Iterative Maximum Likelihood Research Articles

Comparing Pixel- and Object-Based Approaches in Effectively Classifying Wetland-Dominated Landscapes.

Wetland ecosystems straddle both terrestrial and aquatic habitats, performing many ecological functions directly and indirectly benefitting humans. However, global wetland losses are substantial. Satellite remote sensing and classification informs wise wetland management and monitoring. Both pixel- and object-based classification approaches using parametric and non-parametric algorithms may be effectively used in describing wetland structure and habitat, but which approach should one select? We conducted both pixel- and object-based image analyses (OBIA) using parametric (Iterative Self-Organizing Data Analysis Technique, ISODATA, and maximum likelihood, ML) and non-parametric (random forest, RF) approaches in the Barguzin Valley, a large wetland (~500 km2) in the Lake Baikal, Russia, drainage basin. Four Quickbird multispectral bands plus various spatial and spectral metrics (e.g., texture, Non-Differentiated Vegetation Index, slope, aspect, etc.) were analyzed using field-based regions of interest sampled to characterize an initial 18 ISODATA-based classes. Parsimoniously using a three-layer stack (Quickbird band 3, water ratio index (WRI), and mean texture) in the analyses resulted in the highest accuracy, 87.9% with pixel-based RF, followed by OBIA RF (segmentation scale 5, 84.6% overall accuracy), followed by pixel-based ML (83.9% overall accuracy). Increasing the predictors from three to five by adding Quickbird bands 2 and 4 decreased the pixel-based overall accuracy while increasing the OBIA RF accuracy to 90.4%. However, McNemar’s chi-square test confirmed no statistically significant difference in overall accuracy among the classifiers (pixel-based ML, RF, or object-based RF) for either the three- or five-layer analyses. Although potentially useful in some circumstances, the OBIA approach requires substantial resources and user input (such as segmentation scale selection—which was found to substantially affect overall accuracy). Hence, we conclude that pixel-based RF approaches are likely satisfactory for classifying wetland-dominated landscapes.

Bimodality of Directional Distributions in Ocean Wave Spectra: A Comparison of Data-Adaptive Estimation Techniques

AbstractThe properties of directional distributions in ocean wave spectra are studied, with an emphasis on sea states with bimodal directional distributions in the high-frequency tails of single-peaked wave systems. A peak-splitting tendency has been a challenge in the interpretation of results from some data-adaptive estimation methods. After a survey of the theory, mathematical and numerical explanations are presented regarding domains of uni- and bimodality for symmetric Burg and Shannon maximum entropy methods. The study finds that both the Burg and Shannon maximum entropy methods have a tendency to split peaks, and that the domains of uni- and bimodality for these two methods depend on the Fourier coefficients input into the algorithms. Comparisons of data-adaptive methods based on data collected near the Ekofisk oil field in the North Sea and from nonlinear wave simulations are presented. The maximum likelihood (ML) method, the iterative maximum likelihood (IML) method, and the Burg and Shannon maximum entropy methods are applied. A large fraction of the directional wave spectra from Ekofisk shows bimodal features for distributions above the spectral peak for all of the abovementioned methods. In particular, strong similarity in bimodal features between the iterative maximum likelihood and the Burg maximum entropy methods are found. In general, the bimodality is consistent with previous observations, and it seems to be associated with wave and spectral development owing to nonlinear wave–wave interactions rather than being associated with the peak-splitting tendency in the estimates from any of the algorithms. The bimodal directional distributions were sometimes persistent and sometimes formed or decayed within the order of hours.

Propagation of monopole source excited acoustic waves in a cylindrical high-density polyethylene pipeline.

Acoustic wave propagation (up to 50 kHz) within a water-filled high-density polyethylene (HDPE) pipeline is studied using laboratory experiments and theoretical analysis. Experiments were carried out in a 15 m length of cylindrical HDPE pipeline using acoustic transducers to acquire signals uniformly spaced along the axis of the pipe. By proposing the use of the iterative quadratic maximum likelihood algorithm to this experimental configuration, wavenumbers, attenuations, and mode amplitudes could be accurately extracted from the measurement data. To allow comparisons with theoretical analysis, dispersion curves of the wavenumbers, attenuations, and acoustic power characteristics of the axisymmetric and nonaxisymmetric modes are predicted by extending an existing waveguide model. The model extensions included the introduction of a monopole acoustic source into the water medium so that amplitude variations with respect to individual modes and frequencies could be investigated in detail. In addition, stiffness coefficients of HDPE material are carefully used to account for viscoelastic effects. The comparisons between the theoretical predictions and experimental results demonstrate a very good match and are a validation of the theoretical model.

Analysis of the maximum likelihood channel estimator for OFDM systems in the presence of unknown interference

This paper is a theoretical analysis of the maximum likelihood (ML) channel estimator for orthogonal frequency-division multiplexing (OFDM) systems in the presence of unknown interference. The following theoretical results are presented. Firstly, the uniqueness of the ML solution for practical applications, i.e., when thermal noise is present, is analytically demonstrated when the number of transmitted OFDM symbols is strictly greater than one. The ML solution is then derived from the iterative conditional ML (CML) algorithm. Secondly, it is shown that the channel estimate can be described as an algebraic function whose inputs are the initial value and the means and variances of the received samples. Thirdly, it is theoretically demonstrated that the channel estimator is not biased. The second and the third results are obtained by employing oblique projection theory. Furthermore, these results are confirmed by numerical results.

Improving the reliability and availability of railway track switching by analysing historical failure data and introducing functionally redundant subsystems.

Track switches are safety critical assets that not only provide flexibility to rail networks but also present single points of failure. Switch failures within dense-traffic passenger rail systems cause a disproportionate level of delay. Subsystem redundancy is one of a number of approaches, which can be used to ensure an appropriate safety integrity and/or operational reliability level, successfully adopted by, for example, the aeronautical and nuclear industries. This paper models the adoption of a functional redundancy approach to the functional subsystems of traditional railway track switching arrangements in order to evaluate the potential increase in the reliability and availability of switches. The paper makes three main contributions. First, 2P-Weibull failure distributions for each functional subsystem of each common category of points operating equipment are established using a timeline and iterative maximum likelihood estimation approach, based on almost 40,000 sampled failure events over 74,800 years of continuous operation. Second, these results are used as baselines in a reliability block diagram approach to model engineering fault tolerance, through subsystem redundancy, into existing switching systems. Third, the reliability block diagrams are used with a Monte-Carlo simulation approach in order to model the availability of redundantly engineered track switches over expected asset lifetimes. Results show a significant improvement in the reliability and availability of switches; unscheduled downtime reduces by an order of magnitude across all powered switch types, whilst significant increases in the whole-system reliability are demonstrated. Hence, switch designs utilising a functional redundancy approach are well worth further investigation. However, it is also established that as equipment failures are engineered out, switch reliability/availability can be seen to plateau as the dominant contributor to unreliability becomes human error.

Robust Calibration of Radio Interferometers in Non-Gaussian Environment

The development of new phased array systems in radio astronomy, as the low frequency array (LOFAR) and the square kilometre array (SKA), formed of a large number of small and flexible elementary antennas, has led to significant challenges. Among them, model calibration is a crucial step in order to provide accurate and thus meaningful images and requires the estimation of all the perturbation effects introduced along the signal propagation path, for a specific source direction and antenna position. Usually, it is common to perform model calibration using the a priori knowledge regarding a small number of known strong calibrator sources but under the assumption of Gaussianity of the noise. Nevertheless, observations in the context of radio astronomy are known to be affected by the presence of outliers which are due to several causes, e.g., weak non-calibrator sources or man made radio frequency interferences. Consequently, the classical Gaussian noise assumption is violated leading to severe degradation in performances. In order to take into account the outlier effects, we assume that the noise follows a spherically invariant random distribution. Based on this modeling, a robust calibration algorithm is presented in this paper. More precisely, this new scheme is based on the design of an iterative relaxed concentrated maximum likelihood estimation procedure which allows to obtain closed-form expressions for the unknown parameters with a reasonable computational cost. This is of importance as the number of estimated parameters depends on the number of antenna elements, which is large for the new generation of radio interferometers. Numerical simulations reveal that the proposed algorithm outperforms the state-of-the-art calibration techniques.

Experimental infrared point-source detection using an iterative generalized likelihood ratio test algorithm.

This work documents the performance of a recently proposed generalized likelihood ratio test (GLRT) algorithm in detecting thermal point-source targets against a sky background. A calibrated source is placed above the horizon at various ranges and then imaged using a mid-wave infrared camera. The proposed algorithm combines a so-called "shrinkage" estimator of the background covariance matrix and an iterative maximum likelihood estimator of the point-source parameters to produce the GLRT statistic. It is clearly shown that the proposed approach results in better detection performance than either standard energy detection or previous implementations of the GLRT detector.

Mitigating Multipath Bias Using a Dual-Polarization Antenna: Theoretical Performance, Algorithm Design, and Simulation.

It is well known that multipath effect remains a dominant error source that affects the positioning accuracy of Global Navigation Satellite System (GNSS) receivers. Significant efforts have been made by researchers and receiver manufacturers to mitigate multipath error in the past decades. Recently, a multipath mitigation technique using dual-polarization antennas has become a research hotspot for it provides another degree of freedom to distinguish the line-of-sight (LOS) signal from the LOS and multipath composite signal without extensively increasing the complexity of the receiver. Numbers of multipath mitigation techniques using dual-polarization antennas have been proposed and all of them report performance improvement over the single-polarization methods. However, due to the unpredictability of multipath, multipath mitigation techniques based on dual-polarization are not always effective while few studies discuss the condition under which the multipath mitigation using a dual-polarization antenna can outperform that using a single-polarization antenna, which is a fundamental question for dual-polarization multipath mitigation (DPMM) and the design of multipath mitigation algorithms. In this paper we analyze the characteristics of the signal received by a dual-polarization antenna and use the maximum likelihood estimation (MLE) to assess the theoretical performance of DPMM in different received signal cases. Based on the assessment we answer this fundamental question and find the dual-polarization antenna’s capability in mitigating short delay multipath—the most challenging one among all types of multipath for the majority of the multipath mitigation techniques. Considering these effective conditions, we propose a dual-polarization sequential iterative maximum likelihood estimation (DP-SIMLE) algorithm for DPMM. The simulation results verify our theory and show superior performance of the proposed DP-SIMLE algorithm over the traditional one using only an RHCP antenna.

Maximum Likelihood Estimation for Multiple Camera Target Tracking on Grassmann Tangent Subspace.

In this paper, we introduce a likelihood model for tracking the location of object in multiple view systems. Our proposed model transforms conventional nonlinear Euclidean estimation model to an estimation model based on the manifold tangent subspace. In this paper, we show that by decomposition of input noise into two parts and description of model by exponential map, real observations in the Euclidean geometry can be transformed to the manifold tangent subspace. Moreover, by obtained tangent subspace likelihood function, we propose two iterative and noniterative maximum likelihood estimation approaches which numerical results show their good performance.

Analyzing pathogen suppressiveness in bioassays with natural soils using integrative maximum likelihood methods in R.

The potential of soils to naturally suppress inherent plant pathogens is an important ecosystem function. Usually, pathogen infection assays are used for estimating the suppressive potential of soils. In natural soils, however, co-occurring pathogens might simultaneously infect plants complicating the estimation of a focal pathogen’s infection rate (initial slope of the infection-curve) as a measure of soil suppressiveness. Here, we present a method in R correcting for these unwanted effects by developing a two pathogen mono-molecular infection model. We fit the two pathogen mono-molecular infection model to data by using an integrative approach combining a numerical simulation of the model with an iterative maximum likelihood fit. We show that in presence of co-occurring pathogens using uncorrected data leads to a critical under- or overestimation of soil suppressiveness measures. In contrast, our new approach enables to precisely estimate soil suppressiveness measures such as plant infection rate and plant resistance time. Our method allows a correction of measured infection parameters that is necessary in case different pathogens are present. Moreover, our model can be (1) adapted to use other models such as the logistic or the Gompertz model; and (2) it could be extended by a facilitation parameter if infections in plants increase the susceptibility to new infections. We propose our method to be particularly useful for exploring soil suppressiveness of natural soils from different sites (e.g., in biodiversity experiments).

Iterative Maximum Likelihood and Outlier-robust Bipercentile Estimation of Parameters of Compound-Gaussian Clutter With Inverse Gaussian Texture

Compound-Gaussian model with the inverse Gaussian texture (IG–CG) is recognized to be one of the best models to characterize high-resolution sea clutter at low grazing angles. The model parameters are often estimated by the second- and fourth-order amplitude sample moments, which are of low precision and easily interfered by outliers of high power such as returns of ships and reefs and sea spikes. In this letter, an iterative maximum likelihood (ML) estimator and an outlier-robust bipercentile estimator are proposed and are compared with the moment-based estimator. The experimental results show that the iterative ML estimator is better in performance than the moment-based estimator when samples are without outliers and the bipercentile estimator behaves better when samples contain a small number of outliers.

Non‐stationary additive noise modelling in direction‐of‐arrival estimation

The authors report a numerical investigation of a non-stationary noise model, based on the generalised autoregressive conditional heteroscedasticity time series, to perform a direction-of-arrival (DOA) estimation. In many of the studies reported to date, DOA estimation algorithms have been proposed in the presence of stationary noise. The performance of the previous algorithms such as conventional maximum likelihood (CML) and iterative maximum likelihood (IML) is reduced in many practical applications such as sonar where the noise shows a non-stationary behaviour. In this study, a modified IML estimation algorithm is proposed to include a non-stationary noise model. Underwater DOA estimation is studied as an example of DOA estimation in a non-stationary noise environment. To validate the noise model, the experimental data, measured by a single hydrophone 27 m underwater, is applied. The results indicate that the proposed algorithm is able to provide a significant improvement compared with CML and IML in such environments.

Stepwise iterative maximum likelihood clustering approach.

BackgroundBiological/genetic data is a complex mix of various forms or topologies which makes it quite difficult to analyze. An abundance of such data in this modern era requires the development of sophisticated statistical methods to analyze it in a reasonable amount of time. In many biological/genetic analyses, such as genome-wide association study (GWAS) analysis or multi-omics data analysis, it is required to cluster the plethora of data into sub-categories to understand the subtypes of populations, cancers or any other diseases. Traditionally, the k-means clustering algorithm is a dominant clustering method. This is due to its simplicity and reasonable level of accuracy. Many other clustering methods, including support vector clustering, have been developed in the past, but do not perform well with the biological data, either due to computational reasons or failure to identify clusters.ResultsThe proposed SIML clustering algorithm has been tested on microarray datasets and SNP datasets. It has been compared with a number of clustering algorithms. On MLL datasets, SIML achieved highest clustering accuracy and rand score on 4/9 cases; similarly on SRBCT dataset, it got for 3/5 cases; on ALL subtype it got highest clustering accuracy for 5/7 cases and highest rand score for 4/7 cases. In addition, SIML overall clustering accuracy on a 3 cluster problem using SNP data were 97.3, 94.7 and 100 %, respectively, for each of the clusters.ConclusionsIn this paper, considering the nature of biological data, we proposed a maximum likelihood clustering approach using a stepwise iterative procedure. The advantage of this proposed method is that it not only uses the distance information, but also incorporate variance information for clustering. This method is able to cluster when data appeared in overlapping and complex forms. The experimental results illustrate its performance and usefulness over other clustering methods. A Matlab package of this method (SIML) is provided at the web-link http://www.riken.jp/en/research/labs/ims/med_sci_math/.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1184-5) contains supplementary material, which is available to authorized users.

Iterative Frequency Domain Maximum Likelihood OFDM Carrier Frequency Offset Estimation

In this paper we propose an iterative frequency domain maximum likelihood carrier frequency offset estimation algorithm. It exploits only the available pilot grid that is used for channel state information estimation without any additional pilot overhead requirements. Maximum likelihood estimation in frequency domain using non-sequential pilot symbols significantly improves estimation quality. The solution is in closed form and it does not require computationally demanding exhaustive search. The proposed algorithm provides high resolution estimates of carrier frequency offset with moderate computational complexity. We also derive a Cramer---Rao lower bound that corresponds to a general scenario of arbitrarily spaced pilot symbols.

Integrating spatial and biomass planning for the United States

Biomass is low-carbon energy and has tremendous potential as an alternative to fossil fuels. However, the significant role of biomass in future low-carbon energy portfolio depends heavily on its consumption. The paper presents a first attempt to examine the spatial-temporal patterns of biomass consumption in the United States (US), using a novel method-spatial Seemingly Unrelated Regression (SUR) model, in order to strengthen the link between energy planning and spatial planning. In order to obtain the robust parameters of spatial SUR models and estimate the parameters efficiently, an iterative maximum likelihood method, which takes full advantage of the stationary characteristic of maximum likelihood estimation, has been developed. The robust parameters of models can help draw a proper inference for biomass consumption. Then the spatial-temporal patterns of biomass consumption in the US at the state level are investigated using the spatial SUR models with the estimation method developed and data covering the period of 2000–2012. Results show that there are spatial dependences among biomass consumption. The presence of spatial dependence in biomass consumption has informative implications for making sustainable biomass polices. It suggests new efforts to adding a cross-state dimension to state-level energy policy and coordinating some elements of energy policy across states are still needed. In addition, results consistent with classic economic theory further proves the correctness of applying the spatial SUR models to investigate the spatial-temporal patterns of biomass consumption.

MIMO radar target localization and performance evaluation under SIRP clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cramér–Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.

Do pulsar radio fluxes violate the inverse-square law?

Singleton et al (2009) have argued that the flux of pulsars measured at 1400 MHz shows an apparent violation of the inverse-square law with distance ($r$), and it is consistent with $1/r$ scaling. They deduced this from the fact that the convergence error obtained in reconstructing the luminosity function of pulsars using an iterative maximum likelihood procedure is about $10^5$ times larger for a distance exponent of two (corresponding to the inverse-square law) compared to an exponent of one. When we applied the same technique to this pulsar dataset with two different values for the trial luminosity function in the zeroth iteration, we find that neither of them can reproduce a value of $10^5$ for the ratio of the convergence error between these distance exponents. We then reconstruct the differential pulsar luminosity function using Lynden-Bell's $C^{-}$ method after positing both an inverse-linear and an inverse-square scalings with distance. We show this method cannot help in discerning between the two exponents. Finally, when we tried to estimate the power law exponent with a Bayesian regression procedure, we do not get a best-fit value of one for the distance exponent. The model residuals obtained from our fitting procedure are larger for the inverse-linear law compared to the inverse-square law. Moreover, the observed pulsar flux cannot be parameterized only by power-law functions of distance, period, and period derivative. Therefore, we conclude from our analysis using multiple methods that there is no evidence that the pulsar radio flux at 1400 MHz violates the inverse-square law.

Image Reconstruction Techniques for Compton Scattering Based Imaging: An Overview [Compton Based Image Reconstruction Approaches

In recent years, more and more detector systems utilizing Compton scattering effect to detect gamma rays have been developed due to their potential for improved image sensitivity. However, the standard non-electron-tracking Compton based detectors can restrict the origin of the photon only to a cone. Therefore, one key challenge in the data analysis process is the reconstruction of the source distribution, from the measured data. Several different techniques have been developed, ranging from basic back-projections, iterative maximum likelihood and Bayesian techniques, as well as stochastic and analytic methods. This paper reviews the existing image reconstruction techniques developed for Compton imaging, their basic approach, their application areas, their restrictions and difficulties. Keywords: Compton scattering, image reconstruction techniques, inverse problem, medical imaging, nuclear medicine, regularization methods.

Single-platform passive emitter localization with bearing and Doppler-shift measurements using pseudolinear estimation techniques

The maximum-likelihood (ML) estimator for single-platform Doppler-bearing emitter localization does not admit a closed-form solution and must be implemented using computationally demanding iterative numerical search algorithms. The iterative ML solution is vulnerable to convergence problems due to the nonconvex nature of the ML cost function and the threshold effect. To alleviate these problems, this paper presents new closed-form Doppler-bearing emitter localization algorithms in the 2D-plane based on pseudolinear estimation techniques; namely, the pseudolinear estimator (PLE), the bias-compensated PLE and the weighted instrumental variable (WIV) estimator. The bias-compensated PLE aims to remove the instantaneous estimation bias inherent in the PLE. The WIV estimator incorporates the bias-compensated PLE to achieve an asymptotically unbiased estimate of the emitter position. The proposed WIV estimator is proved to be asymptotically efficient for sufficiently small measurement noise. Through simulation examples its performance is shown to be almost identical to that of the ML estimator, exhibiting small bias and approaching the Cramér–Rao lower bound at moderate noise levels.

A Bayesian Approach for Integrated Raindrop Size Distribution (DSD) Retrieval on an X-Band Dual-Polarization Radar Network

AbstractA raindrop size distribution (DSD) retrieval method for a weather radar network consisting of several X-band dual-polarization radars is proposed. An iterative maximum likelihood (ML) estimator for DSD retrieval in a single radar was developed in the authors’ previous work, and the proposed algorithm in this paper extends the single-radar retrieval to radar-networked retrieval, where ML solutions in each single-radar node are integrated based on a Bayesian scheme in order to reduce estimation errors and to enhance accuracy. Statistical evaluations of the proposed algorithm were carried out using numerical simulations. The results with eight radar nodes showed that the bias and standard errors are −0.05 and 0.09 in log(Nw); and Nw (mm−1 m−3) and 0.04 and 0.09 in D0 (mm) in an environment with fluctuations in dual-polarization radar measurements (normal distributions with standard deviations of 0.8 dBZ, 0.2 dB, and 1.5° in ZHm, ZDRm, and ΦDPm, respectively). Further error analyses indicated that the estimation accuracy depended on the number of radar nodes, the ranges of varying μ, the raindrop axis ratio model, and the system bias errors in dual-polarization radar measurements.