Sensor Location Uncertainty Research Articles

An Asymptotically Efficient Estimator for TDOA and FDOA Positioning of Multiple Disjoint Sources in the Presence of Sensor Location Uncertainties

This correspondence considers the problem of locating multiple disjoint sources using time differences of arrival (TDOAs) and frequency differences of arrival (FDOAs) in the presence of sensor position and velocity errors. Previous work applies to one source only with suboptimum performance for near source, or requires joint estimation of the source and sensor locations that could be computation demanding. Through nonlinearly transforming the measurements and converting them with respect to the inaccurate sensor locations, we have developed an algebraic solution to this problem. The solution is shown analytically to achieve the Cramer-Rao lower bound (CRLB) performance over small noise region and does not require joint estimation with sensor locations.

Mode shape expansion using perturbed force approach

A new approach for expanding incomplete experimental mode shapes is presented which considers the modelling errors in the analytical model and the uncertainties in the vibration modal data measurements. The proposed approach adopts the perturbed force vector that includes the effect of the discrepancy in mass and stiffness between the finite element model and the actual tested dynamic system. From the developed formulations, the perturbed force vector can be obtained from measured modal data and is then used for predicting the unmeasured components of the expanded experimental mode shapes. A special case that does not require the experimental natural frequency in the mode shape expansion process is also discussed. A regularization algorithm based on the Tikhonov solution incorporating the generalized cross-validation method is employed to filter out the influence of noise in measured modal data on the predictions of unmeasured mode components. The accuracy and robustness of the proposed approach is verified with respect to the size of measured data set, sensor location, model deficiency and measurement uncertainty. The results from two numerical examples, a plane frame structure and a thin plate structure, show that the proposed approach has the best performance compared with the commonly used existing expansion methods, and can reliably produce the predictions of mode shape expansion, even in the cases with limited modal data measurements, large modelling errors and severe measurement noise.

Multisensor deployment using PCRLBS, incorporating sensor deployment and motion uncertainties

Recently, a general framework for sensor resource deployment (Hernandez, et. al. 2004) has been shown to allow efficient and effective utilization of a multisensor system. The basis of this technique is to use the posterior Cramer-Rao lower bound (PCRLB) to quantify and control the optimal achievable accuracy of target state estimation. In the original formulation (Hernandez, et. al. 2004) it was assumed that the sensor locations were known without error. In the current paper, the authors extend this framework by addressing the issues of imperfect sensor placement and uncertain sensor movement (e.g., sensor drift). The crucial consideration is then how these two forms of uncertainty are factored into the sensor management strategy. If unaccounted for, these uncertainties will render the output of the resource manager inaccurate and overoptimistic. The authors adjust the PCRLB to account for sensor location uncertainty, and we also allow for measurement origin uncertainty due to missed detections and false alarms. The work is motivated by the problem of tracking a submarine by adaptively deploying sonobuoys from a helicopter. Simulation results are presented to show the advantages of accounting for sensor location uncertainty within this focal domain of antisubmarine warfare. The authors note that the generic nature of the technique allows it to be utilized within other problem domains, including tracking ground-based targets using unattended ground sensors (UGSs) or unmanned aerial vehicles (UAVs)

Multisensor target tracking performance with bias compensation

In this paper, multisensor-multitarget tracking performance with bias estimation and compensation is investigated when only moving targets of opportunity are available. First, we discuss the tracking performance improvement with bias estimation and compensation for synchronous biased sensors, and then a novel bias estimation method is proposed for asynchronous sensors with time-varying biases. The performance analysis and simulations show that asynchronous sensors have a slightly degraded performance compared with the "equivalent" synchronous ones. The bias estimates as well as the corresponding Cramer-Rao lower bound (CRLB) on the covariance of the bias estimates, i.e., the quantification of the available information on the sensor biases in any scenario are also given. Tracking performance evaluations with different sources of biases-offset biases, scale biases, and sensor location uncertainties, are also presented and we show that tracking performance is significantly improved with bias estimation and compensation compared with the target tracking using the original biased measurements. The performance is also close to the lower bound obtained in the absence of biases

Toward multidimensional assignment data association in robot localization and mapping

It is well accepted that the data association or the correspondence problem is one of the toughest problems faced by any state estimation algorithm. Particularly in robotics, it is not very well addressed. This paper introduces a multidimensional assignment (MDA)-based data association algorithm for the simultaneous localization and map building (SLAM) problem in mobile robot navigation. The data association problem is cast in a general discrete optimization framework and the MDA formulation for multitarget tracking is extended for SLAM using sensor location uncertainty with the joint likelihood of measurements over multiple frames as the objective function. Methods for feature initialization and management are also integrated into the algorithm. When clutter is high and features are sparse, the compatibility information of features of a single measurement frame is not sufficient to make effective data-association decisions,thus compromising performance of single-frame-based methods. However, in a multiple-measurement-frame approach, the availability of more than one frame of measurement provides for more effective data-association decisions to be made, as consistency of measurements are looked at in several frames of measurement. Simulations are conducted to verify the performance gains over the conventional nearest neighbor (NN) data association algorithm and the joint compatibility branch and bound (JCBB) algorithm, especially in the presence of varying densities of spurious measurements and dynamic objects. Experimental results with ground truth are presented to demonstrate the practicality of the proposed data-association method in complex and large outdoor environments and its effectiveness over single-frame-based NN and JCBB schemes.

Source localization in shallow water in the presence of sensor location uncertainty

The problem of source localization in shallow water in the presence of sensor location uncertainty is considered. The Cramer-Rao Bound is used to carry out a feasibility study for the joint source and sensor location problem when the multipath propagation channel is modeled as a known, deterministic waveguide. Unlike the free-space propagation channel, the boundedness of the shallow-water waveguide along its vertical axis provides the key to joint determination of the source and sensor location parameters. It is seen that, when a set of intuitive identifiability conditions are satisfied, numerical examples indicate that, for the scenarios considered, the resulting loss in accuracy with which the source location can be estimated due to sensor location uncertainty may be tolerable.

The Effect of Imprecisions in Thermal Sensor Location and Boundary Conditions on Optimal Sensor Location and Experimental Accuracy

Optimal sensor locations and the information content obtained when estimating thermal parameters using the inverse method are significantly affected by uncertainties in sensor position and in the system parameters. This paper describes the effects of these uncertainties. It is shown that the effect of sensor location uncertainties can be reduced by placing temperature sensors in locations of minimum heat flux. In transient experiments, the uncertainties in the boundary conditions have the greatest effect at points of high heat flux and cause the optimal sensor locations to move from the boundary with the highest convective heat transfer coefficient to the boundary with the lowest in an abrupt manner.

Sensor location calibration for bearing estimation

New calibration methods are presented for bearing estimation with sensor location uncertainties, which are based on eigenvalue decomposition of the sample covariance matrix and three or more nondisjoint sources in known bearings. The methods can be applied to arbitrary arrays, including linear arrays, require fewer computations, and are suitable for low signal-to-noise ratio (SNR) cases. Computer simulations are given to illustrate the performance of the proposed methods.

Cumulant-based blind optimum beamforming

Sensor response, location uncertainty, and use of sample statistics can severely degrade the performance of optimum beamformers. We propose blind estimation of the source steering vector in the presence of multiple, directional, correlated or coherent Gaussian interferers via higher order statistics. In this way, we employ the statistical characteristics of the desired signal to make the necessary discrimination, without any a-priori knowledge of array manifold and direction-of-arrival (DOA) information about the desired signal. We then improve our method to utilize the data in a more efficient manner. In any application, only sample statistics are available, so we propose a robust beamforming approach that employs the steering vector estimate obtained by cumulant-based signal processing. We further propose a method that employs both covariance and cumulant information to combat finite sample effects. We analyze the effects of multipath propagation on the reception of the desired signal. We show that even in the presence of coherence, cumulant-based beamformer still behaves as the optimum beamformer that maximizes the signal-to-interference-plus-noise ratio (SINR). Finally, we propose an adaptive version of our algorithm simulations demonstrate the excellent performance of our approach in a wide variety of situations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Genetic approach to bearing estimation with sensor location uncertainties

A genetic approach which combines a genetic optimisation algorithm with an adaptive weighting function has been developed to estimate the bearing or direction of arrival (DOA) of multiple sources in the presence of sensor location uncertainties. Computer simulations show the good performance of the proposed approach.

Signal subspace method for calibrating sensor location of direction finder

Sensor location uncertainty of array degrades severely the performance of eigenstructure based direction finding system. A new calibration method of sensor location is presented with three far field sources whose directions are not known accurately. A signal subspace based iteration algorithm for sensor location calibration is developed and its convergence to the global optimal point has been shown. The guide line for selecting directions of calibrating sources is given. Simulation results illustrate that the new method is successful and practicable.

Array shape calibration using eigenstructure methods

Abstract Sensor location uncertainty can severely degrade the accuracy of direction finding system. An eigenstructure based method for simultaneously estimating directions of arrival (DOA) and sensor locations is developed to alleviate this problem. The proposed technique does not require calibration sources at known positions, and can handle non-disjoint sources, (i.e., sources occupying the same frequency band and the same time interval). The procedure is guaranteed to converge and offers an alternative to the procedure presented by Weiss and Friedlander (1990). Numerical examples and Monte-Carlo simulations are used to study the performance of the proposed technique.

Array shape calibration using sources in unknown locations-a maximum likelihood approach

Sensor location uncertainty can severely degrade the performance of direction-finding systems. An iterative maximum-likelihood method for simultaneously estimating directions of arrival (DOA) and sensor locations is developed to alleviate this problem. The case of nondisjoint sources, i.e., sources observed in the same frequency cell and at the same time, is emphasized. The algorithm converges to the global maximum of the likelihood function if the initial conditions are sufficiently good. Numerical examples are presented, illustrating the performance of the proposed technique. A distinctive feature of the algorithm is its ability to locate the sensors accurately without deploying calibration sources at known locations. >

Array shape calibration using sources in unknown locations--Part II: Near-field sources and estimator implementation

Uncertainty concerning sensor locations can seriously degrade the ability of an array to estimate the location of radiating sources. Array calibration then becomes an important issue. This paper deals with array calibration using spectrally disjoint near-field sources whose locations are not known a priori. It calculates Cramer-Rao bounds on source location and array shape errors. It shows that, with mild restrictions on source-array geometry, the array shape errors can be made arbitrarily small by using a sufficient number of sufficiently strong calibrating sources. The required number of calibrating sources is five for a four-sensor array, four for a five-sensor array, and three for an array of six or more sensors. Accurate calibration is not possible for a three-sensor array. While calibration can establish array shape with great accuracy, it cannot resolve a rotational uncertainty in array orientation. This uncertainty translates into a residual error in source bearings, but not in source ranges. Thus, incremental errors in target range due to sensor location uncertainty can be reduced to any desired extent. The paper also proposes an actual calibration procedure and presents simulation results indicating that useful calibration can be obtained with calibrating sources of very moderate signal-to-noise ratio.