An improved atomic search algorithm for optimization and application in ML DOA estimation of vector hydrophone array

<abstract><p>The atom search optimization (ASO) algorithm has the characteristics of fewer parameters and better performance than the traditional intelligent optimization algorithms, but it is found that ASO may easily fall into local optimum and its accuracy is not higher. Therefore, based on the idea of speed update in particle swarm optimization (PSO), an improved atomic search optimization (IASO) algorithm is proposed in this paper. Compared with traditional ASO, IASO has a faster convergence speed and higher precision for 23 benchmark functions. IASO algorithm has been successfully applied to maximum likelihood (ML) estimator for the direction of arrival (DOA), under the conditions of the different number of signal sources, different signal-to-noise ratio (SNR) and different population size, the simulation results show that ML estimator with IASO algorithum has faster convergence speed, fewer iterations and lower root mean square error (RMSE) than ML estimator with ASO, sine cosine algorithm (SCA), genetic algorithm (GA) and particle swarm optimization (PSO). Therefore, the proposed algorithm holds great potential for not only guaranteeing the estimation accuracy but also greatly reducing the computational complexity of multidimensional nonlinear optimization of ML estimator.</p></abstract>

Estimation and computations for Gaussian mixtures with uniform noise under separation constraints

In this paper we study a finite Gaussian mixture model with an additional uniform component that has the role to catch points in the tails of the data distribution. An adaptive constraint enforces a certain level of separation between the Gaussian mixture components and the uniform component representing noise and outliers in the tail of the distribution. The latter makes the proposed tool particularly useful for robust estimation and outlier identification. A constrained ML estimator is introduced for which existence and consistency is shown. One of the attractive features of the methodology is that the noise level is estimated from data. We also develop an EM-type algorithm with proven convergence. Based on numerical evidence we show how the methods developed in this paper are useful for several fundamental data analysis tasks: outlier identification, robust location-scale estimation, clustering, and density estimation.

Radar-Based, Simultaneous Human Presence Detection and Breathing Rate Estimation

Human presence detection is an application that has a growing need in many industries. Hotel room occupancy is critical for electricity and energy conservation. Industrial factories and plants have the same need to know the occupancy status to regulate electricity, lighting, and energy expenditures. In home security there is an obvious necessity to detect human presence inside the residence. For elderly care and healthcare, the system would like to know if the person is sleeping in the room, sitting on a sofa or conversely, is not present. This paper focuses on the problem of detecting presence using only the minute movements of breathing while at the same time estimating the breathing rate, which is the secondary aim of the paper. We extract the suspected breathing signal, and construct its Fourier series (FS) equivalent. Then we employ a generalized likelihood ratio test (GLRT) on the FS signal to determine if it is a breathing pattern or noise. We will show that calculating the GLRT also yields the maximum likelihood (ML) estimator for the breathing rate. We tested this algorithm on sleeping babies as well as conducted experiments on humans aged 12 to 44 sitting on a chair in front of the radar. The results are reported in the sequel.

Estimating logit models with small samples

In small samples, maximum likelihood (ML) estimates of logit model coefficients have substantial bias away from zero. As a solution, we remind political scientists of Firth's (1993, Biometrika, 80, 27–38) penalized maximum likelihood (PML) estimator. Prior research has described and used PML, especially in the context of separation, but its small sample properties remain under-appreciated. The PML estimator eliminates most of the bias and, perhaps more importantly, greatly reduces the variance of the usual ML estimator. Thus, researchers do not face a bias-variance tradeoff when choosing between the ML and PML estimators—the PML estimator has a smaller bias and a smaller variance. We use Monte Carlo simulations and a re-analysis of George and Epstein (1992, American Political Science Review, 86, 323–337) to show that the PML estimator offers a substantial improvement in small samples (e.g., 50 observations) and noticeable improvement even in larger samples (e.g., 1000 observations).

On Time-Frequency Synchronization in LoRa System: From Analysis to Near-Optimal Algorithm

This paper deals with time and frequency synchronization in LoRa system based on the preamble symbols. A thorough analysis of the maximum likelihood (ML) estimator of the delay (time offset) and the frequency offset shows that the resulting cost function is not concave. As a consequence the a priori solution to the maximization problem consists in exhaustively searching over all the possible values of both the delay and the frequency offset. Furthermore, it is shown that these parameters are intertwined and therefore they must be jointly estimated, leading to an extremely complex solution. Alternatively, we show that it is possible to recover the concavity of the cost function, from which we suggest a low-complexity synchronization algorithm, whose steps are described in detail. Simulations results show that the suggested method reaches the same performance as the ML exhaustive search, while the complexity is drastically reduced, allowing for a real-time implementation of a LoRa receiver. <br>

On Time-Frequency Synchronization in LoRa System: From Analysis to Near-Optimal Algorithm

This paper deals with time and frequency synchronization in LoRa system based on the preamble symbols. A thorough analysis of the maximum likelihood (ML) estimator of the delay (time offset) and the frequency offset shows that the resulting cost function is not concave. As a consequence the a priori solution to the maximization problem consists in exhaustively searching over all the possible values of both the delay and the frequency offset. Furthermore, it is shown that these parameters are intertwined and therefore they must be jointly estimated, leading to an extremely complex solution. Alternatively, we show that it is possible to recover the concavity of the cost function, from which we suggest a low-complexity synchronization algorithm, whose steps are described in detail. Simulations results show that the suggested method reaches the same performance as the ML exhaustive search, while the complexity is drastically reduced, allowing for a real-time implementation of a LoRa receiver. <br>

Bivariate Power-Skew-Elliptical Distribution

In this article, we introduce a power-skew-elliptical (PSE) distribution in the bivariate setting. The new bivariate model arises in the context of conditionally specified distributions. The proposed bivariate model is an absolutely continuous distribution whose marginals are univariate PSE distributions. The special case of the bivariate power-skew-normal (BPSN) distribution is studied in details. General properties of the BPSN distribution are derived and the estimation of the unknown parameters by maximum pseudo-likelihood is discussed. Further, a sandwich type matrix, which is a consistent estimator for the asymptotic covariance matrix of the maximum likelihood (ML) estimator is determined. Two applications for real data of the proposed bivariate distribution is provided for illustrative purposes.

Basic Values Survey (BVS) - A 20-nation validation study

The present paper tests the structure and invariance of the Functional Theory of Human Values across 20 countries (N = 21,362). This theory proposes that values have the functions of guiding behaviour and expressing needs. The interplay between these two functions produces six subfunctions that in turn produce distinct content. These subfunctions are operationalised in the Basic Values Survey with three items each, forming an 18-item measure. Although this measure has been used for more than two decades, studies examining its psychometric properties in multiple-group data are scarce. Using multidimensional scaling (MDS), it was found that values were organised in a bidimensional space according to the hypothesised degree of congruence between subfunctions. Also, Confirmatory Factor Analysis (CFA) with a Bayes estimator and approximate zero cross-loadings and residual correlations supported the six-factor structure. A strict CFA with Robust-ML estimator did not support the model. Metric invariance was supported for all the items, except religiosity, using the alignment method and approximate Bayesian invariance.

Low-Complexity Sub-Optimal Cell ID Estimation in NB-IoT System

This paper deals with cell ID estimation in narrowband-internet of things (NB-IoT) system. The cell ID value is carried by<br>the narrowband secondary synchronization signal (NSSS). We suggest a low-complexity sub-optimal estimator, based on the auto-<br>correlation of the received observations. It is up to thirty times less complex than the optimal maximum likelihood (ML) estimator<br>based on cross-correlation. In addition, we present three methods allowing the receiver to take advantage of the different repetitions<br>of the NSSS. They are based on a hard decision after every estimation, a soft combination of the different observations of the NSSS,<br>and an hybrid mix between the two firsts, respectively. The advantages and drawbacks of the presented techniques are stated, and a<br>performance analysis is proposed, which is further discussed through simulations results. It is shown the that different methods reach<br>the performance of ML after several repetitions for a lower overall complexity.

Low-Complexity Sub-Optimal Cell ID Estimation in NB-IoT System

This paper deals with cell ID estimation in narrowband-internet of things (NB-IoT) system. The cell ID value is carried by<br>the narrowband secondary synchronization signal (NSSS). We suggest a low-complexity sub-optimal estimator, based on the auto-<br>correlation of the received observations. It is up to thirty times less complex than the optimal maximum likelihood (ML) estimator<br>based on cross-correlation. In addition, we present three methods allowing the receiver to take advantage of the different repetitions<br>of the NSSS. They are based on a hard decision after every estimation, a soft combination of the different observations of the NSSS,<br>and an hybrid mix between the two firsts, respectively. The advantages and drawbacks of the presented techniques are stated, and a<br>performance analysis is proposed, which is further discussed through simulations results. It is shown the that different methods reach<br>the performance of ML after several repetitions for a lower overall complexity.