Nonlinear Kalman Filters in RKHS

最近，在机器学习和信号处理领域，人们对核方法越来越感兴趣，因为它们为当前信息处理的要求苛刻的应用提供了一种有吸引力的非线性系统设计方法。递归状态估计，特别是卡尔曼滤波器，将受益于这样的努力，因为有许多重要的应用在航空航天，汽车，监视和医疗领域，本质上是非线性的，目前的非线性模型有缺点。该提案将研究（非线性）映射到线性函数空间（再生核希尔伯特空间）的可行性，以实现卡尔曼滤波方程并实现与非线性模型相称的性能。这种方法将被调查的困难之一是不断增长的内存需求，将处理新的稀疏化标准和算法的基础上的信息论。该方法将在脑机接口的设计中进行测试，以帮助四肢瘫痪患者，并在汽车发动机控制中进行测试，其中有可用的数据和基准。两名研究生将致力于这一重要课题。

Recently, there has been an increased interest within the machine learning and signal processing communities in kernel methods because they offer an attractive alternative to design nonlinear systems for the demanding current applications of information processing. Recursive state estimation and in particular the Kalman filter, would benefit from such an effort because there are many important applications in aerospace, automotive, surveillance, and medical fields that are intrinsically nonlinear, and the current nonlinear models have drawbacks. This proposal will study the feasibility of a (nonlinear) mapping to a linear functional space (a Reproducing Kernel Hilbert Space) to implement there the Kalman filter equations and achieve performance commensurate with nonlinear models. One of the difficulties of this approach that will be investigated is the growing memory requirements that will be dealt with novel sparsification criteria and algorithms based on information theory. The approach will be tested in the design of brain machine interfaces to help quadraplegics and also in automotive engine control for which there are data available and benchmarks. Two graduate students will be working on this important topic.