带有先验信息的动态定位贝叶斯滤波算法研究
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摘要
在动态定位、导航和卫星定轨中,目标的运动往往受到外部因素的制约,这些制约往往是一些关于未知状态参数的已知函数式或理论关系,它们可以预先获知,我们称之为先验约束信息,如某个参数为非负或整数,状态的上下界,干扰的形式、大小、范围、统计分布特性等。在动态定位时依据客观条件合理利用约束信息,显然可以简化模型,提高状态参数估计的精度,控制滤波的发散。因为状态约束的存在改变了动态定位问题概率方面的结构,给问题的分析及滤波解算带来了一定的难度。在实际处理时,常用的方法一般是通过状态约束方程消去某些状态参数,然后按一般滤波方法进行处理。对于某些非线性情况,这样处理往往使计算显得复杂,同时也使原来的滤波方程发生较大的改变,在实用上显得不方便。由于科学技术的发展,在动态定位中,观测的手段越来越多,观测资料的积累也越来越多,对任意观测目标或对象的物理、力学性质的了解也越来越充分,根据先验信息建立约束的可能性也就越来越大。利用约束可以相对可靠地描述各种先验信息,因而如果能解决具有先验约束信息的动态滤波的计算及精度分析等问题,它将在动态定位的数据处理中得到广泛的应用,同时把滤波理论推广到带有先验约束信息的情形,使动态滤波数据处理理论得到充分的发展和完善。
本文针对带有先验信息的动态定位滤波算法的现状和存在的问题进行了研究,主要贡献有以下几点：
1.研究了异常噪声对动态定位的影响以及如何利用观测值和状态预报值的时间序列来消除其影响性。在动态定位中,当观测值被污染时,给出了一种抗差Bayes滤波算法能够很好地抵制这种异常影响,由于粗差是属于测量值被污染的情形,所以给出的方法也能够抵制粗差所带来的影响。由于我们事先并不知道粗差是否存在,也不知道污染率的大小,因此,在线估计是非常重要的。论文提供给出了可以抵制粗差所带来的影响的动态定位方法以及一种在线估计污染率的
方法。
2.研究了状态变量存在等式约束时的滤波算法,提出了按序贯平差求解算法以及自适应算法。研究了采用不消去状态参数的方法,在卡尔曼滤波的数学模型中增加约束条件方程,推导出约束状态下的卡尔曼滤波递推方程,其形式与一般的卡尔曼滤波递推方程相似,只要在预报值及其协方差阵中增加一个约束条件改正项即可,因而在应用时非常方便。
3.研究了状态变量存在不等式约束时的滤波算法,提供了两种处理不等式约束的滤波方法,一是先求解无约束的滤波解,再进行优化,二是针对其不等式约束求增益矩阵,直接求得滤波的状态估计。理论分析和仿真计算表明充分利用约束先验信息可以提高滤波解的精度,从而提高了动态定位的精度。
4.借鉴了实数中寻找最优解的思想,在整数解的搜索过程中首先寻找局部最优值,然后沿最快下降的方向寻找下一最优解,给出了一个有效求解测量方程中带有未知整参数的动态定位滤波算法。主要贡献：
1)给出了整型参数θ的浮点解的递推估计。
2)实现了动态估计整型参数θ的变化区间。
3)给出了整型参数θ的快速估计算法。实验结果表明,新算法大大提高了传统分枝定界法和已有相关算法的效率,可以用于模糊度未知时的GPS动态定位解算和整周模糊度的确定。
5.针对道路条件下车辆动态定位问题,提出了带道路约束的H∞滤波算法。该算法利用地面目标的特点建立了带道路约束条件的系统模型,并推导了相应的H∞滤波算法。实验仿真结果表明,论文所提出的带约束条件的H∞滤波算法比标准的H∞滤波算法以及同等条件下的卡尔曼滤波算法具有更好的状态估计性能和更高的滤波精度,对于在复杂环境下车辆动态定位具有现实意义。
6.为了减少因线性化所产生的系统误差,研究了非线性Bayes滤波和粒子滤波在动态定位中的应用,重点研究了动态方程是线性的而观测方程是非线性的解算方法,并给出了相应的Bayes递推滤波算法和粒子滤波算法。
论文首次全面系统地研究了带有先验约束信息的动态定位滤波理论,对带有先验约束信息的获取,模型的建立,滤波的解算方法进行了较为详细的研究,并给出了一些新的滤波解算方法,在非线性卡尔曼滤波方面,针对动态导航定位中测量方程非线性的特点,研究了一些新的算法。论文对给出的算法与已有的算法进行了比较,并进行了数据模拟和实例解算,从而验证了算法的有效性,使得算法能够很好地应用于工程计算和军事导航。
In kinematic positioning, navigation and satellite orbit-determination moving of target is often constrained by external factors which are often known functional formulas or theoretical relationships. These factors which may are anticipatory knowledge are known as prior constraint information, such as non-negative parameter, integral parameter, the upper and lower bound of the state, the form of noise interfere, the size of noise interfere, the range of noise interfere and their statistical distribution properties. According to the actual situation of kinematic positioning, it is obvious that making rational use of constraints information which is based on objective conditions can simplify models, improve the accuracy of parameter estimation and well control the filtering. Because the existence of the state constraint condition changes the probability structure of kinematic positioning and brings a certain degree of difficulty of problem analyzing and filtering solving. In practice, the commonly used method is to eliminate some state parameters through the state constraint equations, and then deal with it as an average filtering. For some nonlinear, such treatment often makes the calculation complex, and changes the original filtering equation, therefore it is inconvenient to use in practice. Due to the development of science and technology, in kinematic positioning, there are more means of observing and more observation data accumulated, so that we get increasingly understanding of any observation objects'physical and mechanical properties, and the possibility of establishing constraints according to priori information. It is relatively reliable to describe all kinds of priori information by using constraints. So if you can resolve the calculation and accuracy analysis of the dynamic filtering with priori restraint information, it will be widely applied to data processing in kinematic positioning, and meanwhile can promote the filtering theory to the case with a priori restraint information, so that it can make kinematic filtering data processing theories fully developing and perfecting.
In this paper, the status and the existing problems of kinematic positioning filtering algorithm with a priori information have been studied, Main contributions are as follows
1. The study about the effects of kinematic positioning that caused by abnormal noise, and temporal series which know how to use the observations and the predicted value, can eliminate its influence. In kinematic positioning, when the observations were contaminated, we can give a robust Bayes filtering algorithm which can resist the abnormal influence well, gross errors belong to the case that the observations are contaminated, so the method which was referred can resist the effects that caused by gross errors. We don't know either the existence of gross errors or the size of the contaminated rates, consequently, it is very important to on-line estimation. The paper provides us the kinematic positioning method and the way of contamination rates.
2. This paper studied the filtering algorithm of the state variable which exist equality restriction, and advanced the solution according to sequential adjustment and the adaptive algorithm. This paper also studied the method which introduced to reserve the state parameter, added the restricted conditional equation of the mathematics model in Kalman filtering, and deduced Kalman filtering recurrence equation under the restricted condition, its style was similar to normal Kalman filtering recurrence equation, This paper could add a restricted conditional correction in the predicted value and its covariance matrix, so it is extraordinary convenience in the application.
3. This paper studied the filtering algorithm of the state variable which existed inequality restriction, and supplied two different filtering methods to deal with inequality restriction, first, solved the nonrestrictive filtering solution, and then continued to optimize it. Second, This paper could get gain matrix in allusion to its inequality restriction, and gained the filtering state estimation. Theoretical analysis and simulating calculation show that we can improve the filtering precision through making the best of restricted priori information, consequently, improve the precision of kinematic positioning.
4. This paper drew on the idea that we sought the optimum solution in real number, at first, sought the local optimum solution during the searching process for the integer solution, and then sought the next optimum solution along the direction of the fastest decline in, at last, given a filtering algorithm for kinematic positioning of an effective measurement equation, which contained unknown integer parameter. Main contributions are as follows
1) Given the integer parameter recursive estimation of the float solution.
2) Achieved to estimate the various interval of integer parameter 9 dynamically.
3) Given a fast algorithm on estimation of integer parameterθ. The experiment showed that the newly algorithm greatly improved the efficiency of the traditional branch-bound algorithm and existing relevant algorithm. It could be applied to the kinematic positioning solution of GPS as the ambiguity was unknown, and the determination of the integer ambiguity.
5. For Vehicle Kinematic Positioning under road condition, H∞Filtering algorithm with road constraint is proposed. Using the characteristics of ground targets, the algorithm sets up a system model with road constraints and the corresponding H∞Filtering algorithm is derived. The simulation results show that the proposed H∞Filtering algorithm with constraint condition has a better state estimation performance and higher filtering accuracy than the standard H∞Filtering algorithm and Kalman Filter algorithm. It has practical significance for Vehicle Kinematic Positioning in a complex environment.
6. In order to reduce the system errors arising from linearization, we studied the application of nonlinear Bayes Filtering and Particle Filtering in Kinematic positioning, focused on the research of the solution that dynamic equation is linear but the observation equation is non-linear, and given the corresponding Bayes Recursive Filtering
and Particle Filtering algorithm.
In this paper, the study of the Kinematic Positioning Filtering theory with a priori constraint information is comprehensively and systematically for the first time. This paper carry out a more detailed research in getting information with the priori constraint, model building, resolving methods of the filtering, and giving some new resolving methods of the filtering. In the non-linear Kalman filtering. The papers studied of some new algorithms for the non-linear characteristics in measurement equation of the kinematic positioning and navigation. The paper compared the given algorithm and the existing algorithm, made data simulation and took some solution example, and consequently verified the validity of the algorithm and made the algorithm well be applied to engineering calculations and military navigation.
本文针对带有先验信息的动态定位滤波算法的现状和存在的问题进行了研究,主要贡献有以下几点：
1.研究了异常噪声对动态定位的影响以及如何利用观测值和状态预报值的时间序列来消除其影响性。在动态定位中,当观测值被污染时,给出了一种抗差Bayes滤波算法能够很好地抵制这种异常影响,由于粗差是属于测量值被污染的情形,所以给出的方法也能够抵制粗差所带来的影响。由于我们事先并不知道粗差是否存在,也不知道污染率的大小,因此,在线估计是非常重要的。论文提供给出了可以抵制粗差所带来的影响的动态定位方法以及一种在线估计污染率的
方法。
2.研究了状态变量存在等式约束时的滤波算法,提出了按序贯平差求解算法以及自适应算法。研究了采用不消去状态参数的方法,在卡尔曼滤波的数学模型中增加约束条件方程,推导出约束状态下的卡尔曼滤波递推方程,其形式与一般的卡尔曼滤波递推方程相似,只要在预报值及其协方差阵中增加一个约束条件改正项即可,因而在应用时非常方便。
3.研究了状态变量存在不等式约束时的滤波算法,提供了两种处理不等式约束的滤波方法,一是先求解无约束的滤波解,再进行优化,二是针对其不等式约束求增益矩阵,直接求得滤波的状态估计。理论分析和仿真计算表明充分利用约束先验信息可以提高滤波解的精度,从而提高了动态定位的精度。
4.借鉴了实数中寻找最优解的思想,在整数解的搜索过程中首先寻找局部最优值,然后沿最快下降的方向寻找下一最优解,给出了一个有效求解测量方程中带有未知整参数的动态定位滤波算法。主要贡献：
1)给出了整型参数θ的浮点解的递推估计。
2)实现了动态估计整型参数θ的变化区间。
3)给出了整型参数θ的快速估计算法。实验结果表明,新算法大大提高了传统分枝定界法和已有相关算法的效率,可以用于模糊度未知时的GPS动态定位解算和整周模糊度的确定。
5.针对道路条件下车辆动态定位问题,提出了带道路约束的H∞滤波算法。该算法利用地面目标的特点建立了带道路约束条件的系统模型,并推导了相应的H∞滤波算法。实验仿真结果表明,论文所提出的带约束条件的H∞滤波算法比标准的H∞滤波算法以及同等条件下的卡尔曼滤波算法具有更好的状态估计性能和更高的滤波精度,对于在复杂环境下车辆动态定位具有现实意义。
6.为了减少因线性化所产生的系统误差,研究了非线性Bayes滤波和粒子滤波在动态定位中的应用,重点研究了动态方程是线性的而观测方程是非线性的解算方法,并给出了相应的Bayes递推滤波算法和粒子滤波算法。
论文首次全面系统地研究了带有先验约束信息的动态定位滤波理论,对带有先验约束信息的获取,模型的建立,滤波的解算方法进行了较为详细的研究,并给出了一些新的滤波解算方法,在非线性卡尔曼滤波方面,针对动态导航定位中测量方程非线性的特点,研究了一些新的算法。论文对给出的算法与已有的算法进行了比较,并进行了数据模拟和实例解算,从而验证了算法的有效性,使得算法能够很好地应用于工程计算和军事导航。
In kinematic positioning, navigation and satellite orbit-determination moving of target is often constrained by external factors which are often known functional formulas or theoretical relationships. These factors which may are anticipatory knowledge are known as prior constraint information, such as non-negative parameter, integral parameter, the upper and lower bound of the state, the form of noise interfere, the size of noise interfere, the range of noise interfere and their statistical distribution properties. According to the actual situation of kinematic positioning, it is obvious that making rational use of constraints information which is based on objective conditions can simplify models, improve the accuracy of parameter estimation and well control the filtering. Because the existence of the state constraint condition changes the probability structure of kinematic positioning and brings a certain degree of difficulty of problem analyzing and filtering solving. In practice, the commonly used method is to eliminate some state parameters through the state constraint equations, and then deal with it as an average filtering. For some nonlinear, such treatment often makes the calculation complex, and changes the original filtering equation, therefore it is inconvenient to use in practice. Due to the development of science and technology, in kinematic positioning, there are more means of observing and more observation data accumulated, so that we get increasingly understanding of any observation objects'physical and mechanical properties, and the possibility of establishing constraints according to priori information. It is relatively reliable to describe all kinds of priori information by using constraints. So if you can resolve the calculation and accuracy analysis of the dynamic filtering with priori restraint information, it will be widely applied to data processing in kinematic positioning, and meanwhile can promote the filtering theory to the case with a priori restraint information, so that it can make kinematic filtering data processing theories fully developing and perfecting.
In this paper, the status and the existing problems of kinematic positioning filtering algorithm with a priori information have been studied, Main contributions are as follows
1. The study about the effects of kinematic positioning that caused by abnormal noise, and temporal series which know how to use the observations and the predicted value, can eliminate its influence. In kinematic positioning, when the observations were contaminated, we can give a robust Bayes filtering algorithm which can resist the abnormal influence well, gross errors belong to the case that the observations are contaminated, so the method which was referred can resist the effects that caused by gross errors. We don't know either the existence of gross errors or the size of the contaminated rates, consequently, it is very important to on-line estimation. The paper provides us the kinematic positioning method and the way of contamination rates.
2. This paper studied the filtering algorithm of the state variable which exist equality restriction, and advanced the solution according to sequential adjustment and the adaptive algorithm. This paper also studied the method which introduced to reserve the state parameter, added the restricted conditional equation of the mathematics model in Kalman filtering, and deduced Kalman filtering recurrence equation under the restricted condition, its style was similar to normal Kalman filtering recurrence equation, This paper could add a restricted conditional correction in the predicted value and its covariance matrix, so it is extraordinary convenience in the application.
3. This paper studied the filtering algorithm of the state variable which existed inequality restriction, and supplied two different filtering methods to deal with inequality restriction, first, solved the nonrestrictive filtering solution, and then continued to optimize it. Second, This paper could get gain matrix in allusion to its inequality restriction, and gained the filtering state estimation. Theoretical analysis and simulating calculation show that we can improve the filtering precision through making the best of restricted priori information, consequently, improve the precision of kinematic positioning.
4. This paper drew on the idea that we sought the optimum solution in real number, at first, sought the local optimum solution during the searching process for the integer solution, and then sought the next optimum solution along the direction of the fastest decline in, at last, given a filtering algorithm for kinematic positioning of an effective measurement equation, which contained unknown integer parameter. Main contributions are as follows
1) Given the integer parameter recursive estimation of the float solution.
2) Achieved to estimate the various interval of integer parameter 9 dynamically.
3) Given a fast algorithm on estimation of integer parameterθ. The experiment showed that the newly algorithm greatly improved the efficiency of the traditional branch-bound algorithm and existing relevant algorithm. It could be applied to the kinematic positioning solution of GPS as the ambiguity was unknown, and the determination of the integer ambiguity.
5. For Vehicle Kinematic Positioning under road condition, H∞Filtering algorithm with road constraint is proposed. Using the characteristics of ground targets, the algorithm sets up a system model with road constraints and the corresponding H∞Filtering algorithm is derived. The simulation results show that the proposed H∞Filtering algorithm with constraint condition has a better state estimation performance and higher filtering accuracy than the standard H∞Filtering algorithm and Kalman Filter algorithm. It has practical significance for Vehicle Kinematic Positioning in a complex environment.
6. In order to reduce the system errors arising from linearization, we studied the application of nonlinear Bayes Filtering and Particle Filtering in Kinematic positioning, focused on the research of the solution that dynamic equation is linear but the observation equation is non-linear, and given the corresponding Bayes Recursive Filtering
and Particle Filtering algorithm.
In this paper, the study of the Kinematic Positioning Filtering theory with a priori constraint information is comprehensively and systematically for the first time. This paper carry out a more detailed research in getting information with the priori constraint, model building, resolving methods of the filtering, and giving some new resolving methods of the filtering. In the non-linear Kalman filtering. The papers studied of some new algorithms for the non-linear characteristics in measurement equation of the kinematic positioning and navigation. The paper compared the given algorithm and the existing algorithm, made data simulation and took some solution example, and consequently verified the validity of the algorithm and made the algorithm well be applied to engineering calculations and military navigation.
引文
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