Source Localization Based on Hybrid AOA, TDOA, and RSS Measurements

In orthogonal frequency division multiplexing (OFDM) systems, the carrier frequency offset can he normalized by the subcarrier bandwidth and then he divided into the integer and the fractional part. This paper focuses on the estimation of the integer carrier frequency offset and derives approximate maximum likelihood (ML) estimators in the presence and in the absence of pilot subcarriers. Simplified approximate ML estimators with reduced complexity are also proposed. The performance of the proposed estimators is compared with that of existing estimators, and it is shown by simulation that the proposed estimators outperform existing estimators.

In this paper, we address the motion parameter estimation problem using time difference of arrival (TDOA) measurements, where a mobile source starts from an initial position with constant velocity. The problem is formulated as three non-convex constrained weighted least squares (CWLS) problems. Owing to their non-convex nature, local convergence may occur when solving them by an iterative algorithm, implying good estimates are not guaranteed. We propose to solve these CWLS problems by applying semidefinite relaxation (SDR) to generate three different semidefinite programming (SDP) problems, namely, the motion unconstrained semidefinite programming (MU-SDP), motion constrained semidefinite programming (MC-SDP), and motion parameter direct semidefinite programming (MPD-SDP). The MU-SDP, MC-SDP, and MPD-SDP methods are then extended to the scenario of unknown propagation speed (PS), which is common in underwater and underground localizations. Specifically, for this scenario, the two-step MU-SDP, two-step MC-SDP, and two-step MPD-SDP methods are designed to keep the relaxed SDP problems tight by introducing the penalty function. Simulation results show that MU-SDP performs worse than MC-SDP and MPD-SDP owing to the ignorance of the motion equation, and MC-SDP and MPD-SDP are able to reach the Cramér-Rao lower bound (CRLB) accuracy.

A method of modeling slowly time-varying binary switching elements with a periodic two-state semi-Markovian parametric model is presented. An optimal Maximum Likelihood (ML) estimator is derived for general holding time distributions. In addition, a slight restriction on the holding time distribution reduces the ML estimator into a Weighted Least Square (WLS) estimator. Finally, a linearization of the WLS equation results in a sub-optimal Linear Least Square (LLS) estimator which is non-iterative and involves finding the solution to a set of matrix equations, where the matrices are correlation matrices.

We can only extract the differential time delay (DTD) measurements between the direct and reflected paths in multistatic localization when there is no synchronization in time between the transmitter and receiver and among the receivers. This paper first addresses the problem of multistatic localization of a fixed object when the transmitter position is not available by using the DTD measurements. We propose a two-step optimization method for jointly estimating the object and transmitter positions. In the first step, we formulate a non-convex constrained weighted least squares (CWLS) problem by transforming the DTD measurement model and introducing nuisance variables. Such a non-convex CWLS problem is then relaxed to a tractable convex semidefinite programming (SDP) problem by applying semidefinite relaxation. In the second step, the error coming from relaxation and approximation in the SDP solution is reduced iteratively through solving a generalized trust region subproblem (GTRS) in each iteration. If the receivers are synchronized such that the time difference of arrival (TDOA) measurements can be acquired in addition to DTD, we formulate a different CWLS problem by utilizing both DTD and TDOA measurements, which is solved by convex relaxation as well. The relaxed SDP problem can achieve the optimal solution of the CWLS problem, and further refinement is no longer needed. We conduct the mean square error (MSE) analysis to validate that both proposed methods are able to achieve the Cramer-Rao Lower Bound (CRLB) performance under small Gaussian noise, which is also validated by simulations.

For the multisensor linear discrete time-invariant systems with correlated measurement noises and with different measurement matrices, based on the linear unbiased minimum variance criterion, a weighted measurement fusion Kalman filtering algorithm is presented. It is identical to that obtained by the Weighted Least Squares(WLS) method, and is numerically identical to the centralized fusion Kalman filtering algorithm, so that it has the global optimality. The optimal weights are given by the Lagrange multiplier method, but its computation burden is large. In order to reduce the computational burden, a reduced dimension weighted measurement fusion Kalman filtering algorithm is derived, which avoids the Lagrange multiplier method, and can significantly reduced the computational burden. The comparison of computational count between two algorithms is given. A simulation example shows effectiveness and correctness of the proposed algorithm.

We revisit the problem of blind calibration of uniform linear sensors arrays for narrowband signals and set the premises for the derivation of the optimal blind calibration scheme. In particular, instead of taking the direct (rather involved) Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, we follow Paulraj and Kailath’s classical approach in exploiting the special (Toeplitz) structure of the observed covariance. However, we offer a substantial improvement over Paulraj and Kailath’s Least Squares (LS) estimate by using asymptotic approximations in order to obtain simple, (quasi-)linear Weighted LS (WLS) estimates of the sensors’ gains and phases offsets with asymptotically optimal weighting. As we show in simulation experiments, our WLS estimates exhibit near-optimal performance, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors, w.r.t. the corresponding ordinary LS estimates. We also briefly explain how the methodology derived in this work may be utilized in order to obtain (by certain modifications) the asymptotically optimal ML estimates w.r.t. the raw data via a (quasi)-linear WLS estimate.

Weibull distribution is widely used in various areas such as life tables, failure rates, and definition of wind speed distribution. Therefore, parameter estimation for the Weibull distribution is an important problem in many real data applications. The least square (LS), the weighted least square (WLS) and the maximum likelihood (ML) are the most popular methods for the parameter estimation in the Weibull distribution. In this study, based on the LS, WLS and ML estimation methods, a multi-objective programming approach is proposed for the parameter estimation of two-parameter Weibull distribution. This new approach evaluates together LS, WLS and ML methods in the estimation process. NSGA-II method, which is a multi-objective heuristic optimization method, is used to solve the proposed multi-objective estimation model. To evaluate the applicability and performance of the proposed approach, a detailed Monte Carlo simulation study based on deficiency criteria and a real data application are designed. The results illustrated that the proposed multi-objective programming approach provides quite accurate parameter estimates for the two parameter Weibull distribution with respect to deficiency criteria.

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 problem of estimating propagation delays of orthogonally modulated signals in asynchronous DS‐CDMA systems over time‐varing Rayleigh‐fading channels is treated in this paper. The maximum likelihood (ML) estimator and its unaffordable complexity for implementation are discussed. Some suboptimal solutions, e.g., whitened sliding correlator, MMSE estimator, subspace‐based estimator, approximate ML estimator, are proposed to combat the multiple access interference in the fading channels. The performance of these estimators are evaluated with the computer simulations and shown to have better acquisition performance than the standard sliding correlator. They also achieve reduced computational complexity compared with the ML estimator, while maintaining an acceptable performance degradation. Copyright © 2003 AEI

This study presents the Kumaraswamy Marshal–Olkin Flexible Weibull Extension (KMO-FWE) distribution, a newly developed probability model designed to extend existing lifetime distributions. This extension enhances the ability to model various hazard rate patterns with greater flexibility. The study explores the fundamental properties of this distribution, including the cumulative distribution function (CDF), probability density function (PDF), survival function, hazard function, moments, moment generating function, quantile function, and order statistics. To estimate the distribution’s parameters, several statistical methods are assessed, with a primary focus on Maximum Likelihood Estimation (MLE). Additionally, alternative estimation techniques such as Maximum Product Spacing (MPS), Least Squares (LS), Weighted Least Squares (WLS), and Percentile Estimation (PE) are considered. A Monte Carlo simulation study is conducted to evaluate the accuracy and efficiency of these estimation approaches under both complete data and Type-II censoring conditions. The results indicate that MLE is highly effective for large sample sizes but may introduce bias in smaller samples. In contrast, MPS provides stable parameter estimates under more complex conditions. While LS and WLS are computationally straightforward, their performance diminishes in the presence of censoring. Meanwhile, PE proves beneficial in reliability analysis based on percentile estimation. Overall, the findings highlight the KMO-FWE distribution as a versatile and reliable model, suitable for applications in reliability engineering, survival analysis, and biomedical research.

In this paper, we derive maximum likelihood estimators (MLEs) and approximate maximum likelihood estimators (AMLEs) of unknown parameters in a generalized half logistic distribution under Type-II hybrid censoring. We also obtain approximate confidence intervals using asymptotic variance and covariance matrices based on the MLEs and the AMLEs. As an illustration, we examine the validity of the proposed estimation using real data. Finally, we compare the proposed estimators in the sense of the mean squared error (MSE), bias, and length of the approximate confidence interval through a Monte Carlo simulation for various censoring schemes.

This paper develops maximum likelihood estimators (MLEs) of unknown param-eters in an exponentiated half-logistic distribution based on a progressively type-IIcensored sample. We obtain approximate con dence intervals for the MLEs by usingasymptotic variance and covariance matrices. Using importance sampling, we obtainBayes estimators and corresponding credible intervals with the highest posterior densityand Bayes predictive intervals for unknown parameters based on progressively type-IIcensored data from an exponentiated half logistic distribution. For illustration pur-poses, we examine the validity of the proposed estimation method by using real andsimulated data.Keywords: Bayes predictive interval, exponentiated half-logistic distribution, HPD cred-ible interval, importance sampling, progressively type-II censored sample. 1. Introduction Many reliability and survival analysis studies have used half-logistic distributions, partic-ularly for censored data. Several studies have drawn inferences about half logistic distribu-tions. Balakrishnan and Puthenpura (1986) introduce the best linear unbiased estimator oflocation and scale parameters of half-logistic distributions by considering linear functionsof order statistics. Balakrishnan and Wong (1991) obtain approximate maximum likelihoodestimators (AMLEs) of location and scale parameters of half-logistic distributions by usinga type-II right-censored sample. Kang et al. (2008) derive AMLEs and MLEs of scale pa-rameters of half-logistic distributions by using progressively type-II censored samples. Kanget al. (2009) propose AMLEs of scale parameters of half-logistic distributions by consideringdouble-hybrid censored samples. Kang and Seo (2011) recently examine exponentiated half-logistic distributions and propose two types of AMLEs of scale parameters and reliabilityfunctions by using progressively type-II right-censored samples. Kim et al. (2011a) deriveBayesian estimators of shape parameters, reliability functions, and failure rate functions

Estimating Spatial Autocorrelation with Sampled Network Data

Spatial autocorrelation is a parameter of importance for network data analysis. To estimate spatial autocorrelation, maximum likelihood has been popularly used. However, its rigorous implementation requires the whole network to be observed. This is practically infeasible if network size is huge (e.g., Facebook, Twitter, Weibo, WeChat, etc.). In that case, one has to rely on sampled network data to infer about spatial autocorrelation. By doing so, network relationships (i.e., edges) involving unsampled nodes are overlooked. This leads to distorted network structure and underestimated spatial autocorrelation. To solve the problem, we propose here a novel solution. By temporarily assuming that the spatial autocorrelation is small, we are able to approximate the likelihood function by its first-order Taylor’s expansion. This leads to the method of approximate maximum likelihood estimator (AMLE), which further inspires the development of paired maximum likelihood estimator (PMLE). Compared with AMLE, PMLE is computationally superior and thus is particularly useful for large-scale network data analysis. Under appropriate regularity conditions (without assuming a small spatial autocorrelation), we show theoretically that PMLE is consistent and asymptotically normal. Numerical studies based on both simulated and real datasets are presented for illustration purpose.

Weighted least squares (WLS), weighted least squares mean-and-variance-adjusted (WLSMV), unweighted least squares mean-and-variance-adjusted (ULSMV), maximum likelihood (ML), robust maximum likelihood (MLR) and Bayesian estimation methods were compared in mixed item response type data via Monte Carlo simulation. The percentage of polytomous items, distribution of polytomous items, categories of polytomous items, average factor loading, sample size and test length conditions were manipulated. ULSMV and WLSMV were found to be the more accurate methods under all simulation conditions. All methods except WLS had acceptable relative bias and relative standard error bias. No method gives accurate results with small sample sizes and low factor loading, however, the ULSMV method can be recommended to researchers because it gives more appropriate results in all conditions.