基于高斯和的滤波算法研究

发布时间：2018-05-29 07:27

本文选题：高斯和滤波 + 非高斯分布　；参考：《西安工程大学》2015年硕士论文

【摘要】：高斯和滤波理论主要用于处理系统噪声为非高斯分布、或非线性系统模型的后验概率密度不能用单个高斯分布来近似的情况。目前,航空航天、电子信息和目标跟踪等领域都广泛和充分的应用了高斯和理论。针对各种特定条件下的系统,学者们结合高斯和思想,推导出了相应特定环境下的滤波算法:例如适用于线性系统的高斯和卡尔曼滤波算法、能够处理弱非线性系统的高斯和扩展卡尔曼滤波算法、能够解决强非线性系统的高斯和粒子滤波算法等。但是目前的研究成果还有两个方面的不足没有得到完全彻底的解决:一方面是由于算法本身的缺陷使得滤波效果不够好,另一方面是某些条件下的滤波问题还没有相应的算法能够处理。因此本课题在现有算法的基础上作进一步的改进和研究,提出滤波精度更高和能够处理其他不同条件下的高斯和滤波算法。本课题完成的研究内容包括:(1)欠观测条件下的高斯和增量卡尔曼滤波算法由于环境和设备的影响,滤波过程中常常带有未知的量测系统误差,欠观测条件下的增量卡尔曼滤波算法能够在很大程度上去除这种误差,很好地进行状态跟踪。然而,当系统过程噪声以及系统量测噪声是非高斯分布的情况下,这种方法不能直接使用。针对该问题,本课题结合高斯和的理论思想,提出一种欠观测条件下的高斯和增量卡尔曼滤波算法。该算法将初始状态、系统过程噪声以及系统量测噪声都用高斯和的方式来近似,接着按照增量卡尔曼滤波的思想对每个高斯项做预测以及更新,最后以累加和的形式近似的表示出系统的状态估计值。仿真结果表明:该算法在非高斯噪声分布的情况下,既能成功地消除量测系统误差,又能有效地提高滤波估计的准确度和可靠性。(2)基于弦线去导的高斯和迭代扩展卡尔曼滤波算法当系统为强非线性高斯分布系统,且量测方程的非线性函数比较复杂,Jacobian矩阵的求解比较困难时,通过采用弦线法去导并结合IEKF算法进行状态估计,但是当系统的非线性较强且满足非高斯分布时,这种算法不再适用。针对该问题,本课题提出基于弦线去导的高斯和迭代扩展卡尔曼滤波算法。该算法使用高斯和滤波理论来处理非高斯分布的情况,同时采用割线法,即求解两点间的割线斜率代替Jacobian矩阵,这样避免了不易求解Jacobian矩阵带来的困扰。仿真实验证明:该算法能够提高滤波精度,能有效地进行状态估计和状态跟踪。(3)有色噪声条件下的高斯和卡尔曼滤波算法标准卡尔曼滤波算法要求系统的过程噪声以及系统的量测噪声的均值都是零而且要是高斯白噪声。然而在实际应用的过程中,经常会遇到噪声是非高斯分布的有色噪声,因此不能直接应用卡尔曼滤波算法。针对该问题,我们结合处理有色噪声的滤波思想以及高斯和滤波理论,提出了有色噪声条件下的高斯和卡尔曼滤波算法。首先,分别采用状态扩维以及量测扩维的方法对系统的过程噪声和系统的量测噪声进行白化处理。然后,根据高斯和滤波思想,用多个高斯项的叠加来近似非高斯分布,实现对系统的状态估计。仿真实验能够证明,本文提出的新算法能够消除有色噪声的影响,有效地追踪目标状态。
[Abstract]:Gauss and filter theory are mainly used to deal with the condition that the system noise is non Gauss distribution, or the posterior probability density of the nonlinear system model can not be approximated by a single Gauss distribution. At present, the aerospace, electronic information and target tracking are widely and fully applied to Gauss and theory. In combination with Gauss and thought, scholars have derived a corresponding filtering algorithm in a specific environment, such as Gauss and Calman filtering algorithms suitable for linear systems, which can handle Gauss and extended Calman filtering algorithms for weak nonlinear systems, and can solve the Gauss and particle filtering algorithms of strong nonlinear systems. There are two deficiencies in the results are not completely solved: on the one hand, because of the defects of the algorithm itself, the filtering effect is not good enough, on the other hand, the filtering problem under certain conditions has no corresponding algorithm to deal with. The wave precision is higher and can deal with the Gauss and filtering algorithms under different conditions. The research contents of this topic include: (1) the Gauss and incremental Calman filtering algorithms under under observed conditions often have unknown measurement system error and incremental Calman filter under the condition of under observation due to the influence of environment and equipment. This method can not be used directly when the noise of the system process and the measurement noise of the system are non Gauss distribution. In view of the problem, this paper proposes a kind of Gauss and increment under the condition of under observation. The Calman filtering algorithm, which approximates the initial state, the system process noise and the system measurement noise in the way of Gauss and the method, then predicts and updates each Gauss term according to the thought of incremental Calman filtering. Finally, the state estimation of the system is approximated in the form of accumulative sum. The simulation results show that: In the case of non Gauss noise distribution, the algorithm can not only successfully eliminate the measurement system error, but also effectively improve the accuracy and reliability of the filter estimation. (2) the Gauss and iterative extended Calman filtering algorithm based on the string to guide the system is strongly nonlinear Gauss distribution system, and the nonlinear function of the measurement equation is complex, Jac When the solution of Obian matrix is difficult, the algorithm is used to estimate the state by using string method and IEKF algorithm. But when the system has strong nonlinearity and satisfies the non Gauss distribution, this algorithm is no longer applicable. In this problem, we propose the Gauss and iterative extended Calman filtering algorithm based on the chord line to guide. The algorithm is used. Gauss and filter theory are used to deal with the non Gauss distribution. At the same time, the secant method is used to solve the secant slope between two points instead of the Jacobian matrix. This avoids the difficulty of solving the problems caused by the Jacobian matrix. The simulation experiment proves that the algorithm can improve the filtering precision and can effectively carry out state estimation and state tracking. (3) colored noise. The standard Calman filtering algorithm for Gauss and Calman filtering algorithms under sound conditions requires that the process noise of the system and the mean of the measurement noise of the system are zero and if Gauss is white noise. However, in the actual application process, the noise is often encountered in the non Gauss distribution of the colored noise, so it can not be directly applied to the Calman filter. In view of this problem, we combine the filtering idea of colored noise and the Gauss and filter theory, and propose a Gauss and Calman filtering algorithm under the colored noise condition. First, the process noise of the system and the measurement noise of the system are whitened with the method of state expansion and measurement expansion. According to Gauss and filter thought, the state estimation of the system is realized by using the superposition of multiple Gauss terms to approximate the state of the system. The simulation experiment can prove that the new algorithm proposed in this paper can eliminate the influence of colored noise and effectively track the state of the target.
【学位授予单位】：西安工程大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713

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