Kutluyil Dogancay

Optimality analysis of sensor-target localization geometries

The problem of target localization involves estimating the position of a target from multiple noisy sensor measurements. It is well known that the relative sensor-target geometry can significantly affect the performance of any particular localization algorithm. The localization performance can be explicitly characterized by certain measures, for example, by the Cramer-Rao lower bound (which is equal to the inverse Fisher information matrix) on the estimator variance. In addition, the Cramer-Rao lower bound is commonly used to generate a so-called uncertainty ellipse which characterizes the spatial variance distribution of an efficient estimate, i.e. an estimate which achieves the lower bound. The aim of this work is to identify those relative sensor-target geometries which result in a measure of the uncertainty ellipse being minimized. Deeming such sensor-target geometries to be optimal with respect to the chosen measure, the optimal sensor-target geometries for range-only, time-of-arrival-based and bearing-only localization are identified and studied in this work. The optimal geometries for an arbitrary number of sensors are identified and it is shown that an optimal sensor-target configuration is not, in general, unique. The importance of understanding the influence of the sensor-target geometry on the potential localization performance is highlighted via formal analytical results and a number of illustrative examples.

Adaptive filtering algorithms with selective partial updates

In some applications of adaptive filtering such as active noise reduction, and network and acoustic echo cancellation, the adaptive filter may be required to have a large number of coefficients in order to model the unknown physical medium with sufficient accuracy. The computational complexity of adaptation algorithms is proportional to the number of filter coefficients. This implies that, for long adaptive filters, the adaptation task can become prohibitively expensive, ruling out cost-effective implementation on digital signal processors. The purpose of partial coefficient updates is to reduce the computational complexity of an adaptive filter by adapting a block of the filter coefficients rather than the entire filter at every iteration. In this paper, we develop a selective-partial-update normalized least-mean-square (NLMS) algorithm, and analyze its stability using the traditional independence assumptions and error-energy bounds. Selective partial updating is also extended to the affine projection (AP) algorithm by introducing multiple constraints. The new algorithms appear to have good convergence performance as attested to by computer simulations with real speech signals.

Optimal angular sensor separation for AOA localization

This paper establishes the angular separation requirements for angle-of-arrival (AOA) sensors in order to achieve the best mean squared error (MSE) localization performance for arbitrary but fixed sensor ranges. Optimal sensor placement for localization arises in several practical applications such as trajectory optimization for moving sensor platforms, e.g., unmanned aerial vehicles (UAVs). In optimal UAV path planning the angular separation between UAVs is an important parameter that has a significant impact on fuel efficiency and inter-UAV distance constraints. The paper shows that optimal angular sensor separation is in general not unique, and that when all sensors are equidistant from the emitter, there may exist optimal sensor configurations with non-uniform angular sensor separation in addition to equiangular separation. The results of the paper are illustrated with extensive simulation studies.

Bias compensation for the bearings-only pseudolinear target track estimator

The bearings-only pseudolinear target track estimator is known to suffer from severe bias problems. This paper presents a bias analysis for the pseudolinear estimator and develops a method of bias compensation, resulting in a closed-form reduced-bias pseudolinear estimator. The reduced-bias estimator is then incorporated into an instrumental variable estimator to produce asymptotically unbiased target motion parameter estimates. Unlike batch iterative estimators, the proposed instrumental variable estimator has a closed-from solution and therefore avoids the convergence problems associated with iterative estimators. The performance of the proposed instrumental variable estimator is illustrated by way of simulation examples and is shown to be almost identical to that of the computationally more demanding iterative maximum likelihood estimator.

Exploiting geometry for improved hybrid AOA/TDOA-based localization

In this paper we examine the geometrically constrained optimization approach to localization with hybrid bearing (angle of arrival, AOA) and time difference of arrival (TDOA) sensors. In particular, we formulate a constraint on the measurement errors which is then used along with constraint-based optimization tools in order to estimate the maximum likelihood values of the errors given an appropriate cost function. In particular we focus on deriving a localization algorithm for stationary target localization in the so-called adverse localization geometries where the relative positioning of the sensors and the target do not readily permit accurate or convergent localization using traditional approaches. We illustrate this point via simulation and we compare our approach to a number of different techniques that are discussed in the literature.

Distributed Least Mean-Square Estimation With Partial Diffusion

Distributed estimation of a common unknown parameter vector can be realized efficiently and robustly over an adaptive network employing diffusion strategies. In the adapt-then-combine implementation of these strategies, each node combines the intermediate estimates of the nodes within its closed neighborhood. This requires the nodes to transmit their intermediate estimates to all their neighbors after each update. In this paper, we consider transmitting a subset of the entries of the intermediate estimate vectors and examine two different schemes for selecting the transmitted entries at each iteration. Accordingly, we propose a partial-diffusion least mean-square (PDLMS) algorithm that reduces the internode communications while retaining the benefits of cooperation and provides a convenient trade-off between communication cost and estimation performance. Through analysis, we show that the PDLMS algorithm is asymptotically unbiased and converges in the mean-square sense. We also calculate its theoretical transient and steady-state mean-square deviation. Our numerical studies corroborate the effectiveness of the PDLMS algorithm and show a good agreement between analytical performance predictions and experimental observations.

On the bias of linear least squares algorithms for passive target localization

The paper derives analytical bias expressions for the least squares bearings-only target localization algorithms. A detailed analysis of the interplay between the target localization geometry and the estimation bias is provided for the cases of elliptical and linear observer trajectories. It is observed that the estimation bias is proportional to the distance between the target and the centre of mass of the observer positions. The effect of the localization geometry parameters on the estimation bias is illustrated analytically and by way of numerical examples. The theoretical findings of the paper are backed up with simulation studies.

UAV Path Planning for Passive Emitter Localization

A path planning algorithm is presented for uninhabited aerial vehicles (UAVs) trying to geolocate an emitter using passive payload sensors. The objective is to generate a sequence of waypoints for each vehicle that minimizes localization uncertainty. The path planning problem is cast as a nonlinear programming problem using an approximation of the Fisher information matrix (FIM) and solved at successive waypoints to generate vehicle trajectories. The effectiveness of the proposed algorithm is illustrated with simulation examples.

Optimality Analysis of Sensor-Target Geometries in Passive Localization: Part 2 - Time-of-Arrival Based Localization

In this paper we characterize the relative sensor-target geometry in R2 in terms of potential localization performance for time-of-arrival based localization. Our aim is to characterize those relative sensor-target geometries which minimize the relative Cramer-Rao lower bound.

Optimality Analysis of Sensor-Target Geometries in Passive Localization: Part 1 - Bearing-Only Localization

In this paper we characterize the relative sensor-target geometry for bearing-only localization in R2. We analyze the geometry in terms of the Cramer-Rao inequality and the corresponding Fisher information matrix, aiming to characterize and state explicit results in terms of the potential localization performance. In particular, a number of interesting results are rigorously derived which highlight erroneous assumptions often made in the existing literature.