Maximum Likelihood Localization Research Articles

Multiband time‐of‐arrival positioning technique using an ultra‐high‐frequency bandwidth availability model for cognitive radio

In this study, the authors present a multiband time-of-arrival (TOA) positioning model and validate the performance in a practical dynamic spectrum access scenario according to results obtained from an ultra-high-frequency (UHF) spectrum occupancy measurement campaign. The statistical analysis of the measured data shows a distinguishable difference between the unoccupied and occupied portion of the UHF band. The bandwidth availability for the UHF band is shown to follow a Gaussian distribution according to the measurement results. The positioning model is verified using the non-linear least squares, linear least squares and two-step maximum-likelihood location estimation algorithms. The root-mean-square error (RMSE) performance evaluation of the proposed model revealed the advantage of utilising five discrete bands to perform TOA estimation, especially in poor signal-to-noise ratio (SNR) conditions ranging from – 10 to 0 dB. At a fixed SNR of 0 dB, an average RMSE improvement of 74 and 82% was observed for a double- and triple-band system when compared with a conventional single-band TOA system. This particular positioning technique can enable improved location estimation in a dynamic spectrum access environment.

Unilateral isolated hypoglossal nerve palsy associated with internal carotid artery dissection

Genetic linkage and deletion studies have led to the proposal that there are at least two loci on the X chromosome which are responsible for X linked retinitis pigmentosa (XLRP)....

Eigenvalue Estimation of Hyperspectral Wishart Covariance Matrices From Limited Number of Samples

Estimation of covariance matrices is a fundamental step in hyperspectral remote sensing where most detection algorithms make use of the covariance matrix in whitening procedures. We present a simple method to estimate all p eigenvalues of a Wishart-distributed sampled covariance matrix (with which an improved covariance can be constructed) when the number of samples (n) is small, n/p >; 1 and less than a few tens. Our method is based on the Marcenko-Pastur (M-P) law, theory of eigenvalue bounds, and energy conservation. We compute an apparent multiplicity for each sampled eigenvalue and then shift the sampled eigenvalues according the maximum likelihood location (M-P mode). We impose energy conservation in two distinct regions; small eigenvalues and large eigenvalues, where the transition between the two regions is found by solving successive first-order regression equation for the sampled data. The method also improves the condition number of the data (small eigenvalues are shifted upward in values), hence, it is also “regularization,” where the regularization is a multiplicative vector regularization as opposed to the traditional additive scalar regularization where all eigenvalues are shifted upward by the same value.

Towards a bandwidth efficient cognitive positioning system

Presented is an efficient bandwidth determination model for the cognitive positioning system by utilising multiple receive antennas. The performance evaluations of the proposed multiple receive antenna positioning system were carried out using the linear least squares and maximum-likelihood location estimation techniques. Simulated results reveal that in a rural scenario, the 1×2 and 1×3 single-input-multiple-output (SIMO) cases display an average bandwidth efficiency with respect to positional accuracy, of 49 and 58%, respectively, over the single-input-single-output (SISO) case. For an urban scenario, the 1×2 and 1×3 SIMO cases display a higher average bandwidth efficiency of 53 and 62%, respectively, over the SISO case.

MPC Constraint Analysis—Bayesian Approach via a Continuous-Valued Profit Function

Model predictive control (MPC) is one of the most studied modern control technologies. Among the various subjects investigated, controller performance assessment of MPC has received considerable attention in recent time. Various approaches and algorithms have been proposed for the assessment of MPCs. In this work, we propose a novel approach to MPC constraint analysis by considering the economic objective function as a continuous-valued function within a Bayesian probabilistic framework. The analysis involves inference of the effect of a decision to adjust the limits of the constrained variables with regards to the achievable profits (decision evaluation) as well as inference of constraint limits that should be adjusted so as to achieve a specified profit value (decision making). The benefits of this approach include a more generalized definition of quality variables, the development of a more rigorous formulation of the problem to address linear and quadratic objective functions and thereby obtaining closed form solutions, and maximum-likelihood location determination of the quality variables in the decision making process. The approach is illustrated with the use of simulations and a pilot-scale experiment.

The Cross-Entropy Method for Maximum Likelihood Location Estimation Based on IEEE 802.15.4 Radio Signals in Sensor Networks

This paper considers the problem of target location estimation in a wireless sensor network based on IEEE 842.15.4 radio signals and proposes a novel implementation of the maximum likelihood (ML) location estimator based on the Cross-Entropy (CE) method. In the proposed CE method, the ML criterion is translated into a stochastic approximation problem which can be solved effectively. Simulations that compare the performance of a ML target estimation scheme employing the conventional Newton method and the conjugate gradient method are presented. The simulation results show that the proposed CE method provides higher location estimation accuracy throughout the sensor field.

ZigBee Based Location Estimation in Home Networking Environments

This paper presents a Maximum Likelihood Location Estimation (MLLE) algorithm for the home network environments. We propose a deployment of cluster-tree topology in the ZigBee networks and derive the MLE under the log-normal models for the Received Signal Strength (RSS) measurements. Experiments are also conducted to validate the effectiveness of the proposed algorithm.

Maximum Likelihood Localization of a Diffusive Point Source Using Binary Observations

In this paper, we investigate the problem of localization of a diffusive point source of gas based on binary observations provided by a distributed chemical sensor network. We motivate the use of the maximum likelihood (ML) estimator for this scenario by proving that it is consistent and asymptotically efficient, when the density of the sensors becomes infinite. We utilize two different estimation approaches, ML estimation based on all the observations (i.e., batch processing) and approximate ML estimation using only new observations and the previous estimate (i.e., real time processing). The performance of these estimators is compared with theoretical bounds and is shown to achieve excellent performance, even with a finite number of sensors

Exact and Approximate Maximum Likelihood Localization Algorithms

Sensors at separate locations measuring either the time difference of arrival (TDOA) or time of arrival (TOA) of the signal from an emitter can determine its position as the intersection of hyperbolae for TDOA and of circles for TOA. Because of measurement noise, the nonlinear localization equations become inconsistent; and the hyperbolae or circles no longer intersect at a single point. It is now necessary to find an emitter position estimate that minimizes its deviations from the true position. Methods that first linearize the equations and then perform gradient searches for the minimum suffer from initial condition sensitivity and convergence difficulty. Starting from the maximum likelihood (ML) function, this paper derives a closed-form approximate solution to the ML equations. When there are three sensors on a straight line, it also gives an exact ML estimate. Simulation experiments have demonstrated that these algorithms are near optimal, attaining the theoretical lower bound for different geometries, and are superior to two other closed form linear estimators.

Performance evaluation of TDOA system based on maximum likelihood location estimation in cellular systems

With the spreading use of cellular phones in recent years, there has been an increasing demand for various services based on location information. The location-dependent information to be used in location estimation can be the TOA (time of arrival), TDOA (time difference of arrival), signal strength, and AOA (angle of arrival). In third-generation cellular phones, whose widespread use is expected, the communications data rate will be increased. The chip resolution will also be improved, making it possible to measure the signal arrival time with higher accuracy. Consequently, this paper presents an evaluation and discussion of the location estimation performance of a TDOA system. An exponential distribution is assumed for the signal delay profile, and the location estimation algorithm is formulated on the basis of maximum likelihood estimation. Then the accuracy of location estimation is compared by simulation for maximum likelihood estimation in the TDOA system and the existing method. The accuracy of location estimation by maximum likelihood is also evaluated for various environments. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 88(6): 47–54, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20155

Maximum likelihood estimation for Tukey's three corners

We use the EM algorithm to derive recursive expressions for maximum likelihood location and scale estimators for Tukey's corner distributions, in particular the one-wild. This now enables optimal estimation for the triefficiency criterion used to appraise robust estimators. The effect of improved estimation for the one-wild case is investigated. Simulations are conducted, both to illustrate the operation of the algorithm, and to reinvestigate the properties of three common location estimates. In particular, the scaling constant c=6 in the one-step biweight M-estimator used in procedures such as loess, is shown to be too small under the triefficiency criterion.

Unconditional Maximum Likelihood Approach for Localization of Near-Field Sources: Algorithm and Performance Analysis

Abstract Localization of near-field sources requires sophisticated estimation algorithms. In this paper, we propose an unconditional maximum likelihood method for estimating direction of arrival and angle parameters of near-field sources. However, the calculation of maximum likelihood estimation from the corresponding likelihood function results in difficult nonlinear constraint optimization problems. We therefore employed an Expectation/Maximization (EM) iterative method for obtaining maximum likelihood estimates. The most important feature of the EM algorithm is that it decomposes the observed data into its components and then estimates the parameters of each signal component separately providing computationally efficient solution to resulting optimization problem. The performance of the unconditional maximum likelihood location estimator for the near-field sources is studied based on the concentrated likelihood approach to obtain Cramér-Rao bounds. Some insights into the achievable performance of the conditional maximum likelihood algorithm is obtained by numerical evaluation of the Cramér-Rao bounds for different test cases.

Maximum-likelihood source localization and unknown sensor location estimation for wideband signals in the near-field

In this paper, we derive the maximum-likelihood (ML) location estimator for wideband sources in the near field of the sensor array. The ML estimator is optimized in a single step, as opposed to other estimators that are optimized separately in relative time-delay and source location estimations. For the multisource case, we propose and demonstrate an efficient alternating projection procedure based on sequential iterative search on single-source parameters. The proposed algorithm is shown to yield superior performance over other suboptimal techniques, including the wideband MUSIC and the two-step least-squares methods, and is efficient with respect to the derived Cramer-Rao bound (CRB). From the CRB analysis, we find that better source location estimates can be obtained for high-frequency signals than low-frequency signals. In addition, large range estimation error results when the source signal is unknown, but such unknown parameter does not have much impact on angle estimation. In some applications, the locations of some sensors may be unknown and must be estimated. The proposed method is extended to estimate the range from a source to an unknown sensor location. After a number of source-location frames, the location of the uncalibrated sensor can be determined based on a least-squares unknown sensor location estimator.

Detection of environmental mismatch in a shallow water waveguide

Performance of source localization, particularly using matched-field processing techniques, is very sensitive to modeling mismatch. This paper presents a novel test for detecting modeling mismatch in a bounded propagation medium, such as shallow water. The test is based on the fact that when there are no model uncertainties, the modal spectrum of the received signal is strictly limited to an a priori known set of modes. Mismatch in the modal eigenfunction of the assumed model causes the modal spectrum out of this band to be nonzero. The proposed test requires no prior knowledge about the radiating sources. The performance of the proposed test is evaluated via computer simulations of a benchmark shallow water channel. It is shown that the test is sensitive to mismatch in the channel depth and in bottom sound speeds. The ability of the test to identify array tilt mismatch is also presented. An application of the test for validation of maximum-likelihood localization results is also discussed.

Maximum likelihood localization of sources propagating in a random media using intensity measurements

A statistical signal processing solution is proposed for locating a monochromatic source propagating in a random media. The media is fully parametrized by the normalized scattering strength γ and scaled range X, which depend upon the physics of the media. M independent intensity measurements are observed, each drawn from the generalized gamma distribution. This has been shown by Ewart [J. Acoust. Soc. Am. 86, 1490–1498 (1989)] to describe sources propagating through internal waves in ocean environments. The parameters of the distribution are related to the scattering parameters, γ and X. Maximum likelihood estimation is used to infer X, given the observations and our knowledge of γ. The estimation performance is well-characterized by the Cramer–Rao lower bound (CRLB). The results show that we can estimate range to a precision of about 20%, for ranges up to half the distance to the focus of the medium. Simulation results verify both the normality of the estimates and the validity of the CRLB as a predictor of the estimator precision at these ranges. The practical value of this method will depend on our ability to gather enough independent measurements, and on the accuracy of the statistical models we assume, including prior knowledge of γ. It can be expected to augment other methods such as matched field processing.

Over‐the‐horizon radar target localization using a hidden Markov model estimated from ionosonde data

Uncertainty about the downrange ionospheric conditions is a well‐known source of localization errors in over‐the‐horizon radar. Statistical modeling of ionospheric parameters has recently been proposed in order to derive a maximum likelihood (ML) localization method which is more robust to ionospheric variability. Maximum likelihood coordinate registration consists of determining the most likely target ground coordinates over an ensemble of ionospheric conditions consistent with the data. For greater computational efficiency the likelihood function is approximated by a hidden Markov model (HMM) for the probability of a sequence of observed slant coordinates given a hypothesized target location. In previous work, estimation of the HMM parameters was achieved assuming that the statistics of the underlying ionosphere were known precisely. This paper addresses the problem of estimating the parameters of the HMM from contemporaneous ionospheric sounder measurements. The approach taken here is to treat the plasma frequency profile as a homogeneous random process over the region around the midpoint between the radar and the dwell illumination region. In particular, spatial sampling of a three‐dimensional (3‐D) ionospheric model, fitted to ionosonde measurements, is used to generate quasi 2‐D plasma frequency profile realizations. Estimates of the hidden Markov model parameters are then obtained by using smoothed bootstrap Monte Carlo resampling. A comparison of ML localization and conventional methods, using full 3‐D ionospheric modeling and 2‐D ray tracing, are given using real data from a known target at a ground range of 2192 km. Results for over 250 radar dwells indicate that the ML localization technique achieves better than a factor of 2 improvement over conventional methods.

Linkage analysis of two Canadian families segregating for X linked spondyloepiphyseal dysplasia.

X linked spondyloepiphyseal dysplasia (SED) is caused by a growth defect of the vertebral bodies leading to characteristic changes in the vertebral bodies and a short trunk. The gene responsible for this disorder has previously been mapped to Xp22, with a maximum likelihood location between markers DXS16 and DXS92. We present linkage data using microsatellite markers on two Canadian X linked SED families, one of Norwegian descent and the other from Great Britain. In the Xp22 region, three recombination events have occurred in these families, two between markers DXS996 and DXS1043 and one between DXS999 and DXS989. One family shows a maximal lod score of 3.0 at theta = 0 with marker DXS1043 and the other family has a maximal lod score of 1.2 at theta = 0 with markers DXS1224 and DXS418. Both families therefore support the previously reported gene localisation.

On maximum-likelihood localization of coherent signals

We consider the problem of localizing multiple signal sources in the special case where all the signals are known a priori to be coherent. A maximum-likelihood estimator (MLE) is constructed for this special case, and its asymptotical performance is analyzed via the Cramer-Rao bound (CRB). It is proved that the CRB for this case is identical to the CRB for the case that no prior knowledge on coherency is exploited, thus establishing a quite surprising result that, asymptotically, the localization errors are not reduced by exploiting this prior knowledge. Also, we prove that in the coherent case the deterministic signals model and the stochastic signals model yield MLE's that are asymptotically identical. Simulation results confirming these theoretical results are included.

Maximum likelihood localization of sources in noise modeled as a stable process

This paper introduces a new class of robust beamformers which perform optimally over a wide range of non-Gaussian additive noise environments. The maximum likelihood approach is used to estimate the bearing of multiple sources from a set of snapshots when the additive interference is impulsive in nature. The analysis is based on the assumption that the additive noise can be modeled as a complex symmetric /spl alpha/-stable (S/spl alpha/S) process. Transform-based approximations of the likelihood estimation are used for the general S/spl alpha/S class of distributions while the exact probability density function is used for the Cauchy case. It is shown that the Cauchy beamformer greatly outperforms the Gaussian beamformer in a wide variety of non-Gaussian noise environments, and performs comparably to the Gaussian beamformer when the additive noise is Gaussian. The Cramer-Rao bound for the estimation error variance is derived for the Cauchy case, and the robustness of the S/spl alpha/S beamformers in a wide range of impulsive interference environments is demonstrated via simulation experiments.

Prediction of the number of coherent signals for mobile communication systems using autoregressive modeling

AbstractOne effective technique for reducing multipath fading in mobile communications is introduction of directional diversity with the help of adaptive arrays. This technique requires direction of arrival (DOA) estimation of coherent signals and relative time delay estimation. Eigenvector analysis or maximum likelihood localization is an efficient technique to estimate DOA. However, for coherent signals, spatial smoothing preprocessing is required and information about the number of signals is needed.This paper proposes to use spatial autoregressive modeling and final prediction error (FPE) to estimate the number of coherent signals. Since FPE drastically decreases with p when the length of prediction filter p is less than the number of coherent signals k and FPE converges to a constant value determined by C/N when p is greater than k, the number of coherent signals can be estimated. Moreover, by appropriately defining the FPE threshold, the number of dominant coherent signals can be estimated under the C/N concept. Numerical experiment indicates that this technique can estimate the number of signals and DOA with sufficient accuracy. Further, by appropriately defining the FPE threshold, the number of dominant coherent signals can be estimated.