Sampling and Reconstruction of Spatial Fields using Mobile Sensors

Spatial sampling is traditionally studied in a static setting where static sensors scattered around space take measurements of the spatial field at their locations. In this paper we study the emerging paradigm of sampling and reconstructing spatial fields using sensors that move through space. We show that mobile sensing offers some unique advantages over static sensing in sensing time-invariant bandlimited spatial fields. Since a moving sensor encounters such a spatial field along its path as a time-domain signal, a time-domain anti-aliasing filter can be employed prior to sampling the signal received at the sensor. Such a filtering procedure, when used by a configuration of sensors moving at constant speeds along equispaced parallel lines, leads to a complete suppression of spatial aliasing in the direction of motion of the sensors. We analytically quantify the advantage of using such a sampling scheme over a static sampling scheme by computing the reduction in sampling noise due to the filter. We also analyze the effects of non-uniform sensor speeds on the reconstruction accuracy. Using simulation examples we demonstrate the advantages of mobile sampling over static sampling in practical problems. We extend our analysis to sampling and reconstruction schemes for monitoring time-varying bandlimited fields using mobile sensors. We demonstrate that in some situations we require a lower density of sensors when using a mobile sensing scheme instead of the conventional static sensing scheme. The exact advantage is quantified for a problem of sampling and reconstructing an audio field.Comment: Submitted to IEEE Transactions on Signal Processing May 2012; revised Oct 201

On Minimal Trajectories for Mobile Sampling of Bandlimited Fields

We study the design of sampling trajectories for stable sampling and the reconstruction of bandlimited spatial fields using mobile sensors. The spectrum is assumed to be a symmetric convex set. As a performance metric we use the path density of the set of sampling trajectories that is defined as the total distance traveled by the moving sensors per unit spatial volume of the spatial region being monitored. Focussing first on parallel lines, we identify the set of parallel lines with minimal path density that contains a set of stable sampling for fields bandlimited to a known set. We then show that the problem becomes ill-posed when the optimization is performed over all trajectories by demonstrating a feasible trajectory set with arbitrarily low path density. However, the problem becomes well-posed if we explicitly specify the stability margins. We demonstrate this by obtaining a non-trivial lower bound on the path density of an arbitrary set of trajectories that contain a sampling set with explicitly specified stability bounds.Comment: 28 pages, 8 figure

Bandlimited Spatial Field Sampling with Mobile Sensors in the Absence of Location Information

Sampling of physical fields with mobile sensor is an emerging area. In this context, this work introduces and proposes solutions to a fundamental question: can a spatial field be estimated from samples taken at unknown sampling locations? Unknown sampling location, sample quantization, unknown bandwidth of the field, and presence of measurement-noise present difficulties in the process of field estimation. In this work, except for quantization, the other three issues will be tackled together in a mobile-sampling framework. Spatially bandlimited fields are considered. It is assumed that measurement-noise affected field samples are collected on spatial locations obtained from an unknown renewal process. That is, the samples are obtained on locations obtained from a renewal process, but the sampling locations and the renewal process distribution are unknown. In this unknown sampling location setup, it is shown that the mean-squared error in field estimation decreases as $O(1/n)$ where $n$ is the average number of samples collected by the mobile sensor. The average number of samples collected is determined by the inter-sample spacing distribution in the renewal process. An algorithm to ascertain spatial field's bandwidth is detailed, which works with high probability as the average number of samples $n$ increases. This algorithm works in the same setup, i.e., in the presence of measurement-noise and unknown sampling locations.Comment: Submitted to IEEE Trans on Signal Processin

One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks

This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive quantization, coding, and field reconstruction scheme is developed and an upper-bound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatio-temporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain weak technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the per-sensor bitrate and sensing-related network overhead rate simultaneously go to zero. The proposed scheme achieves the order-optimal MSE versus sensor density scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review format), 4 figures. Submitted to IEEE Transactions on Signal Processing. Current version is updated for journal submission: revised author list, modified formulation and framework. Previous version appeared in Proceedings of Allerton Conference On Communication, Control, and Computing 200

Efficient Compressive Sampling of Spatially Sparse Fields in Wireless Sensor Networks

Wireless sensor networks (WSN), i.e. networks of autonomous, wireless sensing nodes spatially deployed over a geographical area, are often faced with acquisition of spatially sparse fields. In this paper, we present a novel bandwidth/energy efficient CS scheme for acquisition of spatially sparse fields in a WSN. The paper contribution is twofold. Firstly, we introduce a sparse, structured CS matrix and we analytically show that it allows accurate reconstruction of bidimensional spatially sparse signals, such as those occurring in several surveillance application. Secondly, we analytically evaluate the energy and bandwidth consumption of our CS scheme when it is applied to data acquisition in a WSN. Numerical results demonstrate that our CS scheme achieves significant energy and bandwidth savings wrt state-of-the-art approaches when employed for sensing a spatially sparse field by means of a WSN.Comment: Submitted to EURASIP Journal on Advances in Signal Processin

MScMS-II: an innovative IR-based indoor coordinate measuring system for large-scale metrology applications

According to the current great interest concerning large-scale metrology applications in many different fields of manufacturing industry, technologies and techniques for dimensional measurement have recently shown a substantial improvement. Ease-of-use, logistic and economic issues, as well as metrological performance are assuming a more and more important role among system requirements. This paper describes the architecture and the working principles of a novel infrared (IR) optical-based system, designed to perform low-cost and easy indoor coordinate measurements of large-size objects. The system consists of a distributed network-based layout, whose modularity allows fitting differently sized and shaped working volumes by adequately increasing the number of sensing units. Differently from existing spatially distributed metrological instruments, the remote sensor devices are intended to provide embedded data elaboration capabilities, in order to share the overall computational load. The overall system functionalities, including distributed layout configuration, network self-calibration, 3D point localization, and measurement data elaboration, are discussed. A preliminary metrological characterization of system performance, based on experimental testing, is also presente