Computationally Efficient Adaptive Spline Filters for Nonlinear State Estimation

用于非线性状态估计的计算高效的自适应样条滤波器

• 批准号: 250256-2012
• 负责人: Kirubarajan, Thia
• 金额: $ 2.4万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=570863
• 关键词: Computationally; Efficient; Adaptive; Spline; Filters

The problem of nonlinear/non-Gaussian filtering has generated significant interest in the literature due to the inherent nonlinearity in most practical systems. The nonlinearity in state estimation problems may arise due to its presence in the state-to-measurement equation or in the evolution of the state itself. The presence of multiple objects further complicates the problem by adding data association to the mix. The optimal nonlinear state estimator consists of the computation of the conditional (posterior) pdf of the multitarget state given all the measurements available up to the current time. Optimal multitarget nonlinear filtering is in general a non-tractable problem, not just because of computational complexity but also due to the multimodal nature of multitarget pdf. Under these circumstances, one needs an algorithm that is capable of automatically adapting itself by recognizing the spatio-temporal nonlinearity variations (over one target or across multiple ones). Our multitarget state propagation will be based on multidimensional spline representation. Splines have been used effectively to represent complex (and arbitrary) curves and surfaces in computer science, graphics, aerospace, automobile industry, statistics and mathematics using a finite set of knots. Our innovative approach is to use splines to represent any arbitrary multitarget pdf and then derive the equations for propagating the splines over time based on the standard prediction and update steps. Splines posses a number of desirable properties: they are continuous, can handle multiple models, inherently capable of measuring nonlinearity, do not suffer from degeneracy or need resampling, can incorporate road map-like constraints, are sensor-agnostic and can be adaptive by varying knots spatially and temporally. Significant theoretical extensions to the more realistic state estimation problems with multiple targets, false alarms, missed detections and constraints are proposed in this work.

由于大多数实际系统固有的非线性，非线性/非高斯滤波问题引起了文献的极大兴趣。状态估计问题中的非线性可能由于其存在于状态测量方程或状态本身的演化中而出现。多个对象的存在通过添加数据关联使问题进一步复杂化。最优非线性状态估计器包括计算多目标状态的条件（后验）pdf，其中给出了截至当前时间可用的所有测量值。最优多目标非线性滤波通常是一个难以处理的问题，不仅因为计算复杂性，还因为多目标 pdf 的多模态性质。 在这些情况下，我们需要一种能够通过识别时空非线性变化（在一个目标上或跨多个目标）来自动适应的算法。我们的多目标状态传播将基于多维样条表示。样条曲线已被有效地用于使用一组有限的结来表示计算机科学、图形学、航空航天、汽车工业、统计学和数学中的复杂（和任意）曲线和曲面。我们的创新方法是使用样条线来表示任意多目标 pdf，然后根据标准预测和更新步骤推导随时间传播样条线的方程。样条曲线具有许多理想的特性：它们是连续的，可以处理多个模型，本质上能够测量非线性，不会遭受简并或需要重新采样，可以合并类似路线图的约束，与传感器无关，并且可以通过改变空间和时间上的结。这项工作提出了对多目标、误报、漏检和约束等更现实的状态估计问题的重大理论扩展。