论文标题
具有广义组套索的自主跟踪和状态估计
Autonomous Tracking and State Estimation with Generalised Group Lasso
论文作者
论文摘要
我们解决了在（结构化的）稀疏假设下对海洋血管，自动驾驶汽车和其他动态信号的自主跟踪和状态估计的问题。目的是提高有关古典贝叶斯过滤器和Smoothers的跟踪和估计准确性。我们将估计问题提出为动态的广义组套索问题，并开发出一类平滑和分类方法来解决它。 Levenberg-marquardt迭代的扩展Kalman基于乘数的多块交替方向方法（LM-ieks-MADMM）算法基于乘数的交替方向方法（ADMM）框架。这导致最小化的子问题具有固有的结构，并应用了三个新的增强递归smother。我们的方法可以处理大规模的问题，而无需预处理维度降低。此外，这些方法允许人们求解非滑动非凸优化问题。然后，我们证明在轻度条件下，提出的方法会融合到优化问题的固定点。通过模拟和真实数据实验，包括多传感器范围测量问题，海洋血管跟踪，自动驾驶汽车跟踪和音频信号恢复，我们显示了所提出方法的实际有效性。
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.
