Integrated Gaussian Processes for Tracking

IF 2.9 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC
Fred Lydeard;Bashar I. Ahmad;Simon Godsill
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引用次数: 0

Abstract

In applications such as tracking and localisation, a dynamical model is typically specified for the modelling of an object's motion. An appealing alternative to the traditional parametric Markovian dynamical models is the Gaussian Process (GP). GPs can offer additional flexibility and represent non-Markovian, long-term, dependencies in the target's kinematics. However, a standard GP with constant or zero mean is prone to oscillating around its mean and not sufficiently exploring the state space. In this paper, we consider extensions of the common GP framework such that a GP acts as the driving disturbance term that is integrated over time to produce a new Integrated GP (iGP) dynamical model. It potentially provides a more realistic modelling of agile objects' behaviour. We prove here that the introduced iGP model is, itself, a GP with a non-stationary kernel, which we derive fully in the case of the squared exponential GP kernel. Thus, the iGP is straightforward to implement, with the usual growth over time of the computational burden. We further show how to implement the model with fixed time complexity in a standard sequential Bayesian updating framework using Kalman filter-based computations, employing a sliding window Markovian approximation. Example results from real radar measurements and synthetic data are presented to demonstrate the ability of the proposed iGP modelling to facilitate more accurate tracking compared to conventional GP.
跟踪的集成高斯过程
在跟踪和定位等应用中,通常指定一个动态模型来对对象的运动进行建模。高斯过程(GP)是传统的参数马尔可夫动力学模型的一个有吸引力的替代方案。GPs可以提供额外的灵活性,并表示目标运动学中的非马尔可夫、长期依赖关系。然而,具有常数或零均值的标准GP容易在其均值周围振荡,并且不能充分探索状态空间。在本文中,我们考虑了通用GP框架的扩展,使得GP作为驱动扰动项,随着时间的积分产生一个新的集成GP (iGP)动力学模型。它有可能为敏捷对象的行为提供更真实的建模。本文证明了所引入的iGP模型本身是一个具有非平稳核的GP,在平方指数GP核的情况下,我们得到了完整的非平稳核。因此,iGP很容易实现,计算负担通常会随着时间的推移而增长。我们进一步展示了如何使用基于卡尔曼滤波的计算,采用滑动窗口马尔可夫近似,在标准顺序贝叶斯更新框架中实现具有固定时间复杂度的模型。给出了实际雷达测量和合成数据的示例结果,以证明与传统GP相比,所提出的iGP模型能够实现更精确的跟踪。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
5.30
自引率
0.00%
发文量
0
审稿时长
22 weeks
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