Nonlinear Compressive Particle Filtering

Many systems for which compressive sensing is used today are dynamical. The common approach is to neglect the dynamics and see the problem as a sequence of independent problems. This approach has two disadvantages. Firstly, the temporal dependency in the state could be used to improve the accuracy of the state estimates. Secondly, having an estimate for the state and its support could be used to reduce the computational load of the subsequent step. In the linear Gaussian setting, compressive sensing was recently combined with the Kalman filter to mitigate above disadvantages. In the nonlinear dynamical case, compressive sensing can not be used and, if the state dimension is high, the particle filter would perform poorly. In this paper we combine one of the most novel developments in compressive sensing, nonlinear compressive sensing, with the particle filter. We show that the marriage of the two is essential and that neither the particle filter or nonlinear compressive sensing alone gives a satisfying solution.Comment: Accepted to CDC 201

Dynamic Iterative Pursuit

For compressive sensing of dynamic sparse signals, we develop an iterative pursuit algorithm. A dynamic sparse signal process is characterized by varying sparsity patterns over time/space. For such signals, the developed algorithm is able to incorporate sequential predictions, thereby providing better compressive sensing recovery performance, but not at the cost of high complexity. Through experimental evaluations, we observe that the new algorithm exhibits a graceful degradation at deteriorating signal conditions while capable of yielding substantial performance gains as conditions improve.Comment: 6 pages, 7 figures. Accepted for publication in IEEE Transactions on Signal Processin

Subgradient-Based Markov Chain Monte Carlo Particle Methods for Discrete-Time Nonlinear Filtering

This work shows how a carefully designed instrumental distribution can improve the performance of a Markov chain Monte Carlo (MCMC) filter for systems with a high state dimension. We propose a special subgradient-based kernel from which candidate moves are drawn. This facilitates the implementation of the filtering algorithm in high dimensional settings using a remarkably small number of particles. We demonstrate our approach in solving a nonlinear non-Gaussian high-dimensional problem in comparison with a recently developed block particle filter and over a dynamic compressed sensing (l1 constrained) algorithm. The results show high estimation accuracy

Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation

In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering and smoothing algorithms are equivalent to a particular algorithm for solving this problem. Once this equivalence is established, we present extensions of Kalman smoothing to systems with nonlinear process and measurement models, systems with linear and nonlinear inequality constraints, systems with outliers in the measurements or sudden changes in the state, and systems where the sparsity of the state sequence must be accounted for. All extensions preserve the computational efficiency of the classic algorithms, and most of the extensions are illustrated with numerical examples, which are part of an open source Kalman smoothing Matlab/Octave package.Comment: 46 pages, 11 figure

Dynamic Underwater Glider Network for Environmental Field Estimation

A coordinated dynamic sensor network of autonomous underwater gliders to estimate three-dimensional time-varying environmental fields is proposed and tested. Integration with a network of surface relay nodes and asynchronous consensus are used to distribute local information and achieve the global field estimate. Field spatial sparsity is considered, and field samples are acquired by compressive sensing devices. Tests on simulated and real data demonstrate the feasibility of the approach with relative error performance within 10

Sparsity-fused Kalman filtering for reconstruction of dynamic sparse signals

This article focuses on the problem of reconstructing dynamic sparse signals from a series of noisy compressive sensing measurements using a Kalman Filter (KF). This problem arises in many applications, e.g., Magnetic Resonance Imaging (MRI), Wireless Sensor Networks (WSN) and video reconstruction. The conventional KF does not consider the sparsity structure presented in most practical signals and it is therefore inaccurate when being applied to sparse signal recovery. To deal with this issue, we derive a novel KF procedure which takes the sparsity model into consideration. Furthermore, an algorithm, namely Sparsity-fused KF, is proposed based upon it. The method of iterative soft thresholding is utilized to refine our sparsity model. The superiority of our method is demonstrated by synthetic data and the practical data gathered by a WSN.This work is supported by EPSRC Research Grant (EP/K033700/1); the Natural Science Foundation of China (61401018, U1334202); the State Key Laboratory of Rail Traffic Control and Safety (RCS2014ZT08), Beijing Jiaotong University; the Fundamental Research Funds for the Central Universities (2014JBM149); the Key Grant Project of Chinese Ministry of Education (313006); the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ICC.2015.724938