Parameter Estimation Performance Research Articles

Improving GNSS PPP-RTK through global forecast system zenith wet delay augmentation

The precise point positioning real-time kinematic (PPP-RTK) is a high-precision global navigation satellite system (GNSS) positioning technique that combines the advantages of wide-area coverage in precise point positioning (PPP) and of rapid convergence in real-time kinematic (RTK). However, the PPP-RTK convergence is still limited by the precision of slant ionospheric delays and tropospheric zenith wet delay (ZWD), which affects the PPP-RTK network parameters estimation and user positioning performance. The present study aims to construct a PPP-RTK model augmented with a priori ZWD values derived from the global forecast system (GFS) product (a global numerical weather prediction (NWP) model) to improve the PPP-RTK performance. This study gives a priori ZWD values and conversion based on the GFS products, and the full-rank GFS-augmented undifferenced and uncombined (UDUC) PPP-RTK network model is derived. To verify the performance of GFS-augmented UDUC PPP-RTK, a comprehensive evaluation using 10-day GNSS observation data from three different GNSS station networks in the United States (US), Australia, and Europe is conducted. The results show that with the GFS ZWD a priori information, PPP-RTK performance significantly improves at the initial filtering stage, but this advantage gradually decays over time. Based on 10-day positioning results for all user stations, the GFS ZWD-augmented PPP-RTK approach reduces the average convergence time by 46% from 10.0 to 5.4 min, the three-dimensional root-mean-square (3D-RMS) error by 5.7% from 3.5 to 3.3 cm, and the time to first fix (TTFF) value by 35.8% from 6.7 to 4.3 min, all when compared to the traditional PPP-RTK without GFS ZWD constraints.

An Off-Grid Compressive Sensing Algorithm Based on Sparse Bayesian Learning for RFPA Radar

In the application of Compressive Sensing (CS) theory for sidelobe suppression in Random Frequency and Pulse Repetition Interval Agile (RFPA) radar, the off−grid issues affect the performance of target parameter estimation in RFPA radar. Therefore, to address this issue, this paper presents an off−grid CS algorithm named Refinement and Generalized Double Pareto (GDP) distribution based on Sparse Bayesian Learning (RGDP−SBL) for RFPA radar that utilizes a coarse−to−fine grid refinement approach, allowing precise and cost−effective signal recovery while mitigating the impact of off−grid issues on target parameter estimation. To obtain a high-precision signal recovery, especially in scenarios involving closely spaced targets, the RGDP−SBL algorithm makes use of a three−level hierarchical prior model. Furthermore, the RGDP−SBL algorithm efficiently utilizes diagonal elements during the coarse search and exploits the convexity of the grid energy curve during the fine search, therefore significantly reducing computational complexity. Simulation results demonstrate that the RGDP−SBL algorithm significantly improves signal recovery performance while maintaining low computational complexity in multiple scenarios for RFPA radar.

Numerical analysis of solar air collector with trapezoidal ribbed absorber plate of indirect solar dryer: estimation of performance parameters with proposed pitch for better performance

Numerical analysis of solar air collector with trapezoidal ribbed absorber plate of indirect solar dryer: estimation of performance parameters with proposed pitch for better performance

The Mitigation of Mutual Coupling Effects in Multi-Beam Echosounder Calibration under Near-Field Conditions

The advancement of unmanned platforms is driving the miniaturization and cost reduction of the multi-beam echosounder (MBES). In the process of MBES array calibration, the mutual coupling significantly impacts the performance of parameter estimation. We propose a correction method to mitigate the mutual coupling effects in the calibration of MBES acoustic array. Initially, a near-field focused beamforming model is established to assess the influence of mutual coupling. Subsequently, the covariance matrix in the frequency domain is constructed to enhance algorithm efficiency and simplify solution procedures. This construction eliminates the need for a low-pass filtering step after heterodyning through extracting peak values near zero frequency in the signal frequency domain. Meanwhile, the Toeplitz property is leveraged to render the estimation results independent of the mutual coupling matrix. Finally, the mutual coupling coefficients and the direction of arrival (DOA) are joint-estimated and the Cramér–Rao bound is derived. The presented method effectively addresses the engineering challenge of MBES mutual coupling calibration. Additionally, the performance of the proposed method is verified through the measured data in simulation and tank experiments.

A practice-oriented framework for stationary and nonstationary flood frequency analysis

In flood frequency analysis (FFA), choices of distribution and methods can hinder the reproducibility of results. Besides, changes in climate, land use/cover, and water management can induce nonstationarity. Frameworks to select between stationary FFA (S-FFA) and nonstationary FFA (NS-FFA) are lacking, and NS-FFA tools are limited. Therefore, this paper introduces a systematic and software-supported framework enabling repeatable workflows for both S-FFA and NS-FFA. The framework has three modules to a) process flood series for exploratory data analysis (EDA) and NS-FFA model determination (if needed), b) select the S-FFA or NS-FFA approach underpinned by the EDA, and c) perform FFA including model determination, parameter estimation, uncertainty quantification, and model performance assessment. The framework incorporates various distributions, methods, and metrics, and recent advancements in NS-FFA for model determination and uncertainty quantification and allows for the modeller's intervention while ensuring reproducibility. The software is freely available to the public.

Reliability analysis for two populations Nadarajah-Haghighi distribution under Joint progressive type-II censoring

<abstract><p>In order to evaluate the competitive advantages and dependability of two products in a competitive environment, comparative lifespan testing becomes essential. We examine the inference problems that occur when two product lines follow the Nadarajah-Haghighighi distribution in the setting of joint type-II censoring. In the present study, we derived the maximum likelihood estimates for the Nadarajah-Haghighi population parameters. Additionally, a Fisher information matrix was constructed based on these maximum likelihood estimations. Furthermore, Bayesian estimators and their corresponding posterior risks were calculated, considering both gamma and non-informative priors under symmetric and asymmetric loss functions. To assess the performance of the overall parameter estimators, we conducted a Monte Carlo simulation using numerical methods. Lastly, a real data analysis was carried out to validate the accuracy of the models and methods discussed.</p></abstract>

Making Likelihood Calculations Fast: Automatic Differentiation Applied to RooFit

With the growing datasets of current and next-generation HighEnergy and Nuclear Physics (HEP/NP) experiments, statistical analysis has become more computationally demanding. These increasing demands elicit improvements and modernizations in existing statistical analysis software. One way to address these issues is to improve parameter estimation performance and numeric stability using Automatic Differentiation (AD). AD’s computational efficiency and accuracy are superior to the preexisting numerical differentiation techniques, and it offers significant performance gains when calculating the derivatives of functions with a large number of inputs, making it particularly appealing for statistical models with many parameters. For such models, many HEP/NP experiments use RooFit, a toolkit for statistical modeling and fitting that is part of ROOT. In this paper, we report on the effort to support the AD of RooFit likelihood functions. Our approach is to extend RooFit with a tool that generates overheadfree C++ code for a full likelihood function built from RooFit functional models. Gradients are then generated using Clad, a compiler-based source-codetransformation AD tool, using this C++ code. We present our results from applying AD to the entire minimization pipeline and profile likelihood calculations of several RooFit and HistFactory models at the LHC-experiment scale. We show significant reductions in calculation time and memory usage for the minimization of such likelihood functions. We also elaborate on this approach’s current limitations and explain our plans for the future.

Direct Sequence Spread Spectrum Signal’s Parameters Estimation Bounds

The article discusses the problems of direct spread spectrum signal’s parameters estimation and estimation performance analyzing. The achieved estimation variances compared with the corresponding Cramer ‒ Rao bounds as a rule. The proposed approach makes it possible to determine the bounds for signals of various types of modulation and spectral characteristics. The dependences of the Cramer ‒ Rao bounds on the signal-to-noise ratio, the spread spectrum sequence length and the duration of the observation interval are presented.

Chirp Rate Estimation of LFM Signals Based on Second-Order Synchrosqueezing Transform

For the problem of low time-frequency aggregation of the short-time Fourier transform (STFT), which causes the parameter estimation performance degradation of linear frequency modulation (LFM) signals at low signal-to-noise ratio (SNR), second-order synchrosqueezing transform (SSST) is proposed based on the square of STFT amplitude. The time-frequency resolution and energy aggregation are improved by means of squeezing and reassigning the time-frequency spectrum. Meanwhile, in order to decrease the calculation of classical parameter estimation methods, the Hough transform is used for rough estimation, and then the fractional Fourier transform (FRFT) is used for accuracy estimation based on the Renyi entropy. The simulation result shows that higher estimation accuracy is obtained at low SNR, and it has better robustness.

Real-Time Optical Flow Estimation Method Based on Cross-Stage Network

In this paper, a real-time optical flow estimation method based on a cross-stage network is proposed. The proposed model is designed with a network structure with encoders and decoders. The proposed method combines cross-stage network technology with the network structure of FlowNet2 and RAFT to achieve improved parameter number and estimation performance. For real-time optical flow estimation, it is important to maintain performance while reducing the number of parameters in the network. In the proposed method, structural convergence is performed to increase performance while reducing the number of parameters by applying the cross-stage network structure. The proposed model is designed to solve the bottlenecks in model accuracy and complexity by separating feature extraction and flow estimation processes. Flying Chairs, Flying Things 3D, and KITTI datasets were used to evaluate the performance of the proposed model, and the experimental results show superior performance compared to previous traditional methods.

High‐Frequency‐Based Volatility Model with Network Structure

This paper introduces a novel multi‐variate volatility model that can accommodate appropriately defined network structures based on low‐frequency and high‐frequency data. The model offers substantial reductions in the number of unknown parameters and computational complexity. The model formulation, along with iterative multi‐step‐ahead forecasting and targeting parameterization are discussed. Quasi‐likelihood functions for parameter estimation are proposed and their asymptotic properties are established. A series of simulation studies are carried out to assess the performance of parameter estimation in finite samples. Furthermore, a real data analysis demonstrates that the proposed model outperforms the existing volatility models in prediction of future variances of daily return and realized measures.

Joint Polarization and DOA Estimation Based on Improved Maximum Likelihood Estimator and Performance Analysis for Conformal Array

The conformal array can make full use of the aperture, save space, meet the requirements of aerodynamics, and is sensitive to polarization information. It has broad application prospects in military, aerospace, and communication fields. The joint polarization and direction-of-arrival (DOA) estimation based on the conformal array and the theoretical analysis of its parameter estimation performance are the key factors to promote the engineering application of the conformal array. To solve these problems, this paper establishes the wave field signal model of the conformal array. Then, for the case of a single target, the cost function of the maximum likelihood (ML) estimator is rewritten with Rayleigh quotient from a problem of maximizing the ratio of quadratic forms into those of minimizing quadratic forms. On this basis, rapid parameter estimation is achieved with the idea of manifold separation technology (MST). Compared with the modified variable projection (MVP) algorithm, it reduces the computational complexity and improves the parameter estimation performance. Meanwhile, the MST is used to solve the partial derivative of the steering vector. Then, the theoretical performance of ML, the multiple signal classification (MUSIC) estimator and Cramer-Rao bound (CRB) based on the conformal array are derived respectively, which provides theoretical foundation for the engineering application of the conformal array. Finally, the simulation experiment verifies the effectiveness of the proposed method.

Spatio-temporal physics-informed learning: A novel approach to CT perfusion analysis in acute ischemic stroke.

CT perfusion imaging is important in the imaging workup of acute ischemic stroke for evaluating affected cerebral tissue. CT perfusion analysis software produces cerebral perfusion maps from commonly noisy spatio-temporal CT perfusion data. High levels of noise can influence the results of CT perfusion analysis, necessitating software tuning. This work proposes a novel approach for CT perfusion analysis that uses physics-informed learning, an optimization framework that is robust to noise. In particular, we propose SPPINN: Spatio-temporal Perfusion Physics-Informed Neural Network and research spatio-temporal physics-informed learning. SPPINN learns implicit neural representations of contrast attenuation in CT perfusion scans using the spatio-temporal coordinates of the data and employs these representations to estimate a continuous representation of the cerebral perfusion parameters. We validate the approach on simulated data to quantify perfusion parameter estimation performance. Furthermore, we apply the method to in-house patient data and the public Ischemic Stroke Lesion Segmentation 2018 benchmark data to assess the correspondence between the perfusion maps and reference standard infarct core segmentations. Our method achieves accurate perfusion parameter estimates even with high noise levels and differentiates healthy tissue from infarcted tissue. Moreover, SPPINN perfusion maps accurately correspond with reference standard infarct core segmentations. Hence, we show that using spatio-temporal physics-informed learning for cerebral perfusion estimation is accurate, even in noisy CT perfusion data. The code for this work is available at https://github.com/lucasdevries/SPPINN.

Waveform systematics in identifying strongly gravitationally lensed gravitational waves: posterior overlap method

Gravitational lensing has been extensively observed for electromagnetic signals, but not yet for gravitational waves (GWs). Detecting lensed GWs will have many astrophysical and cosmological applications, and becomes more feasible as the sensitivity of the ground-based detectors improves. One of the missing ingredients to robustly identify lensed GWs is to ensure that the statistical tests used are robust under the choice of underlying waveform models. We present the first systematic study of possible waveform systematics in identifying candidates for strongly lensed GW event pairs, focusing on the posterior overlap method. To this end, we compare Bayes factors from all posteriors using different waveforms included in GWTC data releases from the first three observing runs (O1–O3). We find that waveform choice yields a wide spread of Bayes factors in some cases. However, it is likely that no event pairs from O1 to O3 were missed due to waveform choice. We also perform parameter estimation with additional waveforms for interesting cases, to understand the observed differences. We also briefly explore if computing the overlap from different runs for the same event can be a useful metric for waveform systematics or sampler issues, independent of the lensing scenario.

Mathematical modelling and projection of Buruli ulcer transmission dynamics using classical and fractional derivatives: A case study of Cameroon

The goal of this work is to derive and study a new model which traduces the transmission dynamics of the Buruli ulcer (BU), in which we replace mass action incidences with standard incidences, consider latent period, and by using both integer and fractional derivatives. We first present reported data of Buruli in Cameroon between 01/01/2001 and 31/12/2014, and the statistical model that approximates real data as closely as possible, and thus make a forecasting in the next sixteen years. After that, we formulate a Susceptible humans-Exposed humans-Infectious humans-Recovered humans-Susceptible humans; Susceptible vectors-Infectious vectors (SEIRS-SI) type compartmental model of Buruli Ulcer using integer derivative. We compute the basic reproduction number denoted by R0 and prove the asymptotic stability of the Buruli-free equilibrium whenever R0<1. Then, for R0>1, we prove the existence of an unique endemic equilibrium point and its global stability using the general theory of Lyapunov. We perform parameter estimation to calibrate our model using real data from Cameroon, while sensitivity analysis is conducted to determine important parameters in the BU dynamics. From this model calibration, we obtain R0=2.0843 which is greater than one and implies that BU ulcer is endemic in the country. To determine whether if or not the BU admits one or multiple waves, we compute the strength number denoted by A0. We find that A0≈17>0 which means that Bu admits multiple epidemic waves. We then replace integer derivative with the Caputo fractional derivative. Asymptotic stability of equilibrium points are also performed for the fractional model. This follows by the proof of existence and the uniqueness of solutions of the fractional model. We then construct a numerical scheme based on the Adams–Bashforth–Moulton (ABM) Method. Theoretical results are validated from numerical simulations. These last also permits to evaluate the impact of varying fractional order α in the BU dynamics. This permits to conclude that for α<1, reported cases are closer to model prediction.

BayeSED-GALAXIES. I. Performance Test for Simultaneous Photometric Redshift and Stellar Population Parameter Estimation of Galaxies in the CSST Wide-field Multiband Imaging Survey

The forthcoming Chinese Space Station Telescope (CSST) wide-field multiband imaging survey will produce seven-band photometric spectral energy distributions (SEDs) for billions of galaxies. The effective extraction of astronomical information from these massive data sets of SEDs relies on the techniques of SED synthesis (or modeling) and SED analysis (or fitting). We evaluate the performance of the latest version of the BayeSED code combined with SED models with increasing complexity for simultaneously determining the photometric redshifts and stellar population parameters of galaxies in this survey. By using an empirical statistics–based mock galaxy sample without SED modeling errors, we show that the random observational errors in photometries are more important sources of errors than the parameter degeneracies and Bayesian analysis method and tool. By using a Horizon-AGN hydrodynamical simulation–based mock galaxy sample with SED modeling errors about the star formation histories (SFHs) and dust attenuation laws (DALs), the simple typical assumptions lead to significantly worse parameter estimation with CSST photometries only. SED models with more flexible (or complicated) forms of SFH/DAL do not necessarily lead to better estimation of redshift and stellar population parameters. We discuss the selection of the best SED model by means of Bayesian model comparison in different surveys. Our results reveal that Bayesian model comparison with Bayesian evidence may favor SED models with different complexities when using photometries from different surveys. Meanwhile, the SED model with the largest Bayesian evidence tends to give the best performance of parameter estimation, which is clearer for photometries with higher discriminative power.

Parameter Estimation of LFM Signals Based on FOTD-CFRFT under Impulsive Noise

Due to the short duration and high amplitude characteristics of impulsive noise, these parameter estimation methods based on Gaussian assumptions are ineffective in the presence of impulsive noise. To address this issue, a LFM signal parameter estimation method is proposed based on FOTD and CFRFT. Firstly, the mathematical expression of FOTD is presented and its tracking performance is verified. Secondly, the tracked signal is subjected to discrete time CFRFT, and a mathematical optimization model for LFM signal parameter estimation is established on the fractional spectrum characteristic. Finally, a correction method for non-standard SαS distributed noise is proposed, and the performance of parameter estimation under both standard and non-standard SαS distributions are analyzed. The simulation results show that this method not only effectively suppresses the impact of impulsive noise on the fractional spectrum of LFM signal, but also has better parameter estimation accuracy and stability in the low GSNR. The proposed method is particularly effective under the measured noise environment, as it successfully suppresses the impact of impulsive noise and achieves high-precision parameter estimation.

Application of an Output Filtering Method for an Unstable Wheel-Driven Pendulum System Parameter Identification

This research aims to apply an output filtering method to conduct the system parameter identification of an unstable wheel-driven pendulum system. First, the nonlinear dynamic model of the system is established by utilizing the Lagrangian dynamic theorem. Next, the Least-Square (LS) is introduced for system parameter identification formulation. Nevertheless, considering the real scenario, the wheel displacement is acquired from encoders subject to quantization errors. The pitch angle of the pendulum cart is also accompanied by Gaussian noise. Therefore, using numerical differentiation for angular acceleration in the LS estimations directly would induce incorrect state information seriously. To address this practical issue, an output filtering method is considered. The developed parameter identification algorithm could attenuate the influence of the quantization effect as well as noisy data and thus obtain much more accurate parameter identification results. Comparative simulation reveals that the output filtering method has a superior parameter estimation performance than the direct numerical difference method.

Inductive Matrix Completion and Root-MUSIC-Based Channel Estimation for Intelligent Reflecting Surface (IRS)-Aided Hybrid MIMO Systems

This paper studies the estimation of cascaded channels in passive intelligent reflective surface (IRS)-aided multiple-input multiple-output (MIMO) systems employing hybrid precoders and combiners. We propose a low-complexity solution that estimates the channel parameters progressively. The angles of departure (AoDs) and angles of arrival (AoAs) at the transmitter and receiver, respectively, are first estimated using inductive matrix completion (IMC) followed by root-MUSIC-based super-resolution spectrum estimation. Forward-backward spatial smoothing (FBSS) is applied to address the coherence issue. Using the estimated AoAs and AoDs, the training precoders and combiners are then optimized and the angle differences between the AoAs and AoDs at the IRS are estimated using the least squares (LS) method followed by FBSS and the root-MUSIC algorithm. Finally, the composite path gains of the cascaded channel are estimated using on-grid sparse recovery with a small-size dictionary. The simulation results suggest that the proposed estimator can achieve improved channel parameter estimation performance with lower complexity as compared to several recently reported alternatives, thanks to the exploitation of the knowledge of the array responses and low-rankness of the channel using low-complexity algorithms at all the stages.

High precision control of direct-drive permanent magnet linear motor with adaptive friction compensation

To improve the control precision and stability of Direct-Drive Permanent Magnet Linear Motor (DPMLM) with frictional nonlinearity and uncertain disturbances at a low speed, an adaptive robust integral sign error control algorithm based on friction compensation of dual nonlinear observer is proposed in this study. An improved LuGre friction model is established to describe the friction phenomena of the system. The dual nonlinear observer is designed to observe the internal frictional state of the model. A parameter adaptive law is designed to perform parameter estimation of structured uncertainty. Robust integral of the sign of the error (RISE) term is designed to overcome the frictional nonlinear disturbances. The friction nonlinearity and parameter uncertainty are compensated by feedforward compensation. The bounded stability of the proposed controller is proved by Lyapunov stability theory. As suggested by the experimental results, RMSE index decreased by 10.8% and the control precision was improved effectively by the proposed control algorithm at a low speed.