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/非高斯滤波问题由于在大多数实际系统中固有的非线性而引起了文献的极大兴趣。状态估计问题中的非线性可能是由于状态-测量方程或状态本身的演化而产生的。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包括给定当前所有可用测量值的多目标状态的条件（后验）pdf的计算。最优多目标非线性滤波通常是一个难以处理的问题，这不仅是因为计算的复杂性，而且还因为多目标非线性滤波的多模态特性。