Joshua N. Ash

Locating the nodes: cooperative localization in wireless sensor networks

Accurate and low-cost sensor localization is a critical requirement for the deployment of wireless sensor networks in a wide variety of applications. In cooperative localization, sensors work together in a peer-to-peer manner to make measurements and then forms a map of the network. Various application requirements influence the design of sensor localization systems. In this article, the authors describe the measurement-based statistical models useful to describe time-of-arrival (TOA), angle-of-arrival (AOA), and received-signal-strength (RSS) measurements in wireless sensor networks. Wideband and ultra-wideband (UWB) measurements, and RF and acoustic media are also discussed. Using the models, the authors have shown the calculation of a Cramer-Rao bound (CRB) on the location estimation precision possible for a given set of measurements. The article briefly surveys a large and growing body of sensor localization algorithms. This article is intended to emphasize the basic statistical signal processing background necessary to understand the state-of-the-art and to make progress in the new and largely open areas of sensor network localization research.

On the Relation Between Sparse Reconstruction and Parameter Estimation With Model Order Selection

We examine the relationship between sparse linear reconstruction and the classic problem of continuous parametric modeling. In sparse reconstruction, one wishes to recover a sparse amplitude vector from a measurement that is described as a linear combination of a small number of discrete additive components. Recent results in the compressive sensing literature have provided fast sparse reconstruction algorithms with guaranteed performance bounds for problems with certain structure. In this paper, we show an explicit connection between sparse reconstruction and parameter/order estimation and demonstrate how sparse reconstruction may be used to solve model order selection and parameter estimation problems. The structural assumption used in compressive sensing to guarantee reconstruction performance-the Restricted Isometry Property-is not satisfied in the general parameter estimation context. Nonetheless, we develop a method for selecting sparsity parameters such that sparse reconstruction mimics classic order selection criteria such as Akaike information criterion (AIC) and Bayesian information criterion (BIC). We compare the performance of the sparse reconstruction approach with traditional model order selection/parameter estimation techniques for a sinusoids-in-noise example. We find that the two methods have comparable performance in most cases, and that sparse linear modeling performs better than traditional model-based parameter/order estimation for closely spaced sinusoids with low signal-to-noise ratio.

On optimal anchor node placement in sensor localization by optimization of subspace principal angles

In sensor network self-localization, anchor nodes provide a convenient means to disambiguate scene translation and rotation, thereby affording estimates in an absolute coordinate system. However, localization performance depends on the positions of the anchor nodes relative to the unknown-location nodes. Conventional wisdom in the literature is that anchor nodes should be placed around the perimeter of the network. In this paper, we show analytically why this strategy works well universally. We demonstrate that perimeter placement forces the information provided by the anchor constraints to closely align with the subspace that cannot be estimated from inter-node measurements: the subspace of translations and rotations. Examples quantify the efficacy of perimeter placement of anchors.

An Autofocus Method for Backprojection Imagery in Synthetic Aperture Radar

In this letter, we present an autofocus routine for backprojection imagery from spotlight-mode synthetic aperture radar data. The approach is based on maximizing image sharpness and supports the flexible collection and imaging geometries of BP, including wide-angle apertures and the ability to image directly onto a digital elevation map. While image-quality-based autofocus approaches can be computationally intensive, in the backprojection setting, we demonstrate a natural geometric interpretation that allows for optimal single-pulse phase corrections to be derived in closed form as the solution of a quartic polynomial. The approach is applicable to focusing standard backprojection imagery, as well as providing incremental focusing in sequential imaging applications based on autoregressive backprojection. An example demonstrates the efficacy of the approach applied to real data for a wide-aperture backprojection image.

Detecting Changes in Hyperspectral Imagery Using a Model-Based Approach

Within the hyperspectral community, change detection is a continued area of interest. Interesting changes in imagery typically correspond to changes in material reflectance associated with pixels in the scene. Using a physical model describing the sensor-reaching radiance, change detection can be formulated as a statistical hypothesis test. Complicating the problem of change detection is the presence of shadow, illumination, and atmospheric differences, as well as misregistration and parallax error, which often produce the appearance of change. The proposed physical model incorporates terms to account for both direct and diffuse shadow fractions to help mitigate false alarms associated with shadow differences between scenes. The resulting generalized likelihood ratio test (GLRT) provides an indicator of change at each pixel. The maximum likelihood estimates of the physical model parameters used for the GLRT are obtained from the entire joint data set to take advantage of coupled information existing between pixel measurements. Simulation results using synthetic and real imagery demonstrate the efficacy of the proposed approach.

Acoustic time delay estimation and sensor network self-localization: Experimental results

Experimental results are presented on propagation, coherence, and time-delay estimation (TDE) from a microphone array in an outdoor aeroacoustic environment. The primary goal is to understand the achievable accuracy of acoustic TDE using low-cost, commercial off-the-shelf (COTS) speakers and microphones. In addition, through the use of modulated pseudo-noise sequences, the experiment seeks to provide an empirical understanding of the effects of center frequency, bandwidth, and signal duration on TDE effectiveness and compares this to the theoretical expectations established by the Weiss-Weinstein lower bound. Finally, sensor network self-localization is performed using a maximum likelihood estimator and the time-delay estimates. Experimental network localization error is presented as a function of the acoustic calibration signal parameters.

Robust system multiangulation using subspace methods

Sensor location information is a prerequisite to the utility of most sensor networks. In this paper we present a robust and low-complexity algorithm to self-localize and orient sensors in a network based on angle-of-arrival (AOA) information. The proposed non-iterative subspace-based method is robust to missing and noisy measurements and works for cases when sensor orientations are either known or unknown. We show that the computational complexity of the algorithm is O(mn2), where m is the number of measurements and n is the total number of sensors. Simulation results demonstrate that the error of the proposed subspace algorithm is only marginally greater than an iterative maximum-likelihood estimator (MLE), while the computational complexity is two orders of magnitude less. Additionally, the iterative MLE is prone to converge to local maxima in the likelihood function without accurate initialization. We illustrate that the proposed subspace method can be used to initialize the MLE and obtain near-Cramer-Rao performance for sensor localization. Finally, the scalability of the subspace algorithm is illustrated by demonstrating how clusters within a large network may be individually localized and then merged.

On the Relative and Absolute Positioning Errors in Self-Localization Systems

This paper considers the accuracy of sensor node location estimates from self-calibration in sensor networks. The total parameter space is shown to have a natural decomposition into relative and centroid transformation components. A linear representation of the transformation parameter space is shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). The centroid transformation subspace-which includes representations of rotation, translation, and scaling-is characterized for a number of measurement models including distance, time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), and angle-difference-of-arrival (ADOA) measurements. The error decomposition may be applied to any localization algorithm in order to better understand its performance characteristics, and it may be applied to the Cramer-Rao bound (CRB) to determine performance limits in the relative and transformation domains. A geometric interpretation of the constrained CRB is provided based on the principal angles between the measurement subspace and the constraint subspace. Examples are presented to illustrate the utility of the proposed error decomposition into relative and transformation components.

Modeling and estimation of signal-dependent noise in hyperspectral imagery.

The majority of hyperspectral data exploitation algorithms are developed using statistical models for the data that include sensor noise. Hyperspectral data collected using charge-coupled devices or other photon detectors have sensor noise that is directly dependent on the amplitude of the signal collected. However, this signal dependence is often ignored. Additionally, the statistics of the noise can vary spatially and spectrally as a result of camera characteristics and the calibration process applied to the data. Here, we examine the expected noise characteristics of both raw and calibrated visible/near-infrared hyperspectral data and provide a method for estimating the noise statistics using calibration data or directly from the imagery if calibration data is unavailable.

Dynamic Dictionary Algorithms for Model Order and Parameter Estimation

In this paper, we present and evaluate dynamic dictionary-based estimation methods for joint model order and parameter estimation. In dictionary-based estimation, a continuous parameter space is discretized, and vector-valued dictionary elements are formed for specific parameter values. A linear combination of a subset of dictionary elements is used to represent the model, where the number of elements used is the estimated model order, and the parameters corresponding to the selected elements are the parameter estimates. In static-based methods, the dictionary is fixed; while in the dynamic methods proposed here, the parameter sampling, and hence the dictionary, adapt to the data. We propose two dynamic dictionary-based estimation algorithms in which the dictionary elements are dynamically adjusted to improve parameter estimation performance. We examine the performance of both static and dynamic algorithms in terms of probability of correct model order selection and the root mean-squared error of parameter estimates. We show that dynamic dictionary methods overcome the problem of estimation bias induced by quantization effects in static dictionary-based estimation, and we demonstrate that dictionary-based estimation methods are capable of parameter estimation performance comparable to the Cramér-Rao lower bound and to traditional ML-based model estimation over a wide range of signal-to-noise ratios.