Intelligence-Aware Batch Processing for TMA with Bearings-Only Measurements

The reverberation power spectral density (PSD) is often required for dereverberation and noise reduction algorithms. In this work, we compare two maximum likelihood (ML) estimators of the reverberation PSD in a noisy environment. In the first estimator, the direct path is first blocked. Then, the ML criterion for estimating the reverberation PSD is stated according to the probability density function of the blocking matrix (BM) outputs. In the second estimator, the speech component is not blocked. Instead, the ML criterion for estimating the speech and reverberation PSD is stated according to the probability density function of the microphone signals. To compare the expected mean square error (MSE) between the two ML estimators of the reverberation PSD, the Cramer–Rao Bounds (CRBs) for the two ML estimators are derived. We show that the CRB for the joint reverberation and speech PSD estimator is lower than the CRB for estimating the reverberation PSD from the BM outputs. Experimental results show that the MSE of the two estimators indeed obeys the CRB curves. Experimental results of multimicrophone dereverberation and noise reduction algorithm show the benefits of using the ML estimators in comparison with another baseline estimators.

Cooperative communication combats the effects offadingwithoutthe need for multiple antennas.The cooperative networks use multiple distributed nodes that virtually behave like multiple antennas each having their own local oscillators. But the oscillators cause multiple Carrier Frequency Offsets (CFO), unknown channel gains and Multiple Timing Offsets (MTO). For a good performance of the system perfect synchronization is needed which is achieved by estimation and compensation of multiple offsets. Also, the coverage and capacity can be improved by employing intermediate nodes called relays within cooperative networks. These cooperative relay networks can perform in a better manner even when considering MCFOs, MTOs and unknown channel gains by having more computationally efficient decoders that can use Maximum Likelihood (ML) estimation subject to the Cramer-Rao Lower Bound (CRLB) on the variance of any impartial estimate. The simulation results show that frequency offset still exist after Amplify and Forward (AF) relaying. The performance of a conventional cooperative network seems to have improved with respect to Bit Error Rate of the system when an AF relay is hosted. The estimate of the frequency offset is chosen such that it gives the signal, a high probability of occurrence using ML estimator. In ML estimate, since the bias and variance is difficult to compute, a lower bound called the CRLB on the variance of any unbiased estimate is derived which is satisfied by the ML estimator.Keywords: AF, Cooperative Communication, CFO, ML Estimation and Compensation, OFDM

The problem of distributed parameter estimation from binary quantized observations is studied when the unquantized observations are corrupted by combined multiplicative and additive Gaussian noise. These results are applicable to sensor networks where the sensors observe a parameter in combined additive and nonadditive noise and to a case where dispersed receivers are employed with analog communication over fading channels where the receivers employ binary quantization before noise-free digital communications to a fusion center. We first discuss the case in which all the quantizers use an identical threshold. The parameter identifiability condition is given, and, surprisingly, it is shown that unless the common threshold is chosen properly and the parameter lies in an open interval, the parameter will not generally be identifiable, in contrast to the additive noise case. The best achievable mean square error (MSE) performance is characterized by deriving the corresponding Cramer-Rao Lower Bound (CRLB). A closed-form expression describing the corresponding maximum likelihood (ML) estimator is presented. The stability of the performance of the ML estimators is improved when a nonidentical threshold strategy is utilized to estimate the unknown parameter. The thresholds are designed by maximizing the minimum asymptotic relative efficiency (ARE) between quantized and unquantized ML estimators. Although the ML estimation problem is nonconvex, it is shown that one can relax the optimization to make it convex. The solution to the relaxed problem is used as an initial solution in a gradient algorithm to solve the original problem. Next, the case where both the variances of the additive noise and multiplicative noise are unknown is studied. The corresponding CRLB is obtained, and the ML estimation problem is transformed to a convex optimization, which can be solved efficiently. Finally, numerical simulations are performed to substantiate the theoretical analysis.

Maximum-likelihood (ML) estimation is an established paradigm for the assessment of imaging system performance in nonlinear quantitation tasks. At high signal-to-noise ratio (SNR), ML estimates are asymptotically Gaussian-distributed, unbiased and efficient, thereby attaining the Cramer–Rao bound (CRB). Therefore, at high SNR the CRB is useful as a predictor of the variance of ML estimates and, consequently, as a basis for measures of estimation performance. At low SNR, however, the achievable parameter variances are often substantially larger than the CRB and the estimates are no longer Gaussian-distributed. These departures imply that inference about the estimates that is based on the CRB and the assumption of a normal distribution will not be valid. We have found previously that for some tasks these effects arise at noise levels considered clinically acceptable. We have derived the mathematical relationship between a new measure, χ2pdf-ML, and the expected probability density of the ML estimates, and have justified the use of χ2pdf-ML-isocontours in parameter space to describe the ML estimates. We validated this approach by simulation experiments using spherical objects imaged with a Gaussian point spread function. The parameters, activity concentration and size, were estimated simultaneously by ML, and variances and covariances calculated over 1000 replications per condition from 3D image volumes and from 2D tomographic projections of the same object. At low SNR, where the CRB is no longer achievable, χ2pdf-ML-isocontours provide a robust prediction of the distribution of the ML estimates. At high SNR, the χ2pdf-ML-isocontours asymptotically approach the analogous χ2pdf-F-contours derived from the Fisher information matrix. The χ2pdf-ML model appears to be suitable for characterization of the influence of the noise level and characteristics, the task, and the object on the shape of the probability density of the ML estimates at low SNR. Furthermore, it provides unique insights into the causes of the variability of estimation performance.

In this paper, we consider non-Bayesian parameter estimation in wireless sensor networks (WSNs) with multiple sensors that have different quantization resolutions. Quantized measurements provide improved performance in the sense of energy consumption, communication bandwidth, and hardware complexity, but are less informative than analog, unquantized measurements and may lead to poor estimation performance. In this paper we assume that the WSN contains two types of sensor nodes: 1-bit, quantized measurements and TO-bit, unquantized measurements. We introduce the maximum-likelihood (ML) estimator for this case and derive the Fisher scoring method in order to implement it. The Cramer-Rao lower bound (CRB) has been developed for the considered model. In addition, we characterize the sample allocation rule that determines how many sensors are selected for quantized and unquantized measurements in order to minimize the sum of the CRB and linear sensors costs. Finally, we present simulations that show for the linear Gaussian model the ML estimator achieves the CRB and examine the use of additional analog measurements as a tool for improving robustness.

For time-of-flight-based wireless positioning systems operating in (dense) multipath propagation channels, the accuracy is severely influenced by the signal bandwidth, because the dense multipath component (DMC) interferes with the desired, information-bearing line-of-sight (LoS) signal. Several such systems make use of bandwidth-limited frequency resources, e.g. the industrial, scientific and medical (ISM) bands, therefore the achievable position estimation accuracy is limited. In this paper, we propose a model-based delay-estimation method which takes into account a parametric model of the DMC and thus exploits the signal energy carried in the DMC. The resulting algorithm exhibits an enhanced delay estimation accuracy and remarkable robustness in non-LoS situations. The algorithm is benchmarked against a maximum likelihood (ML) estimator not incorporating a model for the DMC and against the estimated Cramér-Rao lower bound (CRLB) in presence of DMC. Results show a significant performance gain for scenarios where the conventional ML estimator performs poorly. An evaluation of measurement data validates the simulation, showing a root-mean-square error (RMSE) of 33.4 cm compared to 1.89 m for the conventional ML estimator, at a signal bandwidth of 80 MHz.

Ant Colony Optimization (ACO) is a popular meta-heuristic for solving combinatorial optimization problems. ACO uses the concept of ants foraging for food to find good solutions to these types of problems. ACO has been successfully applied to many problems, from the traveling salesman problem (TSP), to the problem of network routing. However, it has been pointed out that ACO does not perform as well as other heuristics in very dynamic problems. At first, this statement seems strange but a close look reveals that the nature strategy that inspires the ACO meta-heuristic has an important element that is lacking in ACO: evolution. This paper proposes a new algorithm, named Evolutionary Ant Colony Optimization (EACO), that combines ACO with elements of traditional Genetic Algorithms (GA), namely: selection, recombination, and mutation. Individual ants are endowed with a genotype that is allowed to evolve through generations of the population. In doing this, the EACO algorithm adds another element of optimization to the ACO algorithm that allows the individual agents (ants) in the algorithm to improve their behavior over several generations. Our results demonstrate that EACO can indeed overcome the hurdles faced by the original ACO.KeywordsGenetic AlgorithmShort PathTravel Salesman ProblemTravel Salesman ProblemSwarm IntelligenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Performance analysis of connectivity-based geolocation in ultra-dense networks (UDNs) is a very important task. Although several performance analyses have been presented for range-free localization, determining the best achievable positioning accuracy of range-free localization remains an open problem. In this paper, we first derive the Cramer-Rao lower bound (CRLB) for the performance evaluation of range-free localization. All the current performance analyses in the literature for range-free localization are used to evaluate the real performance of a given algorithm, whereas the proposed CRLB provides a benchmark to evaluate the performance of any unbiased range-free location algorithm and determines the physical impossibility of the variance of an unbiased estimator being less than the bound. To the best of our knowledge, this is the first time in the literature that the CRLB for range-free localization has been derived. Second, the theoretical variance of centroid-based localization (CL) with an arbitrary node distribution is derived in this paper. In contrast to the existing theoretical variance of CL for uniform node distribution, the proposed theoretical variance can be used to evaluate the performance of CL in the case of an arbitrary node distribution. Additionally, characteristics of the proposed CRLB and theoretical variance are given in this paper. Finally, an optimal estimator based on a maximum likelihood estimator (MLE) is proposed to improve positioning accuracy. Since both prior information on the spatial node distribution and the connectivity property are effectively utilized in our algorithm, the proposed method performs better than the CL method and can asymptotically attain the CRLB.

Over-the-air precision two-way time transfer and ranging (PTTR) uses the signals exchanged between two RF transceivers to estimate the range between them and the offset between their clocks. Our paper makes three significant contributions to the estimation and position, navigation, and timing literature. First, we introduce a propagation channel model characterized by its amplitude (attenuation), phase shift, and propagation delay. This three-parameter formulation is quite practical for modeling signal exchange over line-of-sight channels with arbitrary additive wide-sense stationary noise that also captures electronic effects. Second, we derive the Cramer-Rao Lower Bound (CRLB) for this three parameter channel model. We show that there is a canonical definition of phase shift for which the CRLB is a diagonal matrix. The derived CRLB depends on simple properties of the signal and noise power spectral density (PSD) related to whitened bandwidth and whitened center frequency as well as the signal to noise ratio. Third, we derive a maximum likelihood estimator (MLE) for the amplitude, phase shift, and delay given the reference waveform, received waveform samples, and noise PSD. A novel aspect of the derived MLE is that it is implemented entirely in the frequency domain, which makes the MLE more computationally efficient than a typical time-domain implementation. Using an example reference waveform, we show that the derived MLE achieves an empirical covariance close to the CRLB for sufficiently high signal to noise ratios. The estimation results of our paper are directly relevant to over-the-air PTTR applications operating in direct-path, line-of-sight propagation environments. The generality of the waveform and noise formulations allow our estimator and bounds to be applied to arbitrary PTTR ranging waveforms in colored interference environments. We present a system architecture utilizing this estimator that enables PTTR on existing wireless networks with no changes to the communications protocol or radio hardware or software.

Maximum likelihood estimators (MLE) for time synchronization parameters of receiver-to-receiver protocols are derived. The MLE are first provided for a single-hop model, then generalized to a multi-hop model. The appropriate Cramer-Rao lower bounds (CRLB) for the estimators are then derived, which serves as a theoretical lower bound to any unbiased estimator. The proposed estimators are compared with their respective CRLB through simulation in multi-hop scenarios of up-to eight hops. The results show fast convergence of the estimation precision to the CRLB and demonstrate a high precision, where the mean square error (MSE) does not exceed 10-6 for the skew, and 10-5 for the offset. (6 pages)

In this paper we focus on deriving an approximate Cramer–Rao lower bound (CRLB) for the parameters of a multicomponent linear frequency modulated continuous wave (LFMCW) signal corrupted by complex additive white Gaussian noise. The approximation is necessary due to the discontinuities inherent in the mathematical model of the instantaneous phase of each LFMCW signal model. By comparing our approximate bound to a simulation of the maximum likelihood estimator (MLE) of the LFMCW parameters, we confirm our analysis. In general, the CRLB is a useful tool for feasibility studies or in evaluating the degree of suboptimality that non-MLE methods exhibit. For passive detection and estimation of LFMCW signals, the Generalized Likelihood Ratio Test and the associated MLE are difficult to implement in practice, primarily due to their large computational requirements. So, lower bounds on performance, such as those provided by the CRLB, are necessary to evaluate suboptimal methods that are more suited for practical implementations.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We propose a new hybrid wireless geolocation scheme that requires only one observation quantity, namely, the received signal. The attenuation model is explored herein to capture the propagation features from the received signal. Thus, it provides a more accurate approach for wireless geolocation. To investigate geolocation accuracy, we consider the time-of-arrival (ToA) estimation in the presence of path attenuation. The maximum-correlation (MC) estimator is revisited, and the exact maximum-likelihood (ML) estimator is derived to estimate the ToA. The error performance of the ToA estimates is derived using a Taylor expansion. It is shown that the ML estimate is unbiased and has a smaller error variance than the MC estimate. Numerical results illustrate that, for a low effective bandwidth, the ML estimator well outperforms the MC estimator. Afterward, we derive the CramÉr–Rao bound (CRB) for the mobile position estimation. The obtained result, which is applicable to any value of path loss exponents, gives a generalized form of the CRB for the ordinary geolocation approach. In seven hexagonal cells, numerical examples show that the accuracy of the mobile position estimation exploring the path loss is improved compared with that obtained by the usual geolocation. </para>

In multiple-input multiple-output (MIMO) radar, to estimate the reflection coefficient, spatial location, and Doppler shift of a target, maximum-likelihood (ML) estimation yields the best performance. For this problem, the ML estimation requires the joint estimation of spatial location and Doppler shift, which is a two dimensional search problem. Therefore, the computational complexity of ML estimation is prohibitively high. In this work, to estimate the parameters of a target, a reduced complexity optimum performance algorithm is proposed, which allow two dimensional fast Fourier transform to jointly estimate the spatial location and Doppler shift. To asses the performances of the proposed estimators, the Cramer-Rao-lower-bound (CRLB) is derived. Simulation results show that the mean square estimation error of the proposed estimators achieve the CRLB.

Range, radial velocity, and acceleration MLE using frequency modulation coded LFM pulse train

Dynamic contrast enhanced MRI and pharmacokinetic modelling provide a powerful tool for tumour diagnosis and treatment evaluation. However, several studies show low reproducibility of the technique and poor precision of the transendothelial transfer constant K (trans). This work proposes a theoretical framework describing how finite signal-noise-ratio (SNR) in the MR images is propagated throughout the measurement protocol to uncertainty on the kinetic parameter estimates. After deriving a distribution for the contrast agent concentration, a maximum likelihood estimator (MLM) is proposed that exhibits Cramer-Rao lower bounds (CRLB). An analytical expression is derived for the CRLB that can be used to determine confidence intervals for kinetic parameters and to investigate the influence of protocol parameters as scan time and temporal resolution on K (trans)-precision. K (trans)-uncertainty can be reduced up to 30% by using MLM in comparison with least square estimator. K (trans)-precision is proportional to the SNR and depends strongly on the kinetic parameter values themselves. Minimal scan time and temporal resolution were found to be 15 min and 15 s, respectively, for Gd-DTPA. Temporal resolution should be enhanced by decreasing the NEX parameter (NEX ≤ 1). CRLB provide a golden standard to construct 95% confidence intervals, which can be used to perform protocol optimization and to test the statistical significance of K (trans)-changes in treatment evaluation.