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首页> 外文期刊>IEEE Transactions on Aerospace and Electronic Systems >Nonlinear Filtering With a Polynomial Series of Gaussian Random Variables
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Nonlinear Filtering With a Polynomial Series of Gaussian Random Variables

机译：具有多项式系列高斯随机变量的非线性滤波

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摘要

Filters relying on the Gaussian approximation typically incorporate the measurement linearly, i.e., the value of the measurement is premultiplied by a matrix-valued gain in the state update. Nonlinear filters that relax the Gaussian assumption, on the other hand, typically approximate the distribution of the state with a finite sum of point masses or Gaussian distributions. In this work, the distribution of the state is approximated by a polynomial transformation of a Gaussian distribution, allowing for all moments, central and raw, to be rapidly computed in a closed form. Knowledge of the higher order moments is then employed to perform a polynomial measurement update, i.e., the value of the measurement enters the update function as a polynomial of arbitrary order. A filter employing a Gaussian approximation with linear update is, therefore, a special case of the proposed algorithm when both the order of the series and the order of the update are set to one: it reduces to the extended Kalman filter. At the cost of more computations, the new methodology guarantees performance better than the linear/Gaussian approach for nonlinear systems. This work employs monomial basis functions and Taylor series, developed in the differential algebra framework, but it is readily extendable to an orthogonal polynomial basis.
机译：依赖于高斯近似的滤波器通常用线性地包含测量，即，通过状态更新中的矩阵值增益，测量值预先增加。另一方面，放松高斯假设的非线性过滤器通常近似于具有有限的点质量或高斯分布的状态的分布。在这项工作中，状态的分布由高斯分布的多项式转换近似，允许全部，中央和原始，以封闭形式快速计算。然后采用对高阶矩的知识来执行多项式测量更新，即，测量值进入更新功能作为任意顺序的多项式。因此，使用线性更新的高斯近似的过滤器是当系列的顺序和更新的顺序都设置为一个特殊情况，所提出的算法是一个：它减少到扩展的卡尔曼滤波器。以更高计算的成本，新方法保证性能优于非线性系统的线性/高斯方法。这项工作采用单体基本函数和泰勒系列，在差动代数框架中发展，但它易于伸展到正交多项式基础。

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