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Risk-sensitive filtering and smoothing via reference probabilitymethods

机译：通过参考概率方法进行风险敏感的过滤和平滑

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摘要

We address the risk-sensitive filtering problem which is minimizing the expectation of the exponential of the squared estimation error multiplied by a risk-sensitive parameter. Such filtering can be more robust to plant and noise uncertainty than minimum error variance filtering. Although optimizing a differently formulated performance index to that of the so-called H∞ filtering, risk-sensitive filtering leads to a worst case deterministic noise estimation problem given from the differential game associated with H ∞ filtering. We consider a class of discrete-time stochastic nonlinear state-space models. We present linear recursions in the information state and the result for the filtered estimate that minimizes the risk-sensitive cost index. We also present fixed-interval smoothing results for each of these signal models. In addition, a brief discussion is included on relations of the risk-sensitive estimation problem to minimum variance estimation and a worst case estimation problem in a deterministic noise scenario related to minimax dynamic games. The technique used in this paper is the so-called reference probability method which defines a new probability measure where the observations are independent and translates the problem to the new measure. The optimization problem is solved using simple estimation theory in the new measure, and the results are interpreted as solutions in the original measure
机译：我们解决了风险敏感的过滤问题，该问题使对估计​​误差平方乘以风险敏感参数的指数期望最小化。与最小误差方差过滤相比，这种过滤对植物和噪声不确定性的鲁棒性更高。尽管优化了与所谓的H∞滤波不同的性能指标，但是风险敏感型滤波会导致最坏的情况，即与H∞滤波相关的差分博弈给出的确定性噪声估计问题。我们考虑一类离散时间随机非线性状态空间模型。我们提出了信息状态下的线性递归，以及经过过滤的估算结果，该估算使风险敏感性成本指数最小。我们还给出了每个信号模型的固定间隔平滑结果。此外，在与最小极大动态博弈有关的确定性噪声场景中，对风险敏感估计问题与最小方差估计和最坏情况估计问题之间的关系进行了简短讨论。本文中使用的技术是所谓的参考概率方法，该方法定义了一种新的概率测度，其中观测值是独立的，并将问题转化为新的测度。在新度量中使用简单估计理论解决了优化问题，并将结果解释为原始度量中的解决方案

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