We address the problem of autonomous tracking and state estimation for marine vessels, autonomous vehicles, and other dynamic signals under a (structured) sparsity assumption. The aim is to improve the tracking and estimation accuracy with respect to classical Bayesian filters and smoothers. We formulate the estimation problem as a dynamic generalised group Lasso problem and develop a class of smoothing-and-splitting methods to solve it. The Levenberg--Marquardt iterated extended Kalman smoother-based multi-block alternating direction method of multipliers (LM-IEKS-mADMM) algorithms are based on the alternating direction method of multipliers (ADMM) framework. This leads to minimisation subproblems with an inherent structure to which three new augmented recursive smoothers are applied. Our methods can deal with large-scale problems without pre-processing for dimensionality reduction. Moreover, the methods allow one to solve nonsmooth nonconvex optimisation problems. We then prove that under mild conditions, the proposed methods converge to a stationary point of the optimisation problem. By simulated and real-data experiments including multi-sensor range measurement problems, marine vessel tracking, autonomous vehicle tracking, and audio signal restoration, we show the practical effectiveness of the proposed methods.
翻译:我们根据一个(结构化的)宽度假设,处理海洋船只、自主车辆和其他动态信号的自主跟踪和国家估算问题,目的是改进古典贝叶西亚过滤器和滑动器的跟踪和估算准确性;我们将估算问题作为一个动态的通用群体提出来,Lasso问题,并开发一种平滑和分解的方法来解决它;Levenberg-Marquardt 焊接热的Levenberg-Marquardt 扩展卡尔曼平滑的多区段交替法(LM-IEKS-MADMMM)乘数算法(LM-IEKS-MADMM)基于乘数交替方向法框架。这导致一个内在结构的最小化小问题,即三个新的循环顺畅器得到应用。我们的方法可以处理大规模问题,而无需预先处理来降低维度。此外,这种方法可以解决非移动的非convex优化问题。然后证明,在温和条件下,拟议的方法将集中到优化问题的固定点。通过模拟和真实的信号跟踪,包括多式的船舶的自动测量方法,显示我们所拟的磁测测测测测,显示多波范围的问题。