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.

非线性/非高斯过滤的问题由于大多数实用系统的固有非线性而引起了文献的重大兴趣。国家估计问题的非线性可能是由于其在州到测量方程中的存在或国家本身的进化而出现的。通过将数据关联添加到混合物中，多个对象的存在使问题进一步复杂化。最佳的非线性状态估计器包括多坐状态的条件（后）PDF的计算，并且给定当前时间可用的所有测量值。一般而言，最佳的多毒性非线性过滤是一个不可扣除的问题，这不仅是由于计算复杂性，而且还因为Multitarget PDF的多模式性质。 在这种情况下，需要一种能够通过识别时空非线性变化（超过一个目标或多个目标）来自动适应自身的算法。我们的多坐状状态传播将基于多维样条表示。花键已被有效地代表计算机科学，图形，航空航天，汽车行业，统计和数学的复杂（和任意）曲线，并使用有限的结。我们的创新方法是使用花键来表示任何任意的多坐Multitarget PDF，然后根据标准预测和更新步骤得出随着时间的推移传播花样的方程式。花键具有许多理想的特性：它们是连续的，可以处理多种模型，本质上能够测量非线性，不会遭受退化或需要重新采样，可以结合路线图的约束，可以通过空间和时间上的变化来适应传感器 - 敏锐的约束，并且可以适应。在这项工作中提出了针对多个目标，虚假警报，遗漏检测和约束的更现实状态估计问题的重要理论扩展。