convergence. It is becoming one of the hot and important points in the research of nonlinear estimation theory at present and in the future. In this paper, the research of variational nonlinear filtering method is carried out around the application demand of underwater vehicle integrated navigation system. The main research work of this paper is summarized as follows: aiming at the characteristics of underwater vehicle integrated navigation system, The state estimation model is established, and the weak solution equation (i.e. stochastic differential model) is given through the forward Kolmoglof equation. Therefore, the idea of using variable decomposition method to explore filter design is put forward. For low dimensional state space, cubic spline interpolation and biquadratic interpolation are used to approximate the state probabilistic solutions of one-dimensional and two-dimensional systems. The theoretical derivation and algorithm flow are given, and the computational complexity and convergence rate of the algorithm are analyzed. In the simulation experiment, nonlinear system model is used to evaluate the performance of the interpolation method. The experimental results show that the interpolation method has good stability and high consistency with the target curve, that is, the interpolation method can track the change of the system state. Compared with the particle filter algorithm, the estimation accuracy is higher. The simulation results show that the interpolation method is feasible to approximate the probabilistic solution of the stochastic differential model in the low-dimensional state space. For high dimensional state space system, a nonlinear filtering method (Finite Element Method based filter based on finite element recursive estimation (Finite Element Method based filter FEMF) is proposed. The process of approaching the probabilistic solution of navigation state in function space is derived theoretically by using the idea of region partition and piecewise interpolation. The convergence, convergence speed and computational complexity of the algorithm are analyzed. By comparing with extended Kalman filter, unscented Kalman filter and particle filter, it is shown that the finite element method can improve the estimation accuracy of the filter. Simulation results show that this method has better performance than particle filter algorithm. A hybrid filtering algorithm based on Yau-Yau Method and finite element method is proposed to solve the problem of low real-time performance of FEMF method. The algorithm uses Yau-Yau Method to estimate the estimated points in the model and finite element method to estimate the probabilistic solution of the system state. The efficiency of the algorithm is improved effectively. Compared with the FEMF method, this method greatly reduces the computational complexity of the algorithm, and the programming is simpler than the finite element method. The simulation results show that the YY-FEMF method is more suitable to deal with the nonlinear non-Gao Si state estimation problems with higher real-time and precision requirements such as target tracking by using the nonlinear non-Gao Si system model. A projection filtering algorithm based on Hermit basis function is proposed to limit the smoothness of interpolation function by FEMF method. This algorithm can establish an interpolation function with the property of high-order differential derivative in the whole continuous space, and the matrix and integral operation are not involved in the solution process, which greatly reduces the computational complexity and improves the real-time performance of the filtering algorithm. The convergence of the algorithm is analyzed theoretically. In the simulation experiment, two nonlinear models are used, the projection filter and the extended Kalman filter, the unscented Kalman filter and the particle filter algorithm are compared and the experimental results show that the algorithm can improve the performance of the filter estimation effectively. Finally, two new integrated navigation modes, inertial / topographic, inertial / geomagnetic, are selected to evaluate the performance of the filtering algorithm. The simulation results show that the proposed methods have good output accuracy and application effect.
【學(xué)位授予單位】：哈爾濱工程大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：U666.1;TN713;TN967.2
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1 張?jiān)?鄭南寧,袁澤劍;一種改進(jìn)的圖像自適應(yīng)非線性濾波方法[J];西安交通大學(xué)學(xué)報(bào);2004年02期
2 李俊生;圖像非線性濾波技術(shù)的研究[J];常州工學(xué)院學(xué)報(bào);2005年02期
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4 馮馳;杜云明;;一種高效的非線性濾波技術(shù)[J];應(yīng)用科技;2007年04期
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