Iterative Maximum Likelihood Estimation Research Articles

Iterative maximum-likelihood estimation algorithm for clock offset and skew correction in UWB systems assisted by 5G NR multipath

High-precision location services such as unmanned driving, indoor navigation, and mine positioning have been benefiting significantly with the breakthroughs in Fifth-Generation (5G) technology. This paper proposes a collaborative Time of Flight (TOF) measurement framework for 5G New Radio (NR) in Release 17 and Ultra-Wideband (UWB). The method proposed improves the positioning accuracy by tackling the issues of UWB clock offset and clock skew. To this end, we have designed an innovative correction algorithm that effectively utilizes 5G multipath measurement and Timing Error Group (TEG) identifiers. The algorithm employs a low-complexity iterative maximum likelihood estimation (MLE) method to accurately estimate error parameters and calibrate UWB TOF measurement results. Simulation results show that this algorithm significantly enhances positioning precision and robustness. It reduces positioning error by 24 % and 35 % compared to the baseline algorithm in two representative scenarios. These improvements make it suitable for UWB systems in real-time and complex environments.

Robust speckle covariance matrix estimation of sea clutter based on spectral symmetry

Speckle covariance matrix estimation plays an important role in adaptive target detection of maritime radars. Spatial heterogeneity of sea clutter incurs insufficient secondary data in estimation, which degrades detection performance. It is an effective way of estimation improvement to exploit the Doppler spectrum knowledge of sea clutter for structural dimension reduction of the speckle covariance matrix. This paper proposes a speckle covariance matrix estimation method based on the spectral symmetry knowledge of sea clutter, indicating that the spectrum of sea clutter is symmetric with respect to the Doppler offset. First of all, the spectral symmetry of sea clutter is analyzed by using the measured data from several opened databases and the results show that most of the data excluding sea spikes have symmetric Doppler spectra. Secondly, the spectral symmetry constrains the speckle covariance matrix into the Hadamard product of a special rank-one Toeplitz matrix and a real positive definite symmetric matrix. The degrees of freedom are reduced to almost half of that of a Hermitian matrix and thus fewer secondary data are required. Thirdly, a robust iterative maximum likelihood estimator is proposed to estimate the speckle covariance matrix with structural constraint and is free of the clutter texture distribution. The performance of the estimator is verified by the measured data and the results show that it is superior to traditional estimators, particularly in fewer secondary data.

The link between functional response and longevity of Trichogramma evanescens strains indigenous to Türkiye: A comparative assessment of parameters

AbstractA previous comprehensive survey in the Mediterranean and Southeastern regions of Türkiye investigating the natural egg parasitism of lepidopteran maize pests, Sesamia spp, (Lepidoptera: Noctuidae) Ostrinia nubilalis Hbn. and Chilo partellus (Swinhoe; Lepidoptera: Crambidae) by Trichogramma evanescens Westwood (Hymenoptera: Trichogrammatidae) yielded successful establishment of laboratory cultures of six strains molecularly clustering into two main groups. In this study, the functional response and adult longevity of the strains reared and tested on a factitious host, Ephestia kuehniella Zeller (Lepidoptera: Pyralidae) were investigated to provide insights into their potential as candidate biocontrol agents under constant laboratory conditions. The functional response modelling process consisted of two main sequential steps: model selection using polynomial logistic regression and parameter estimation using an iterative maximum likelihood estimation method. The functional response of two strains showed negative linear parameters (type II): HAP068M and HAP268S. Although their attack rate did not differ, the handling time of HAP268S was longer than that of HAP068M. In contrast, four strains had positive linear and negative quadratic parameters (type III) in their functional response: HAP044S, HAP070S, HAP210S, and HAP258M. The strains exhibiting type III functional response did not differ in their handling time, while HAP044S had a higher attack coefficient than HAP070S, HAP210S, and HAP258M. The longevity of both female and male adults significantly differed between strains. More importantly, the females belonging to strains exhibiting type II functional response presented a shorter longevity, compared to those with type III functional response. Males also showed a similar trend in their longevity. This paper discusses the differences in functional response types and estimated parameters of the strains in relation to their relevance for biological control programs and reveals a link between their functional response and longevity as potential reciprocal predictors.

Experimental 3D super-localization with Laguerre–Gaussian modes

Improving three-dimensional (3D) localization precision is of paramount importance for super-resolution imaging. By properly engineering the point spread function (PSF), such as utilizing Laguerre–Gaussian (LG) modes and their superposition, the ultimate limits of 3D localization precision can be enhanced. However, achieving these limits is challenging, as it often involves complicated detection strategies and practical limitations. In this work, we rigorously derive the ultimate 3D localization limits of LG modes and their superposition, specifically rotation modes, in the multi-parameter estimation framework. Our findings reveal that a significant portion of the information required for achieving 3D super-localization of LG modes can be obtained through feasible intensity detection. Moreover, the 3D ultimate precision can be achieved when the azimuthal index l is zero. To provide a proof-of-principle demonstration, we develop an iterative maximum likelihood estimation (MLE) algorithm that converges to the 3D position of a point source, considering the pixelation and detector noise. The experimental implementation exhibits an improvement of up to two-fold in lateral localization precision and up to twenty-fold in axial localization precision when using LG modes compared to Gaussian mode. We also showcase the superior axial localization capability of the rotation mode within the near-focus region, effectively overcoming the limitations encountered by single LG modes. Notably, in the presence of realistic aberration, the algorithm robustly achieves the Cramér-Rao lower bound. Our findings provide valuable insights for evaluating and optimizing the achievable 3D localization precision, which will facilitate the advancements in super-resolution microscopy.

Passive localization by a single moving observer using TOA only with unknown SRI: Observability analysis and algorithm

Passive localization by a single moving observer using Time of Arrival (TOA) only with an unknown Signal Repetition Interval (SRI) is investigated in this paper. Observability analysis is performed first. The observability condition for uniquely determining the emitter position and SRI is derived. The conditional Cramer-Rao Lower Bound (CRLB) is also analyzed. It is found that the ambiguity of the SRI integer of the first TOA does not affect the theoretical estimation precision of the emitter position and SRI. A Reference-Fixed Differential TOA (RFDTOA)-based Iterative Maximum Likelihood Estimator (IMLE) is proposed, which only needs O(M) computational operations. Theoretical analysis and simulation results show that the Mean Square Error (MSE) of the proposed algorithm could attain the CRLB with moderate Gaussian measurement noise.

Joint localization and channel estimation in flow-assisted molecular communication systems

In this paper, we present a joint localization and channel parameter estimation method in the presence of signal-dependent noise and inter-symbol interference for diffusive molecular communication systems. The joint parameter estimation of the nanomachine can provide reliable communication in a generic diffusive molecular communication system. In particular, an iterative maximum likelihood estimation (MLE) approach for jointly estimating locations, flow velocity, and diffusion coefficient is carried out. The Cramer–Rao lower bound on the variance of channel parameters and location is derived. The normalized estimation error is marginally higher for unknown parameters case than that of some known parameters. The individual result (location estimation or channel parameters estimation) outperforms the existing methods.

Estimating the Reliability for the Sequential System of Two Truncated Exponential Distribution

The reliability of sequential system is one of the most important subjects in the current industrial system. In life testing, it has become a great challenge to assess the reliability with consecutive failure time, especially when some units of failure time are deleting. The majority of research in this field in oriented towards illustrating a unique truncated distribution, whereas our study identified two truncated exponential distributions where the failure time units are recorded before time T. In addition, we represent the new algorithm for iterative maximum likelihood (IMLE) to estimate the parameters and the reliability function. After that, a Visual Basic simulation program is successfully created to reflect on the efficiency of the used algorithm. An example and then a randomly data set for three models are chosen to find the values of reliability function. In conclusion, the paper shows that the IMLE estimator

Quantum State Tomography with Conditional Generative Adversarial Networks.

Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two dueling neural networks, a generator and a discriminator, learn multimodal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity, using orders of magnitude fewer iterative steps, and less data, than both accelerated projected-gradient-based and iterative maximum-likelihood estimation. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pretrained on similar quantum states.

An Efficient Distributed Elliptic Positioning for Underground Remote Sensing

Remote surveying of unknown bound geometries, such as the mapping of underground water supplies and tunnels, remains a challenging task. The obstacles and absorption in media make the long-distance telecommunication and localization process inefficient due to mobile sensors’ power limitations. This work develops a new short-range sequential localization approach to reduce the required amount of signal transmission power. The developed algorithm is based on a sequential localization process that can utilize a multitude of randomly distributed wireless sensors while only employing several anchors in the process. Time delay elliptic and frequency range techniques are employed in developing the proposed algebraic closed-form solution. The proposed method is highly effective as it reaches the Cramer–Rao Lower Bound performance level. The estimated positions can act as initializations for the iterative Maximum Likelihood Estimator (MLE) via the Taylor series linearization to acquire even higher positioning accuracy as needed. By reducing the need for high power at the transmit modules in the sensors, the developed localization approach can be used to design a compact sensor with low power consumption and greater longevity that can be utilized to explore unknown bounded geometries for life-long efficient observation mapping.

Forest Height and Underlying Topography Inversion Using Polarimetric SAR Tomography Based on SKP Decomposition and Maximum Likelihood Estimation

The key point of forest height and underlying topography inversion using synthetic aperture radar tomography (TomoSAR) depends on the accurate positioning of the phase centers of different scattering mechanisms. The traditional nonparametric spectrum analysis methods (such as beamforming and Capon) have limited vertical resolution and cannot accurately distinguish closely spaced scatterers. In addition, it is very difficult to accurately estimate the ground or canopy heights with single polarimetric SAR images because there is no guarantee that the vertical profile will generate two clear and separate peaks for all resolution cells. A polarimetric TomoSAR method based on SKP (sum of Kronecker products) decomposition and iterative maximum likelihood estimation is proposed in this paper. On the one hand, the iterative maximum likelihood TomoSAR method has a higher vertical resolution than that of the traditional methods. On the other hand, the separation of the canopy scattering mechanism and the ground scattering mechanism is conducive to the positioning of the phase centers. This method was applied to the inversion of forest height and underlying topography in a tropical forest over the TropiSAR2009 test site in Paracou, French Guiana with six passes of polarimetric SAR images. The inversion accuracy of underlying topography of the proposed method was up to 1.489 m and the inversion accuracy of forest height was up to 1.765 m. Compared with the traditional polarimetric beamforming and polarimetric capon methods, the proposed method greatly improved the inversion accuracy of forest height and underlying topography.

AN EFFICIENT MAXIMUM LIKELIHOOD ESTIMATOR FOR TWO-DIMENSIONAL FRACTIONAL BROWNIAN MOTION

For pattern recognition, natural scenes and medical images are often modeled as two-dimensional fractional Brownian motion (2D FBM), which can be easily described by the Hurst exponent ([Formula: see text], a real number between 0 and 1. The Hurst exponent is directly related to the fractal dimension ([Formula: see text]) by [Formula: see text]–[Formula: see text], and hence it very suitably serves as a characteristic index. Therefore, how to estimate the Hurst exponent effectively and efficiently is very important in pattern recognition. In this paper, a partially iterative algorithm, simply called an iterative maximum likelihood estimator (MLE) for 2D DFBM is first proposed and then a more sufficiently iterative algorithm, simply called an efficient MLE for 2D DFBM, is further proposed via a perfect structure of the log-likelihood function related to the Hurst exponent. Except for theoretical knowledge, two practical algorithms are also correspondingly provided for easy applications. Experimental results show that the MLE for 2D DFBM is effective and workable; its accuracy gets higher as the image size increases, and hence its recognition resolution is much finer to identify small difference among patterns. Furthermore, the efficient MLE is much quicker than the iterative MLE, especially at larger image sizes.

Nonuniform Clustering of Wireless Sensor Network Node Positioning Anomaly Detection and Calibration

In order to detect and correct node localization anomalies in wireless sensor networks, a hierarchical nonuniform clustering algorithm is proposed. This paper designs a centroid iterative maximum likelihood estimation location algorithm based on nonuniformity analysis, selects the nonuniformity analysis algorithm, gives the flowchart of node location algorithm, and simulates the distribution of nodes with MATLAB. Firstly, the algorithm divides the nodes in the network into different network levels according to the number of hops required to reach the sink node. According to the average residual energy of nodes in each layer, the sink node selects the nodes with higher residual energy in each layer of the network as candidate cluster heads and selects a certain number of nodes with lower residual energy as additional candidate cluster heads. Then, at each level, the candidate cluster heads are elected to produce the final cluster heads. Finally, by controlling the communication range between cluster head and cluster members, clusters of different sizes are formed, and clusters at the level closer to the sink node have a smaller scale. By simulating the improved centroid iterative algorithm, the values of the optimal iteration parameters α and η are obtained. Based on the analysis of the positioning errors of the improved centroid iterative algorithm and the maximum likelihood estimation algorithm, the value of the algorithm conversion factor is selected. Aiming at the problem of abnormal nodes that may occur in the process of ranging, a hybrid node location algorithm is further proposed. The algorithm uses the ℓ2, 1 norm to smooth the structured anomalies in the ranging information and realizes accurate positioning while detecting node anomalies. Experimental results show that the algorithm can accurately determine the uniformity of distribution, achieve good positioning effect in complex environment, and detect abnormal nodes well. In this paper, the hybrid node location algorithm is extended to the node location problem in large‐scale scenes, and a good location effect is achieved.

Iterative maximum likelihood estimation of the compound inverse Gaussian clutter parameters

This Letter aims at proposing a cost-effective method for estimating the parameters of the compound inverse Gaussian distributed clutter. Under the assumption of the absence of thermal noise, an iterative maximum likelihood estimator (IMLE) is proposed and compared with existing MLE, the [zlog(z)] estimator, the non-integer order moments estimator and the higher order moment estimator. The results obtained show that the IMLE method outperforms all the other methods and has similar estimation performance than the MLE method but requires lower computational time.

Noise can speed backpropagation learning and deep bidirectional pretraining

We show that the backpropagation algorithm is a special case of the generalized Expectation–Maximization (EM) algorithm for iterative maximum likelihood estimation. We then apply the recent result that carefully chosen noise can speed the average convergence of the EM algorithm as it climbs a hill of probability or log-likelihood. Then injecting such noise can speed the average convergence of the backpropagation algorithm for both the training and pretraining of multilayer neural networks. The beneficial noise adds to the hidden and visible neurons and related parameters. The noise also applies to regularized regression networks. This beneficial noise is just that noise that makes the current signal more probable. We show that such noise also tends to improve classification accuracy. The geometry of the noise-benefit region depends on the probability structure of the neurons in a given layer. The noise-benefit region in noise space lies above the noisy-EM (NEM) hyperplane for classification and involves a hypersphere for regression. Simulations demonstrate these noise benefits using MNIST digit classification. The NEM noise benefits substantially exceed those of simply adding blind noise to the neural network. We further prove that the noise speed-up applies to the deep bidirectional pretraining of neural-network bidirectional associative memories (BAMs) or their functionally equivalent restricted Boltzmann machines. We then show that learning with basic contrastive divergence also reduces to generalized EM for an energy-based network probability. The optimal noise adds to the input visible neurons of a BAM in stacked layers of trained BAMs. Global stability of generalized BAMs guarantees rapid convergence in pretraining where neural signals feed back between contiguous layers. Bipolar coding of inputs further improves pretraining performance.

Localization of a Moving Object With Sensors in Motion by Time Delays and Doppler Shifts

This paper investigates the problem of active localization of a moving object in its initial position and velocity, using time delay only or with Doppler shift measurements acquired by a number of monostatic sensors. Each sensor has non-negligible motion during the observation period, causing it at different positions when it sends and receives the signal, with the separation proportional to the signal travel time in reaching the object and returning back. The object is not at the same position when it reflects the signals from various sensors due to its motion. Both motion effects lead to recursive model equations for time delay and Doppler shift, making the localization problem interesting and challenging. We shall derive the measurement model equations under this scenario, evaluate the Cramer-Rao lower bound (CRLB) of the estimation problem and analyze the proposed models by contrasting with the performance loss when ignoring the object and sensor motion effects. The Maximum Likelihood Estimators (MLEs) are next developed, using the Gauss-Newton or Quasi-Newton iterations. Algebraic solution for the special case of moving object non-moving sensors is derived and analyzed, and it can serve as an effective initialization of the iterative MLEs if sensor motion is present. Both the theoretical analysis and simulation studies corroborate the importance of taking the object and sensor motions into consideration during the observation period, when the relative velocity between the object and sensor is significant compared to the signal propagation speed, such as in an acoustic or underwater environment.

SPICE-ML Algorithm for Direction-of-Arrival Estimation.

Sparse iterative covariance-based estimation, an iterative direction-of-arrival approach based on covariance fitting criterion, can simultaneously estimate the angle and power of incident signal. However, the signal power estimated by sparse iterative covariance-based estimation approach is inaccurate, and the estimation performance is limited to direction grid. To solve the problem above, an algorithm combing the sparse iterative covariance-based estimation approach and maximum likelihood estimation is proposed. The signal power estimated by sparse iterative covariance-based estimation approach is corrected by a new iterative process based on the asymptotically minimum variance criterion. In addition, a refinement procedure is derived by minimizing a maximum likelihood function to overcome the estimation accuracy limitation imposed by direction grid. Simulation results verify the effectiveness of the proposed algorithm. Compared with sparse iterative covariance-based estimation approach, the proposed algorithm can achieve more accurate signal power and improved estimation performance.

Maximum likelihood estimation of high-dimensional Student-[formula omitted] copulas

This paper suggests a simple iterative and robust maximum likelihood estimation method for the parameters of a high-dimensional Student t-distribution that is substantially faster than direct maximum likelihood approaches.

Convex Relaxation Methods for Unified Near-Field and Far-Field TDOA-Based Localization

This paper develops two convex relaxation solutions for the unified localization of a signal source using time difference of arrival measurements, regardless of whether the source is in the near field for coordinate positioning or in the far field for the direction of arrival estimation. The previous study on unified estimation only derived an iterative solution, which is sensitive to initialization. Albeit a coarse initialization was supplied to start the iteration, it may not be sufficient to ensure convergence to the global solution especially when the source is close to the sensors. The proposed solutions come from two novel formulations for optimization, one using the weighted least squares with the modified polar representation of the source position as variable and the other applying fractional programming with the Cartesian coordinate representation instead. Both the optimization problems are solved by first performing semidefinite relaxation and then tightening the relaxed problem by including a set of second-order cone constraints. The two formulations are created from different approaches. Nevertheless, we are able to prove that both the formulations reduce to solving exactly the same mixed semidefinite/second-order cone program and thus establish their equivalence. Furthermore, the proposed solution method is extended to the more practical scenario when sensor position errors are present. The results from both the simulated and real experiments show that the proposed method achieves almost the same performance of the iterative maximum likelihood estimator under ideal initialization.

Homogenizing Estimates of Heritability Among SOLAR-Eclipse, OpenMx, APACE, and FPHI Software Packages in Neuroimaging Data.

Imaging genetic analyses use heritability calculations to measure the fraction of phenotypic variance attributable to additive genetic factors. We tested the agreement between heritability estimates provided by four methods that are used for heritability estimates in neuroimaging traits. SOLAR-Eclipse and OpenMx use iterative maximum likelihood estimation (MLE) methods. Accelerated Permutation inference for ACE (APACE) and fast permutation heritability inference (FPHI), employ fast, non-iterative approximation-based methods. We performed this evaluation in a simulated twin-sibling pedigree and phenotypes and in diffusion tensor imaging (DTI) data from three twin-sibling cohorts, the human connectome project (HCP), netherlands twin register (NTR) and BrainSCALE projects provided as a part of the enhancing neuro imaging genetics analysis (ENIGMA) consortium. We observed that heritability estimate may differ depending on the underlying method and dataset. The heritability estimates from the two MLE approaches provided excellent agreement in both simulated and imaging data. The heritability estimates for two approximation approaches showed reduced heritability estimates in datasets with deviations from data normality. We propose a data homogenization approach (implemented in solar-eclipse; www.solar-eclipse-genetics.org) to improve the convergence of heritability estimates across different methods. The homogenization steps include consistent regression of any nuisance covariates and enforcing normality on the trait data using inverse Gaussian transformation. Under these conditions, the heritability estimates for simulated and DTI phenotypes produced converging heritability estimates regardless of the method. Thus, using these simple suggestions may help new heritability studies to provide outcomes that are comparable regardless of software package.

A THIRD GENERATION TOMOGRAPHY SYSTEM WITH FIFTEEN DETECTORS SIMULATED BY MONTE CARLO METHOD

This paper describes the Monte Carlo simulation, using MCNP4C, of a multichannel third generation tomography system containing a two radioactive sources 192I (316.5 – 468 KeV) and 137Cs (662 KeV), and a set of fifteen NaI(Tl) detectors, with dimensions of 1 inch diameter and 2 inches thick, in fan beam geometry, positioned diametrically opposite. Each detector moves 10 steps of 0,24o, totalizing 150 virtual detectors per projection, and then the system rotate 2 degrees. The Monte Carlo simulation was performed to evaluate the viability of this configuration. For this, a multiphase phantom containing polymethyl methacralate (PMMA ((r @ 1.19 g/cm3)), iron (r @ 7.874 g/cm3), aluminum (r @ 2.6989 g/cm3) and air (r @ 1.20479E-03 g/cm3) was simulated. The simulated number of histories was 1.1E+09 per projection and the tally used were the F8, which gives the pulse height of each detector. The data obtained by the simulation was used to reconstruct the simulated phantom using the statistical iterative Maximum Likelihood Estimation Method Technique (ML-EM) algorithm. Each detector provides a gamma spectrum of the sources, and a pulse height analyzer (PHA) of 10% on the 316.5 KeV and 662 KeV photopeaks was performed. This technique provides two reconstructed images of the simulated phantom. The reconstructed images provided high spatial resolution, and it is supposed that the temporal resolution (spending time for one complete revolution) is about 2.5 hours.