Alon Amar

A Low Complexity Blind Estimator of Narrowband Polynomial Phase Signals

Consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array. In practice, it is difficult to maintain a precisely calibrated array. The array manifold is then assumed to be unknown, and the estimation is referred to as blind estimation. To date, only an approximated maximum likelihood estimator (AMLE) was suggested for blindly estimating the polynomial coefficients of each signal. However, this estimator requires a multidimensional search over the entire coefficient space. Instead, we propose an estimation approach which is based on two steps. First, the signals are separated using a blind source separation technique, which exploits the constant modulus property of the signals. Then, the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal. This estimator does not involve any search in the coefficient spaces. The computational complexity of the proposed estimator increases linearly with respect to the polynomial order, whereas that of the AMLE increases exponentially. Simulation results show that the proposed estimator achieves the Cramér-Rao lower bound at moderate or high signal to noise ratio.

Extending the Classical Multidimensional Scaling Algorithm Given Partial Pairwise Distance Measurements

We consider the problem of node localization given partial pairwise distance measurements. Current solutions first complete the missing distances and then apply the classical multidimensional scaling (MDS) algorithm. Instead, we extend the classical MDS to a setup where the sensor network is composed of a fully connected group of nodes that communicate with each other (e.g., beacons), and a group of nodes that cannot communicate with each other, but each one of them communicates with each node in the first group. The positions of all nodes are unknown. We localize the fully connected nodes by exploiting their distance measurements to the disconnected nodes. At the same time, the positions of the disconnected nodes are obtained up to a translation relative to the positions of the connected nodes. Recovering this translation, can be obtained with an additional step. Simulation results show that the proposed algorithm outperforms current MDS-like solutions to the problem.

Direct geolocation of stationary wideband radio signal based on time delays and Doppler shifts

Contrary to the suboptimal (two-step) geolocation procedures, we propose a maximum likelihood estimation for the position of a stationary transmitter which its delayed and Doppler shifted signal is observed by moving receivers. The position is estimated based on the same data used in common methods. However, it is performed in a single step by maximizing a cost function that depends on the unknown position only.

The Effect of Local Scattering on the Gain and Beamwidth of a Collaborative Beampattern for Wireless Sensor Networks

Collaborative beamforming is an approach where sensor nodes in a wireless sensor network, deployed randomly in an area of interest, transmit a common message by forming a beampattern towards a destination. Previous statistical analysis of the averaged power beampattern considered multipath-free conditions. Herein, we express the averaged power beampattern when the signal is observed at the destination in the presence of local scattering. Assuming the spreading angles are uniformly distributed around the destination direction, we derive closed-form expressions for the maximum gain and numerically examine the beamwidth as a function of the number of nodes, the cluster size, and the scattering parameters, for node positions with a uniform distribution or a Gaussian distribution.

Recursive Implementation of the Distributed Karhunen-Loève Transform

In the distributed linear source coding problem, a set of distributed sensors observe subsets of a data vector with noise, and provide the fusion center linearly encoded data. The goal is to determine the encoding matrix of each sensor such that the fusion center can reconstruct the entire data vector with minimum mean square error. The recently proposed local Karhunen-Loève transform approach performs this task by optimally determining the encoding matrix of each sensor assuming the other matrices are fixed. This approach is implemented iteratively until convergence is reached. Herein, we propose a greedy algorithm. In each step, one of the encoding matrices is updated by appending an additional row. The algorithm selects in a greedy fashion a single sensor that provides the largest improvement in minimizing the mean square error. This algorithm terminates after a finite number of steps, that is, when all the encoding matrices reach their predefined encoded data size. We show that the algorithm can be implemented recursively, and compared to the iterative approach, the algorithm reduces the computational load from cubic dependency to quadratic dependency on the data size. This makes it a prime candidate for on-line and real-time implementations of the distributed Karhunen-Loève transform. Simulation results suggest that the mean square error performance of the suggested algorithm is equivalent to the iterative approach.

Emitter Localization Given Time Delay and Frequency Shift Measurements

Given time and frequency differences of arrival measurements, we estimate the position and velocity of an emitter by jointly eliminating nonlinear nuisance parameters with an orthogonal projection matrix. Although simulation results show that this estimator does not always perform as well as the two-step estimator, the benefit is its computational simplicity. Whereas the complexity of the two-step estimator increases cubically with respect to the number of sensors, the complexity of the proposed estimator increases quadratically.

A reference-free time difference of arrival source localization using a passive sensor array

Least squares source position estimation techniques from time difference of arrival measurements are based on choosing a reference sensor. Selecting different reference sensors may affect the positioning accuracy by a considerable amount. We suggest a closed-form least squares position estimation using all the available distinct time differences, which does not involve the selection of a reference sensor. The nonlinear terms, associated with the distances between the sensors and the source, are eliminated with an orthogonal projection matrix. Simulation results show that the proposed approach outperforms previous closed-form least squares solutions.

Efficient Estimation of a Narrow-Band Polynomial Phase Signal Impinging on a Sensor Array

The parameters of interest of a polynomial phase signal observed by a sensor array include the direction of arrival and the polynomial coefficients. The direct maximum likelihood estimation of these parameters requires a nonlinear multidimensional search. In this paper, we present a two-step estimation approach. The estimation requires only a one-dimensional search in the direction of arrival space and involves a simple least squares solution for the polynomial coefficients. The efficiency of the estimates is corroborated by Monte Carlo simulations.

Cooperative mobile network localization via subspace tracking

Two novel cooperative localization algorithms for mobile wireless networks are proposed. To continuously localize the mobile network, given the pairwise distance measurements between different wireless sensor nodes, we propose to use subspace tracking to track the variations in signal eigenvectors and corresponding eigenvalues of the double-centered distance matrix. We compare the computational complexity of the new algorithms with a recently developed algorithm exploiting the extended Kalman filter (EKF) and show that our proposed algorithms are computationally efficient, and hence, appropriate for practical implementations compared to the EKF. Simulation results further illustrate that the proposed algorithms are more accurate when the distance errors are small (low noise scenarios) in comparison with the EKF, while being more robust to the sampling period in high noise scenarios.

Direct Position Determination: A Single-Step Emitter Localization Approach

Publisher Summary Direct position determination (DPD) is a promising approach that yields superior results in difficult conditions such as low signal-to-noise ratio (SNR), model errors, and NLOS. It requires good synchronization between base stations, both in frequency and time, which can be easily achieved by exploiting the global positioning system (GPS). It also requires the transfer of raw data between stations and therefore larger communication bandwidth. Apart from DPD, emitter localization attracts significant interest in the signal processing, radar, sonar, bioengineering, seismology, and astronomy literature. Emitter location techniques are currently used for many purposes, such as emergency cellular phone location, radio spectrum monitoring, medical imaging, law enforcement (and law breaking), fraud detection, and homeland security. The localization process is based on the exchange of signals between the emitter and a number of reference stations. There are mainly two types of positioning situations: self-positioning, where emitter position is determined based on the transmitted signals from the stations, and remote positioning, where the system determines emitter position.