Local strong convexity of maximum-likelihood TDOA-Based source localization and its algorithmic implications

We pose the estimation of the parameters of multiple superimposed exponential signals in additive Gaussian noise problem as a maximum likelihood (ML) estimation problem. The ML problem is non linear and hard to solve. Some previous works focused on finding alternative estimation procedures, for example by denoising. In contrast, we tackle the ML estimation problem directly. First, we use the same transformation as the first step of iterative quadratic maximum likelihood (IQML) and transform the ML problem into another optimization problem that gets rid of the amplitude coefficients. Second, we solve the remaining optimization problem with a gradient descent approach ("pseudo-quadratic maximum likelihood"). We also use this algorithm for ultra-wideband channel estimation and estimate ranging in non-line of sight environment.

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.

The oscillator phase hit (PH) results in a temporary link loss in the communication system and bears an expensive cost on the operator companies. In this work, we propose a double-stage solution to mitigate the PH. In the first stage, we use Neyman-Pearson binary hypothesis testing to develop a low-cost PH detection algorithm, in which a likelihood ratio test is designed, and the optimal detection threshold is analytically calculated. The proposed PH detection scheme entails small real-time computations while using the existing pilot symbols in the system. Hence, no extra pilot overhead is required. In the second stage, the maximum likelihood (ML) estimation is used to develop a PH correction scheme. In particular, the phase noise and the PH are jointly mitigated by solving an ML estimation problem. By applying the proposed correction scheme, the number of remaining erroneous symbols due to PH (if any) is within the error correction capability of modern forward error-correcting codes. Numerical results verify the effectiveness of the proposed scheme in detecting and correcting the PH.

Source localization in a wireless sensor network (WSN) is sensitive to the sensors' positions. In practice, due to mobility, the receivers' positions may be known inaccurately, leading to non-negligible degradation in source localization estimation performance. The goal of this paper is to develop a semidefinite programming (SDP) method using time-difference-of arrival (TDOA) and frequency-difference-of-arrival (FDOA) by taking the sensor position uncertainties into account. Specifically, we transform the commonly used maximum likelihood estimator (MLE) problem into a convex optimization problem to obtain an initial estimation. To reduce the coupling between position and velocity estimator, we also propose an iterative method to obtain the velocity and position, by using weighted least squares (WLS) method and SDP method, respectively. Simulations show that the method can approach the Cramér-Rao lower bound (CRLB) under both mild and high noise levels.

The Maximum Likelihood (ML) and Best Linear Unbiased (BLU) estimators of the location and scale parameters of an extreme value distribution (Lawless [1982]) are compared under conditions of small sample sizes and Type I censorship. The comparisons were made in terms of the mean square error criterion. According to this criterion, the ML estimator of σ in the case of very small sample sizes (n < 10) and heavy censorship (low censoring time) proved to be more efficient than the corresponding BLU estimator. However, the BLU estimator for σ attains parity with the corresponding ML estimator when the censoring time increases even for sample sizes as low as 10. The BLU estimator of σ attains equivalence with the ML estimator when the sample size increases above 10, particularly when the censoring time is also increased. The situation is reversed when it came to estimating the location parameter μ, as the BLU estimator was found to be consistently more efficient than the ML estimator despite the improved performance of the ML estimator when the sample size increases. However, computational ease and convenience favor the ML estimators. Keywords: maximum likelihood estimatorsbest linear unbiased estimatorslife-testingreliability

We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_{2}$). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof that the maximum likelihood estimator (MLE) for such distributions exists based on $n\geq2$ observations, irrespective of the underlying dimension. Slawski and Hein [Linear Algebra Appl. 473 (2015) 145–179], who first proved this result, also provided empirical evidence showing that the $\mathrm{MTP}_{2}$ constraint serves as an implicit regularizer and leads to sparsity in the estimated inverse covariance matrix, determining what we name the ML graph. We show that we can find an upper bound for the ML graph by adding edges corresponding to correlations in excess of those explained by the maximum weight spanning forest of the correlation matrix. Moreover, we provide globally convergent coordinate descent algorithms for calculating the MLE under the $\mathrm{MTP}_{2}$ constraint which are structurally similar to iterative proportional scaling. We conclude the paper with a discussion of signed $\mathrm{MTP}_{2}$ distributions.

We consider the problem of maximum likelihood estimation of logistic sinusoidal regression models and develop some asymptotic theory including the consistency and joint rates of convergence for the maximum likelihood estimators. The key techniques build upon a synthesis of the results of Walker and Song and Li for the widely studied sinusoidal regression model and on making a connection to a result of Radchenko. Monte Carlo simulations are also presented to demonstrate the finite-sample performance of the estimators

The Multiple Comparison Procedures with Modeling Techniques (MCP-Mod) framework has been recently approved by the U.S. Food, Administration, and European Medicines Agency as fit-for-purpose for phase II studies. Nonetheless, this approach relies on the asymptotic properties of Maximum Likelihood (ML) estimators, which might not be reasonable for small sample sizes. In this paper, we derived improved ML estimators and correction for their covariance matrices in the censored Weibull regression model based on the corrective and preventive approaches. We performed two simulation studies to evaluate ML and improved ML estimators with their covariance matrices in (i) a regression framework (ii) the Multiple Comparison Procedures with Modeling Techniques framework. We have shown that improved ML estimators are less biased than ML estimators yielding Wald-type statistics that controls type I error without loss of power in both frameworks. Therefore, we recommend the use of improved ML estimators in the MCP-Mod approach to control type I error at nominal value for sample sizes ranging from 5 to 25 subjects per dose.

For a balanced two‐way mixed model, the maximum likelihood (ML) and restricted ML (REML) estimators of the variance components were obtained and compared under the non‐negativity requirements of the variance components by Lee and Kapadia (1984). In this note, for a mixed (random blocks) incomplete block model, explicit forms for the REML estimators of variance components are obtained. They are always non‐negative and have smaller mean squared error (MSE) than the analysis of variance (AOV) estimators. The asymptotic sampling variances of the maximum likelihood (ML) estimators and the REML estimators are compared and the balanced incomplete block design (BIBD) is considered as a special case. The ML estimators are shown to have smaller asymptotic variances than the REML estimators, but a numerical result in the randomized complete block design (RCBD) demonstrated that the performances of the REML and ML estimators are not much different in the MSE sense.

Over-the-air computation (OAC) is a promising technique to realize fast model aggregation in the uplink of federated edge learning (FEEL). OAC, however, hinges on accurate channel-gain precoding and strict synchronization among edge devices, which are challenging in practice. As such, how to design the maximum likelihood (ML) estimator in the presence of residual channel-gain mismatch and asynchronies is an open problem. To fill this gap, this paper formulates the problem of misaligned OAC for FEEL and puts forth a whitened matched filtering and sampling scheme to obtain oversampled, but independent samples from the misaligned and overlapped signals. Given the whitened samples, a sum-product ML (SP-ML) estimator and an aligned-sample estimator are devised to estimate the arithmetic sum of the transmitted symbols. In particular, the computational complexity of our SP-ML estimator is linear in the packet length, and hence is significantly lower than the conventional ML estimator. Extensive simulations on the test accuracy versus the average received energy per symbol to noise power spectral density ratio (EsN0) yield two main results: 1) In the low EsN0 regime, the aligned-sample estimator can achieve superior test accuracy provided that the phase misalignment is not severe. In contrast, the ML estimator does not work well due to the error propagation and noise enhancement in the estimation process. 2) In the high EsN0 regime, the ML estimator attains the optimal learning performance regardless of the severity of phase misalignment. On the other hand, the aligned-sample estimator suffers from a test-accuracy loss caused by phase misalignment.

We consider the problem of maximum likelihood estimation of directions of arrival of multiple source signals in the presence of unknown spatially correlated Gaussian noise. Oblique projections are used to separate the structured noise from the signal and an approximate maximum likelihood solution is derived. The estimates are obtained by maximizing the modified cost function using a nonlinear optimization technique. Numerical simulations are provided to assess the performance of the proposed approach. Simulations include comparison to the stochastic maximum likelihood and to the weighted subspace fitting, as well as to the Cramer-Rao bound.

Maximum likelihood estimation of time delays in multipath acoustic channel

The problem of maximum likelihood estimation of the parameters of Mallows’ ranking model based on partial rankings (with a fixed number of tie groups) has been approached by Beckett (1992), applying the EM algorithm to estimate both the center and the scale parameter. This paper offers an alternative procedure for maximum likelihood estimation without relying on the EM algorithm:the center is estimated by minimizing the sum of the distances between the center and the observed partial rankings, and the scale parameter is estimated by solving a relatively simple equation.

This letter addresses the problem of source localization in non-line of sight (NLOS) environment using received signal strength (RSS) and time of arrival (TOA) measurements when both transmission time and power are unknown. To mitigate the NLOS bias, a robust weighted least square (RWLS) problem is formulated from original non-convex maximum-likelihood (ML) estimation problem using a set of tight approximations. The RWLS problem is further tightened by a novel convex-hull constraint and is ultimately solved using second-order cone programming (SOCP). Simulation results confirm the optimal performance of the proposed robust method in various network scenarios and also validate its excellence over state-of-art methods.

Recent work has shown that the resonate-and-fire neuronal model is both computationally efficient and suitable for large network simulations. In this paper, we examine the estimation problem of a resonate-and-fire neuronal model with stochastic firing threshold. The model parameters are divided into two sets. The first set is associated with the subthreshold behaviour and can be estimated by a least squares algorithm, while the second set includes parameters associated with the firing threshold and its identification is formulated as a maximum likelihood estimation problem. The latter is in turn solved by a simulated annealing approach that avoids local optima. The proposed identification approach is evaluated using both simulated and in-vitro data, which shows a good match between prediction by identified model and the actual data, concluding the efficiency and accuracy of the proposed approach.