A linear-circular regression using a finite mixture of the generalized linear regression models

One typical use of sensor networks is monitoring targets. The sensor networks classify, detect, locate, and track targets. The ML (Maximum likelihood) estimation algorithm is one of the estimation algorithms of target location. The ML estimation algorithm has high accuracy to estimate target location. However, the calculation amount of the ML estimation algorithm is large. The EM (Expectation Maximization) algorithm is proposed to reduce the complexity of the ML estimation algorithm. However, the EM algorithm sometimes traps into local minimum. These conventional algorithms to estimate target location use all the sensors' receiving signals. The transmission signal from the target is attenuated with distance. In particular, the effects of noise on the received signals of the sensors far apart from the target are large. The received signals thus do not help a lot to improve the estimation accuracy. In this paper, we propose the new algorithm to estimate a target location with a smaller amount of calculation than the ML estimation algorithm and higher estimation accuracy than the EM algorithm. Moreover, we propose the low complexity source localization method, where we use only the sensors' information with receiving energy higher than threshold. From the simulation results, we show that the proposed algorithm has a smaller amount of calculation than the ML estimation algorithm and higher estimation accuracy than the EM algorithm. We also show that proposed method can reduce the calculation amount while keeping the estimation accuracy by setting threshold appropriately in the ML estimation algorithm and the proposed algorithm.

We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modelling approach of a wrapped normal distribution that describes angular variables and angular distributions and advances them for a linear-circular regression analysis. Some previous works model a circular variable as projection of a bivariate Gaussian random vector on the unit square, and the statistical inference of the resulting model involves complicated sampling steps. The proposed model treats circular responses as the result of the modulo operation on unobserved linear responses. The resulting model is a mixture of multiple linear-linear regression models. We present two EM algorithms for maximum likelihood estimation of the mixture model, one for a parametric model and another for a nonparametric model. The estimation algorithms provide a great trade-off between computation and estimation accuracy, which was numerically shown using five numerical examples. The proposed approach was applied to a problem of estimating wind directions that typically exhibit complex patterns with large variation and circularity.

An adaptive receiver structure is considered for obtaining timing information for a direct-sequence code-division multiple-access (CDMA) communication network operating in a near-far environment. The receiver consists of a chip matched filter followed by an adaptive equalizer. By using a simple channel-access protocol, the timing information for a new system user can be extracted from the weights of the adaptive equalizer. In order to obtain this timing information, the receiver only requires knowledge of the spreading code of the new user. A maximum-likelihood (ML) estimation algorithm is given based on several simplistic assumptions on the statistical properties of the adaptive filter tap weights. Several different CDMA environments were simulated, and the performance of the ML estimation algorithm is presented. These results show that even though simplistic assumptions were used in the derivation of the ML estimation algorithm, this receiver structure is applicable to extracting timing information for a direct-sequence CDMA system operating in a near-far environment. >

Target localization is one of the momentous research subjects in wireless sensor networks (WSNs). Several methods have been initiated so far for the aim of target (e.g. sniper) localization using the acoustic signals produced, such as muzzle blast and shock wave in WSNs. One of the preeminent available methods is maximum likelihood estimation (MLE) algorithm, using time difference of arrival (TDOA) of the target signal received at sensor nodes. Although the MLE algorithm is asymptotically optimum and obtains high level of accuracy in comparison with other methods, nevertheless, using MLE has two major challenges. Firstly, the crucial need of this method to begin with a proper initial guess, and secondly, the possibility of not converging to a global minimum. Moreover, employing WSNs constrains the amount of power consumption that is practically possible. In this paper, to overcome the aforementioned obstacles, a two-step algorithm is proposed which in first step, a fast spherical interpolation (SI) method is utilized to prepare an appropriate initial guess for the MLE algorithm. In the second step, a clustering-based network is described to attain less power consumption across the WSN. Furthermore, to increase the probability of convergence, a cooperative incremental cluster-based estimation strategy is proposed. In addition, major issues that can affect the performance of the proposed method are investigated. Simulation results prove the capability of this method and support the claims.

Multi-resolution grid computation is a technique used to speed up source localization with a Maximum Likelihood Estimation (MLE) algorithm. In the case where the source is located midway between grid points, the MLE algorithm may choose an incorrect location, causing following iterations of the search to close in on an area that does not contain the source. To address this issue, we propose a modification to multi-resolution MLE that expands the search area by a small percentage between two consecutive MLE iterations. At the cost of slightly more computation, this modification allows consecutive iterations to accurately locate the target over a larger portion of the field than a standard multi-resolution localization. The localization and computation performance of our approach is compared to both standard multi-resolution and single-resolution MLE algorithms. Tests are performed using seven data sets representing different scenarios of a single radiation source located within an indoor field of detectors. Results show that our method (i) significantly improves the localization accuracy in cases that caused initial grid selection errors in traditional MLE algorithms, (ii) does not have a negative impact on the localization accuracy in other cases, and (iii) requires a negligible increase in computation time relative to the increase in localization accuracy.

A synchronous algorithm applicable for time domain synchronous orthogonal frequency division multiplexing (TDS-OFDM) carrier frequency offset (CFO) is proposed in the thesis. This algorithm is based on pseudonoise (PN) sequence and two kinds of maximum likelihood estimation (MLE) algorithms are employed in frequency offset estimation. The first MLE could be implemented by fast Fourier transform (FFT), which is applicable for the calibration of integral frequency offset. The second MLE algorithm is employed in the estimation of decimal frequency offset. Although the MLE themselves are very common, these two MLE algorithms could compensate the deficiencies of each other, and could obtain satisfying results. The Cramer-Rao (CRO) lower bound of the algorithm is deduced in the thesis so as to evaluate the performance of the algorithm. According to the simulation results, even if under the circumstances of a very low SNR, the estimations on different frequency offsets are close to the CRO lower bound.

It is known that when the maximum likelihood estimator (MLE) algorithm passes a certain point, it produces images that begin to deteriorate. We propose a quantitative criterion with a simple probabilistic interpretation that allows the user to stop the algorithm just before this effect begins. The MLE algorithm searches for the image that has the maximum probability to generate the projection data. The underlying assumption of the algorithm is a Poisson distribution of the data. Therefore, the best image, according to the MLE algorithm, is the one that results in projection means which are as close to the data as possible. It is shown that this goal conflicts with the assumption that the data are Poisson-distributed. We test a statistical hypothesis whereby the projection data could have been generated by the image produced after each iteration. The acceptance or rejection of the hypothesis is based on a parameter that decreases as the images improve and increases as they deteriorate. We show that the best MLE images, which pass the test, result in somewhat lower noise in regions of high activity than the filtered back-projection results and much improved images in low activity regions. The applicability of the proposed stopping rule to other iterative schemes is discussed.

The authors present polynomial-based Newton algorithms for maximum likelihood estimation (MLE) of the parameters of multiple exponential signals in noise. This formulation can be used in the estimation, for example, of the directions of arrival of multiple noise-corrupted narrowband plane waves using uniform linear arrays and the frequencies of multiple noise-corrupted complex sine waves. The algorithms offer rapid convergence and exhibit the computation efficiency associated with the polynomial approach. Compact, closed-form expressions are presented for the gradients and Hessians. Various model assumptions concerning the statistics of the underlying signals are considered. Numerical simulations are presented to demonstrate the algorithms' performance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We propose a new methodology for maximum likelihood estimation in mixtures of non linear mixed effects models (NLMEM). Such mixtures of models include mixtures of distributions, mixtures of structural models and mixtures of residual error models. Since the individual parameters inside the NLMEM are not observed, we propose to combine the EM algorithm usually used for mixtures models when the mixture structure concerns an observed variable, with the Stochastic Approximation EM (SAEM) algorithm, which is known to be suitable for maximum likelihood estimation in NLMEM and also has nice theoretical properties. The main advantage of this hybrid procedure is to avoid a simulation step of unknown group labels required by a full version of SAEM. The resulting MSAEM (Mixture SAEM) algorithm is now implemented in the Monolix software. Several criteria for classification of subjects and estimation of individual parameters are also proposed. Numerical experiments on simulated data show that MSAEM performs well in a general framework of mixtures of NLMEM. Indeed, MSAEM provides an estimator close to the maximum likelihood estimator in very few iterations and is robust with regard to initialization. An application to pharmacokinetic (PK) data demonstrates the potential of the method for practical applications.

We present an EM algorithm for Maximum Likelihood (ML) estimation of the location, structure matrix, skew or drift, and shape parameters of Barndorff-Nielsen's Generalized Hyperbolic distribution, which is the Gaussian Location Scale mixture (or Normal Variance Mean Mixture) with Generalized Inverse Gaussian (GIG) scale mixing distribution. We use the GLSM representation along with the closed form posterior expectations possible with the GIG distribution to derive an EM algorithm for computing ML parameter estimates.

The restricted EM algorithm under inequality restrictions on the parameters

In this paper, we perform numerical and experimental studies on preamble based nonlinear least squares (NLS) and maximum likelihood estimation (MLE) algorithms used for carrier frequency offset estimation in orthogonal frequency division multiplexing (OFDM) communication systems. Further, a reduced complexity data aided nonlinear least squares (NLS) algorithm for carrier frequency offset estimation is proposed. The estimator uses the short symbols in the preamble field for estimating the carrier frequency offset. The proposed NLS estimator is also the maximum likelihood estimator (MLE) when the additive noise is white and Gaussian. The estimator maintains estimation accuracy and offers the widest estimation range. The mean square error performance of the algorithm is compared against other preamble based NLS and MLE algorithms under several practical scenarios. The simulation results are verified using the data obtained from Stevens wireless testbed.

This paper proposes a high level language constituted of only a few primitives and macros for describing recursive maximum likelihood (ML) estimation algorithms. This language is applicable to estimation problems involving linear Gaussian models, or processes taking values in a finite set (only the first case is considered here). The use of high level primitive allows the development of highly modular ML estimation algorithms based on only few numerical blocks. The primitives, which correspond to the combination of different measurements, the extraction of sufficient statistics, and the conversion of the status of a variable from unknown to observed ones, or vice versa, are first defined for linear Gaussian relations specifying mixed deterministic/stochastic information about the system variables. These primitives are used to define other macros, and are illustrated by considering the filtering and smoothing problems for linear descriptor systems, as well as failure detection and isolation. >

This paper proposes a high-level language constituted of a small number of primitives and macros for describing recursive maximum likelihood (ML) estimation algorithms. This language is applicable to estimation problems involving linear Gaussian models or processes taking values in a finite set. The use of high-level primitives allows the development of highly modular ML estimation algorithms based on simple numerical building blocks. The primitives, which correspond to the combination of different measurements, the extraction of sufficient statistics, and the conversion of the status of a variable from unknown to observed, or vice versa, are first defined for linear Gaussian relations specifying mixed deterministic/stochastic information about the system variables. These primitives are used to define other macros and are illustrated by deriving new filtering and smoothing algorithms for linear descriptor systems. The primitives are then extended to finite state processes and used to implement the Viterbi ML state sequence estimator for a hidden Markov model.

A joint Maximum Likelihood (ML) estimation algorithm for the synchronization impairments such as Carrier Frequency Offset (CFO), Sampling Frequency Offset (SFO) and Symbol Timing Error (STE) in single user MIMO-OFDM system is investigated in this work. A received signal model that takes into account the nonlinear effects of CFO, SFO, STE and Channel Impulse Response (CIR) is formulated. Based on the signal model, a joint ML estimation algorithm is proposed. Cramer-Rao Lower Bound (CRLB) for the continuous parameters CFO and SFO is derived for the cases of with and without channel response effects and is used to compare the effect of coupling between different estimated parameters. The performance of the estimation method is studied through numerical simulations.