Maximum Likelihood Estimation Algorithm Research Articles

Improvement of OFDM Timing Synchronization Algorithm Based on Cyclic Prefix

Abstract Based on the classical maximum likelihood (ML) estimation algorithm, the performance of the multipath fading channel becomes poor. In order to improve the multipath performance of the maximum likelihood estimation algorithm, the set correlation algorithm is used to calculate the delay point in the multipath channel. Timing estimation is performed using a portion of the cyclic prefix (CP) that is not contaminated by the multipath channel. The simulation results show that the improved maximum likelihood estimation algorithm improves the timing accuracy under multipath channels.

3V-JMLE: a three-valued score matrix-based joint parameter estimation algorithm in computerised adaptive testing

During the development of a Computerised Adaptive Testing (CAT) system, certain inadequacies were found in the popular Joint Maximum Likelihood Estimation (JMLE) algorithm utilised to acquire the ideal binary score matrix. When we attempted to acquire a question-response matrix from a traditional online test item pool system, more than 90% response elements were NA in the matrix. An ideal binary score matrix could scarcely be derived from it. Thus, we proposed a revised algorithm named three-valued JMLE (3V-JMLE) in this paper. When the response could not generate an ideal binary score matrix, we can transform the non-ideal binary matrix into a three-valued score matrix, and the parameters can be estimated simply by using 3V-JMLE. Experiment results show that 3V-JMLE has the same estimation accuracy and computational efficiency as JMLE. In addition, 3V-JMLE has an extensive range of applications and high testing efficiency.

Joint Scan Rate and Emitter Location Estimation Algorithm in SBR System Based on AOA and DTOST Measurements

A joint scan rate and emitter location estimation algorithm in scan-based radar (SBR) system based on the angle-of-arrival (AOA) and the difference time of scan time (DTOST) measurements is proposed in this paper. SBR localization is a kind of passive geolocation technique for stationary pulsed radars. To date, a huge number of passive localization techniques using AOA, DTOST or other measurements for SBR have been developed assuming prior knowledge of the scan rate. However, it is usually hard to obtain the accurate scan velocity in most of practical civilian and military applications. In this paper, by using the linear correlation between AOA and DTOST, the maximum likelihood (ML) estimation algorithm based on linear constraints is given to obtain the scan rate of SBR. And the new AOA information after fusion is acquired on this basis. Then the weighted least square (WLS) method is used for SBR localization and the Cramer-Rao lower bound (CRLB) is derived for SBR location estimation. A detailed analysis of scan rate and emitter location estimation process is given and the effectiveness of the proposed localization algorithm is illustrated with computer simulations.

Single-Anchor Positioning: Multipath Processing With Non-Coherent Directional Measurements

High-accuracy indoor radio positioning can be achieved by using (ultra) wideband (UWB) radio signals. Multiple fixed anchor nodes are needed to compute the position or alternatively, specular multipath components (SMCs) extracted from radio signals can be exploited. In this work, we study a multipath-based, single-anchor positioning system that acquires directional measurements non-coherently. These non-coherent measurements can be obtained, e.g., from a single-chain mm-wave transceiver with analog beam steering or from a low-complexity ultra-wideband transceiver with switched directional antennas. The directional antennas support the separation of SMCs and the suppression of the undesired diffuse multipath component (DMC) with the benefit that the required signal bandwidth can be drastically reduced. The paper analyzes the Cramer-Rao lower bound (CRLB) on the position estimation error to gain insight in the influence of the system design parameters as well as the impact of the DMC on the position error. The CRLB is compared between the non-coherent antenna setup, a conventional array with coherent processing, and a single-antenna setup. A maximum-likelihood position estimation algorithm is formulated. Its performance is evaluated with synthetically generated data as well as with UWB measurements. We show that the accuracy and robustness are significantly improved due to the processing of angular information. Analyzing the measured data for a line-of-sight link, the median error decreases from 22 down to 7 cm, the measurements better than 20 cm increase from 46 to 95 %, and outliers above 50 cm reduce from 12 to 0%.

Model Error Modelling using a Stochastic Embedding approach with Gaussian Mixture Models for FIR systems

In this paper a Maximum Likelihood estimation algorithm for error-model modelling using a stochastic embedding approach is developed. The error-model distribution is approximated by a finite Gaussian mixture. An Expectation-Maximization based algorithm is proposed to estimate the nominal model and the distribution of the parameters of the error-model by using the data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

Parameter Estimation of the Lognormal-Rician Channel Model Using Saddlepoint Approximation

In this article, the challenges of effective channel estimation for the lognormal-Rician turbulence model are addressed. We present a novel maximum likelihood estimation algorithm involving a saddlepoint approximation (SAP) method to estimate the shaping parameters of the lognormal-Rician distribution. An additional parameter k needs to be estimated in addition to r and σ z 2 under the SAP representation. The accuracy of the proposed estimator is investigated by using the mean square error and normalized mean square error. The simulated results show that the proposed estimator exhibits satisfactory performance over a wide range of turbulence conditions, and it can be easily applied to both noiseless and noisy situations. The effect of the estimated shaping parameters errors on the bit error rate (BER) for the on-off key (OOK) modulation is also investigated; it is shown that the BER performance derived with the SAP estimator becomes closer to the system performance with perfect shaping parameters as r increases. In particular, we present a qualitative comparison between the proposed SAP estimator and other algorithms available in the literature.

Truncated Hawkes point process modeling: System theory and system identification

Point processes have a growing list of applications, including, neuroscience, high frequency finance, genomics and more recently, streaming data. Perhaps the most used parameterized dynamic (aka self-exciting i.e. history dependent) model is the (linear) Hawkes model. But the Hawkes model assumes the infinite past is available and has to be truncated for empirical use. Here we develop, for the first time, the system theory for the truncated Hawkes process. This includes: necessary and sufficient conditions for stability; a Wold decomposition; and an asymptotic spectrum. We then discuss various parameterizations (Exponential, Laguerre, Binomial-autoregression) and their properties. Using the Laguerre parameterization, we next develop a new continuous time multiplicative EM algorithm for maximum likelihood estimation and develop some of its properties. It turns out that the multiplicative EM algorithm does not guarantee stability and so we develop a modified multiplicative EM that does. We also derive, for the first time for self-exciting processes, the Cramer–Rao bound as well as a BIC model selection criterion. We illustrate with simulations, comparing the Laguerre approach to the popular binomial-autoregression and then with an application to neural data recorded from a cat’s brain under visual stimuli.

An improved Kalman filter positioning method in NLOS environment

In the precision positioning system, NLOS (Non Line of Sight) propagation and clock synchronization error caused by multiple base stations are the main reasons for reducing the reliability of communication and positioning accuracy. So, in the NLOS environment, it has an important role to eliminate the clock synchronization problem in the positioning system. In order to solve this problem, this paper proposes an improved Kalman filter localization method NLOS-K (Non Line of Sight-Kalman filter). First, the maximum likelihood estimation algorithm is used to iterate. Then, the Kalman filter algorithm is implemented and the Kalman gain matrix is redefined. The clock drift is compensated so that the clock between the master and slave base stations remains synchronized. The experimental results show that in the non-line-of-sight environment, compared with other algorithms, the positioning accuracy error of the improved algorithm is about 5 cm, and the accuracy compared with other algorithms is 97%. In addition, the influence of bandwidth and spectral density on the method is analyzed, and the accuracy and stability of positioning are improved as a whole.

A mixture of linear-linear regression models for a linear-circular regression

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.

Determination of Hypocentre and Seismic Velocity Structure in Guntur Volcano Using Seismic Data from 2010 to 2014

DOI: 10.17014/ijog.6.3.279-289Guntur Volcano was in a dormant state even though its seismicity had increased on April, 2013 and August, 2013. In this study, determination of hypocentre and seismic velocity structure was conducted using seismic data from 2010 to 2014 as recorded by a seismic station of the Centre for Volcanology and Geological Hazard Mitigation of Indonesia (CVGHM). Volcano-Tectonic (VT) earthquakes were identified and carefully picked for P-and S-wave arrival times. More than 600 events of VT earthquakes from 2010 - 2014 were located using maximum likelihood estimation algorithm. The initial 1-D seismic velocity was calculated using Velest method in order to get the initial velocity as the input for the tomographic inversion. The results show distribution of VT hypocentres were clustered in three regions, namely Guntur Volcano, Kamojang geothermal area, and Darajat geothermal area. At the Guntur Volcano region, the VT events were located mostly at the northern part of the crater with the depth of hypocentre ranges from 0 - 4 km. The distribution of the VT events made alignment from the southwest to the northeast with the depth of hypocentre mostly ranges from 0 - 2 km at Kamojang region. Meanwhile, at Darajat geothermal area, the VT events were located at the depth of 0 - 2 km and made alignment from the southeast to the northwest. The low velocity zone associated with hot material or fluids was located at the depth of 5 km beneath the Guntur Crater. The location of VT earthquakes at the depth of 0 - 4 km beneath Guntur Crater was coincided with the area with high Vp and Vs anomalies. The low velocity zones were also found at Kamojang Crater and Cipanas hotspring area. It was predicted that the low velocity zone at the Kamojang Crater was related to a high temperature of the vapour system, whereas the reservoir of water was preferred to be dominated at the Cipanas hotspring.

Comparison of penalized logistic regression models for rare event case

The occurrence rate of the event of interest might be quite small (rare) in some cases, although sample size is large enough for Binary Logistic Regression (LR) model. In studies where the sample size is not large enough, the parameters to be estimated might be biased because of rare event case. Parameter estimations of LR model are usually obtained using Newton–Raphson (NR) algorithm for Maximum Likelihood Estimation (MLE). It is known that these estimations are usually biased in small samples but asymptotically unbiased. On the other hand, initial parameter values are sensitive for parameter estimation in NR for MLE. Our aim of the study is to present an approach on parameter estimation bias using inverse conditional distributions based on distribution assumption giving true parameter values and to compare this approach on different penalized LR methods. With this aim, LR, Firth LR, FLIC and FLAC methods were compared in terms of parameter estimation bias, predicted probability bias and Root Mean Squared Error (RMSE) for different sample sizes, event and correlation rates conducting a detailed Monte Carlo simulation study. Findings suggest that FLIC method should be preferred in rare event and small sample cases.

Research on Two Types of Estimation Algorithms in Carrier Tracking Loop

This paper analyzes two estimation algorithms in the carrier loop, i.e. maximum likelihood estimation (MLE) and modern filtering based on Bayesian recursion. The limitations of the MLE algorithm are pointed out by establishing the MLE model. In addition, several modern filters based on Bayesian recursion are analyzed. In this process, the article draws two inferences affecting high dynamics and low signal-to-noise ratio (SNR) carrier tracking from two aspects of state equation and measurement equation. Thus, the optimal algorithm using unscented Kalman filter (UKF) is proposed by the inferences mentioned. at the end, simulation results demonstrate the combined strong tracking algorithm has advantages in case of high dynamic and low SNR.

Pyvine: The Python Package for Regular Vine Copula Modeling, Sampling and Testing

Regular vine copula provides rich models for dependence structure modeling. It combines vine structures and families of bivariate copulas to construct a number of multivariate distributions that can model a wide range dependence patterns with different tail dependence for different pairs. Two special cases of regular vine copulas, C-vine and D-vine copulas, have been extensively investigated in the literature. We propose the Python package, pyvine, for modeling, sampling and testing a more generalized regular vine copula (R-vine for short). R-vine modeling algorithm searches for the R-vine structure which maximizes the vine tree dependence in a sequential way. The maximum likelihood estimation algorithm takes the sequential estimations as initial values and uses L-BFGS-B algorithm for the likelihood value optimization. R-vine sampling algorithm traverses all edges of the vine structure from the last tree in a recursive way and generates the marginal samples on each edge according to some nested conditions. Goodness-of-fit testing algorithm first generates Rosenblatt’s transformed data $${\varvec{E}}$$ and then tests the hypothesis $$H_0^*: {\varvec{E}} \sim C_{\perp }$$ by using Anderson–Darling statistic, where $$C_{\perp }$$ is the independence copula. Bootstrap method is used to compute an adjusted p-value of the empirical distribution of replications of Anderson–Darling statistic. The computing of related functions of copulas such as cumulative distribution functions, H-functions and inverse H-functions often meets with the problem of overflow. We solve this problem by reinvestigating the following six families of bivariate copulas: Normal, Student t, Clayton, Gumbel, Frank and Joe’s copulas. Approximations of the above related functions of copulas are given when the overflow occurs in the computation. All these are implemented in a subpackage bvcopula, in which subroutines are written in Fortran and wrapped into Python and, hence, good performance is guaranteed.

An indoor location algorithm based on Kalman filter fusion of ultra-wide band and inertial measurement unit

Indoor positioning technology has been widely used in today’s life, but due to the influence of multipath effect, the positioning signal is attenuated or even interrupted seriously, resulting in obvious reduction or even failure of positioning accuracy. Therefore, the emerging multi-sensor joint positioning has become the general trend of the development of positioning technology, in which Ultra-Wide Band (UWB) and Inertial Measurement Unit (IMU) have their own features in positioning and navigation. So this paper combines the advantages of UWB and IMU to achieve accurate positioning in complex environment. Firstly, the signal transmission law in complex environment is obtained by distinguishing Line of Sight (LOS) from NLOS (Non Line of Sight) environment. Secondly, the maximum likelihood estimation algorithm is used to eliminate the influence of NLOS on the transmitted signal, and then the extended Kalman filter information fusion strategy is used. The ranging information of UWB and the angle information of IMU are fused to realize the accurate positioning of UWB in complex environment. Finally, the experimental results show that the performance of the joint positioning proposed in this paper is obviously better than that of a single sensor compared with single UWB and single IMU positioning. It provides more solutions for accurate indoor positioning of multi-sensor fusion.

F-SAEM: A fast stochastic approximation of the EM algorithm for nonlinear mixed effects models

The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to perform such sampling, but this method is known to converge slowly for medium dimensional problems, or when the joint structure of the distributions to sample is spatially heterogeneous. The main contribution consists of an independent Metropolis–Hastings (MH) algorithm based on a multidimensional Gaussian proposal that takes into account the joint conditional distribution of the random effects and does not require any tuning. Indeed, this distribution is automatically obtained thanks to a Laplace approximation of the incomplete data model. Such approximation is shown to be equivalent to linearizing the structural model in the case of continuous data. Numerical experiments based on simulated and real data illustrate the performance of the proposed methods. For fitting nonlinear mixed effects models, the suggested MH algorithm is efficiently combined with a stochastic approximation version of the EM algorithm for maximum likelihood estimation of the global parameters.

Leveraging nonlinear dynamic models to predict progression of neuroimaging biomarkers.

Using biomarkers to model disease course effectively and make early prediction is a challenging but critical path to improving diagnostic accuracy and designing preventive trials for neurological disorders. Leveraging the domain knowledge that certain neuroimaging biomarkers may reflect the disease pathology, we propose a model inspired by the neural mass model from cognitive neuroscience to jointly model nonlinear dynamic trajectories of the biomarkers. Under a nonlinear mixed-effects model framework, we introduce subject- and biomarker-specific random inflection points to characterize the critical time of underlying disease progression as reflected in the biomarkers. A latent liability score is shared across biomarkers to pool information. Our model allows assessing how the underlying disease progression will affect the trajectories of the biomarkers, and, thus, is potentially useful for individual disease management or preventive therapeutics. We propose an EM algorithm for maximum likelihood estimation, where in the E step, a normal approximation is used to facilitate numerical integration. We perform extensive simulation studies and apply the method to analyze data from a large multisite natural history study of Huntington's Disease (HD). The results show that some neuroimaging biomarker inflection points are early signs of the HD onset. Finally, we develop an online tool to provide the individual prediction of the biomarker trajectories given the medical history and baseline measurements.

Design of OFDM Joint Synchronization Algorithm Based on Cyclic Prefix

By studying the Maximum Likelihood (ML) algorithm and applying it to Orthogonal Frequency Division Multiplexing (OFDM) system, we analyze its performance. OFDM system has obvious advantages over other wireless communication systems, but it also has disadvantages, such as being sensitive to synchronization errors. The ML algorithm can solve this shortcoming of OFDM system. ML algorithm uses the redundant information carried by the cyclic prefix in OFDM code element. At the same time, ML algorithm calculates its maximum likelihood estimation algorithm to complete the code element timing synchronization and carrier frequency synchronization. Compared with other synchronization algorithms, ML algorithm can complete initial capture and synchronous tracking in one step, so it is widely used in OFDM systems. In this paper, we build a traditional OFDM system and apply the ML algorithm to OFDM synchronization simulation. By changing the design of relevant parameters, we describe the ML algorithm in detail and obtain the same results as the theory.

A note on identifiability and maximum likelihood estimation for a heterogeneous capture-recapture model

This article discusses identifiability and maximum likelihood estimation for a closed population capture-recapture model with heterogeneity in capture probabilities. The model assumes that the individual capture probabilities arise from a discrete distribution over the interval Considering the complete likelihood, without applying any conditioning, we prove that identifiability holds under a restriction on the number of support points of the mixing distribution. Under this identifiability assumption, we present a simple closed-form iterative algorithm for maximum likelihood estimation. Interval estimation is carried by a bootstrap resampling procedure. The proposed methods are illustrated on a literature real data set and a simulation study is carried to assess the frequentist merits of different population size estimators.

Optimal Uncalibrated RSS Indoor Positioning and Optimal Reference Node Placement Using Cramér-Rao Lower Bound

In this paper we propose a global positioning algorithm of multiple assets based on Received Signal Strength (RSS) measurements that takes into account the gain uncertainties of each hardware transceiver involved in the system, as well as the uncertainties on the Log-Distance Path Loss (LDPL) parameters. Such a statistical model is established and its Maximum Likelihood Estimator (MLE) is given with the analytic expression of the Cramér-Rao Lower Bound (CRLB). Typical values of those uncertainties are given considering whether calibration is done in production, in situ, or if hardware is used uncalibrated, in order to know what is the expected accuracy in function of the calibration setup. Results are tested by numerical simulations and confronted to real measurements in different room configurations, showing that the theoretical bound can be reached by the proposed MLE algorithm.

Pricing S&P500 barrier put option of American type under Heston–CIR model with regime-switching

In this paper, we consider the regime-switching Heston–CIR model, where the parameters of the volatility process are modulated by a Hidden Markov chain and the unobserved regimes. Then, we calibrate the parameters of the volatility and interest rate processes by the expectation maximization (EM) and maximum likelihood estimation (MLE) algorithms, respectively. Next, we use the least square Monte-Carlo (LSM) algorithm to determine the S&P500 American barrier put option under the Heston–CIR model. Finally, by the binomial tree method as a benchmark, we provide some numerical experiments to illustrate the accuracy of the achieved results.