Projection Filtering with Observed State Increments with Applications in Continuous-Time Circular Filtering.
Projection Filtering with Observed State Increments with Applications in Continuous-Time Circular Filtering.
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DOI：
10.1109/tsp.2022.3143471
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发表时间：
2022
影响因子：
5.4
通讯作者：
Drugowitsch, Jan
中科院分区：
文献类型：
--
作者：
Kutschireiter, Anna;Rast, Luke;Drugowitsch, Jan
关键词：
角路径积分是系统从潜在噪声角速度（或增量）观测值估计其自身航向的能力。依赖于这些噪声增量的总和的用于角路径积分的非概率算法没有适当地考虑这样的观测的可靠性，这对于适当地权衡针对传入信息的当前航向方向估计是必要的。在概率环境中，角路径积分可以用公式表示为具有观测状态增量的连续时间非线性滤波问题（循环滤波）。航向方向的圆形对称性使得该推理任务固有地非线性，从而排除了使用流行的推理算法（例如卡尔曼滤波器），使得问题无法解析。在这里，我们推导出一个近似的解决方案，循环连续时间滤波，它集成了状态增量观测，同时保持一个固定的表示，通过状态传播和观测更新。具体而言，我们扩展了既定的投影过滤方法，以考虑到观察到的状态增量，并将此框架应用于循环过滤问题。我们进一步提出了一个生成模型的连续时间角值直接观察的隐藏状态，我们无缝集成到投影滤波器。应用所得到的计划的概率角路径积分模型，我们推导出一个算法的圆形滤波，我们称之为圆形卡尔曼滤波器。重要的是，该算法是可分析的，可解释的，并且优于基于高斯近似的替代滤波器。
Angular path integration is the ability of a system to estimate its own heading direction from potentially noisy angular velocity (or increment) observations. Non-probabilistic algorithms for angular path integration, which rely on a summation of these noisy increments, do not appropriately take into account the reliability of such observations, which is essential for appropriately weighing one’s current heading direction estimate against incoming information. In a probabilistic setting, angular path integration can be formulated as a continuous-time nonlinear filtering problem (circular filtering) with observed state increments. The circular symmetry of heading direction makes this inference task inherently nonlinear, thereby precluding the use of popular inference algorithms such as Kalman filters, rendering the problem analytically inaccessible. Here, we derive an approximate solution to circular continuous-time filtering, which integrates state increment observations while maintaining a fixed representation through both state propagation and observational updates. Specifically, we extend the established projection-filtering method to account for observed state increments and apply this framework to the circular filtering problem. We further propose a generative model for continuous-time angular-valued direct observations of the hidden state, which we integrate seamlessly into the projection filter. Applying the resulting scheme to a model of probabilistic angular path integration, we derive an algorithm for circular filtering, which we term the circular Kalman filter. Importantly, this algorithm is analytically accessible, interpretable, and outperforms an alternative filter based on a Gaussian approximation.
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DOI：
10.3390/e21050505
发表时间：
2019-05-17
期刊：
Entropy (Basel, Switzerland)
影响因子：
--
作者：
Nüsken N;Reich S;Rozdeba PJ
通讯作者：
Rozdeba PJ
影响因子：
19.9
作者：
Fiser, Jozsef;Berkes, Pietro;Orban, Gergo;Lengyel, Mate
通讯作者：
Lengyel, Mate
影响因子：
2.2
作者：
Doucet, A;Godsill, S;Andrieu, C
通讯作者：
Andrieu, C
影响因子：
6.8
作者：
Brigo, D;Hanzon, B;LeGland, F
通讯作者：
LeGland, F
影响因子：
2.2
作者：
Gatto, Riccardo
通讯作者：
Gatto, Riccardo