Delay Model Research Articles

Positioning Technology Without Ground Control Points for Spaceborne Synthetic Aperture Radar Images Using Rational Polynomial Coefficient Model Considering Atmospheric Delay

This study addresses the issue of atmospheric delay correction for the rational polynomial coefficient (RPC) model associated with spaceborne synthetic aperture radar (SAR) imagery under conditions lacking ephemeris data, proposing a novel approach to enhance the geometric positioning accuracy of RPC models. A satellite position inversion method based on the vector-autonomous intersection technique was developed, incorporating ionospheric delay and neutral atmospheric delay models to derive atmospheric delay errors. Additionally, an RPC model reconstruction approach, which integrates atmospheric correction, is proposed. Validation experiments using GF-3 satellite imagery demonstrated that the atmospheric delay values obtained by this method differed by only 0.0001 m from those derived using the traditional ephemeris-based approach, a negligible difference. The method also exhibited high robustness in long-strip imagery. The reconstructed RPC parameters improved image-space accuracy by 18–44% and object-space accuracy by 19–32%. The results indicate that this approach can fully replace traditional ephemeris-based methods for atmospheric delay extraction under ephemeris-free conditions, significantly enhancing the geometric positioning accuracy of SAR imagery RPC models, with substantial application value and development potential.

Analytical and Computational Investigations of Stochastic Functional Integral Equations: Solution Existence and Euler–Karhunen–Loève Simulation

This paper presents a comprehensive investigation into the solution existence of stochastic functional integral equations within real separable Banach spaces, emphasizing the establishment of sufficient conditions. Leveraging advanced mathematical tools including probability measures of noncompactness and Petryshyn’s fixed-point theorem adapted for stochastic processes, a robust analytical framework is developed. Additionally, this paper introduces the Euler–Karhunen–Loève method, which utilizes the Karhunen–Loève expansion to represent stochastic processes, particularly suited for handling continuous-time processes with an infinite number of random variables. By conducting thorough analysis and computational simulations, which also involve implementing the Euler–Karhunen–Loève method, this paper effectively highlights the practical relevance of the proposed methodology. Two specific instances, namely, the Delay Cox–Ingersoll–Ross process and modified Black–Scholes with proportional delay model, are utilized as illustrative examples to underscore the effectiveness of this approach in tackling real-world challenges encountered in the realms of finance and stochastic dynamics.

Deep Neural Networks for Refining Vertical Modeling of Global Tropospheric Delay

AbstractKinematic airborne platforms are becoming increasingly vital for Earth observation. They highlight the critical need for accurate tropospheric delay corrections across varying altitudes, especially as most existing models are limited to Earth's surface. Although analytical functions have been used to model vertical reductions in tropospheric delays, they struggle to capture the intricate vertical variations of atmospheric state. In response, we introduce a novel approach that utilizes deep neural networks (DNN) to reconstruct global three‐dimensional zenith hydrostatic delay (ZHD) and zenith wet delays (ZWD) derived from numerical weather models (NWM). Our method reconstructs NWM‐derived ZHD and ZWD globally up to 14 km above the Earth's surface, with average precision levels of 0.4 and 0.8 mm, respectively. Compared to the analytical third‐order exponential model, the DNN approach demonstrates substantial improvement with global average root‐mean‐square reductions of 63% for ZHD and 36% for ZWD.

Comparative analysis of eco-epidemic model with disease in prey and gestation delay in predator: implications for population dynamics

Gestation is a very significant phenomenon in predator-prey dynamics. It influences the future predation rates and the growth of species. Gestation is the period of development of an embryo or fetus in a female mammal, from conception to birth. It plays a critical role in population dynamics and reproductive strategies in ecological studies. This article presents a comparative study of eco-epidemic models with and without time delay terms. The model takes into account a prey-predator system, dividing the prey population into susceptible and infected compartments. This article incorporates a time delay into the predator growth term to represent gestation delay. This article investigates the impact of time delay as a gestation delay on the model’s dynamics and compares the results with those of the non-delay model. Our analytical and numerical studies reveal that the time delay stabilizes the model, exhibits switching behaviour, and leads to chaotic behaviour through periodic doubling. Moreover, the gestation delay destabilizes the model by causing Hopf bifurcations to emerge at multiple points. Our findings indicate that the delay model has richer dynamics than the non-delay model. The numerical simulations using MATLAB, along with the DDE-biftool and Matcont packages, illustrate the bifurcation analysis, phase portraits, and time series plots for both models. Our findings highlight the significant effects of gestation delay on the dynamics of eco-epidemic models.

A movement-based delay model for signalised alternative intersections

Analytical models play a crucial role in evaluating Alternative Intersections and Interchanges (AIIs) and developing their signal plans. A key application is comparing O-D movement delays to measure the operational benefits of AIIs over conventional intersections. However, existing models often fail to account for time-varying arrival patterns and the segregation of O-D movements within the same lane group. This paper addresses these gaps by proposing new appropriate delay models that incorporate the Queue Accumulation Polygon (QAP) concept for uniform delay calculations. The QAP enables realistic modelling of arrival patterns and segregates delays by queues formed from different movements. Other delay terms are also developed to reflect AII operating conditions. Validation using various AIIs and traffic scenarios shows the proposed models align with field observations and movement-specific microsimulation results, outperforming widely used U.S. analytical models. These improvements enhance the accuracy of delay estimation and support better AII design and analysis.

Compartment model of strategy-dependent time delays in replicator dynamics.

Real-world processes often exhibit temporal separation between actions and reactions - a characteristic frequently ignored in many modelling frameworks. Adding temporal aspects, like time delays, introduces a higher complexity of problems and leads to models that are challenging to analyse and computationally expensive to solve. In this work, we propose an intermediate solution to resolve the issue in the framework of evolutionary game theory. Our compartment-based model includes time delays while remaining relatively simple and straightforward to analyse. We show that this model yields qualitatively comparable results with models incorporating explicit delays. Particularly, we focus on the case of delays between parents' interaction and an offspring joining the population, with the magnitude of the delay depending on the parents' strategy. We analyse Stag-Hunt, Snowdrift, and the Prisoner's Dilemma game and show that strategy-dependent delays are detrimental to affected strategies. Additionally, we present how including delays may change the effective games played in the population, subsequently emphasising the importance of considering the studied systems' temporal aspects to model them accurately.

An enhanced tropospheric fusion model based on China’s National continuously operating reference stations

ABSTRACT This study introduces a multi-source data fusion model of the tropospheric delay over China and uses GNSS data, meteorological data, and Global Pressure and Temperature 2 wet (GPT2w) model data to derive the model coefficients. Fifty-one nationwide GNSS stations were selected to evaluate the accuracy of the fusion model through a detailed analysis of the model performance based on factors including the overall accuracy, seasonal accuracy, and impact of the station location. The results show that the multi-source data fusion model integrates the advantages of various individual models and thus has a higher accuracy and stability despite the occurrence of a certain degree of decline in accuracy in the individual models under certain conditions. A comparison with previous models developed using only GNSS data demonstrates that this fusion model improves the overall accuracy by 17.7%.

Bifurcation and stability analysis of within host HIV dynamics with multiple infections and intracellular delay.

Human immunodeficiency virus (HIV) manifests multiple infections in CD4+ T cells, by binding its envelope proteins to CD4 receptors. Understanding these biological processes is crucial for effective interventions against HIV/AIDS. Here, we propose a mathematical model that accounts for the multiple infections of CD4+ T cells and an intracellular delay in the dynamics of HIV infection. We study the model system and establish the conditions under which the disease-free equilibrium point and the endemic equilibrium point are locally and globally asymptotically stable. We further provide the conditions under which these equilibrium points undergo forward or backward transcritical bifurcations for the autonomous model and Hopf bifurcation for both the delay model and autonomous models. Our simulation results show that an increase in the rate of multiple infections of CD4+ T cells stabilizes the endemic equilibrium point through Hopf bifurcation. However, in the presence of an intracellular delay, the model system evinces three types of stability scenarios at the endemic equilibrium point-instability switch, stability switch, and stability invariance and is demonstrated using bi-parameter diagrams. One of the novel aspects of this study is exhibiting all these interesting nonlinear dynamical results within a single model incorporating a single time delay.

Dynamic switching of transmission modes hydroacoustic communication MAC protocols

In recent years, the hydroacoustic communication MAC (Medium Access Control) protocol has attracted wide attention. Hydroacoustic communication networks suffer from issues such as long propagation delays and rapid dynamic changes in network load, which prevent the maximization of network performance through the use of a single transmission mode. In this paper, we propose a Dynamic Switching Transmission MAC protocol called the DSTM-MAC protocol. Firstly, the protocol realizes the design of dynamic switching transmission mode by adapting to changes in network load, introduces a more accurate model for total system delay, and computes parameters such as the switching threshold L and the optimal fixed contention window. Secondly, it carries out parameter design for different transmission modes and realizes dynamic concurrent transmission based on these modes, ultimately achieving the goal of maximizing network performance improvement. Finally, experiments demonstrate that the DSTM-MAC protocol surpasses the traditional DCF protocol in terms of end-to-end delay and system throughput.

Modified ionosphere delay fitting model with atmosphere uncertainty grids for wide-area real-time positioning

ABSTRACT Precise atmospheric delay and proper constraints are critical for achieving rapid convergence and accurate positioning. However, ionospheric delay models over wide-area face challenges due to significant spatial and temporal variations, impacting real-time correction precision. To address this, we propose a novel ionospheric slant delay fitting model that adaptively selects the optimal reference path within coverage areas, describing differences between the reference propagation path and others through trigonometric functions. With ten coefficients, the model surpasses legacy polynomial fitting accuracy. Using a 166-station, 150 km-spaced European networks for atmospheric delays and 113 external stations for validation, our model achieves a 59.6% standard deviation reduction compared to the legacy model. Compared to the legacy ionospheric delay model, new model positioning convergence time (≤10 cm) accelerates by 37.7% and 34.2% for horizontal and vertical components, respectively. Meanwhile, two 2° × 2° uncertainty grids, generated from tropospheric and ionospheric delay fitting residuals at 15-min intervals, accurately describe fitting performance in all coverage areas with a maximum of 475 points. Adaptive constraints from uncertainty grids can reduce convergence time by 42.1% and 28.8% for horizontal and vertical, surpassing three-time modeling sigma solutions. These findings underscore the effectiveness of our novel ionospheric delay fitting model and the associated uncertainty grids in providing precise information across extensive regions with minimal coefficients.

ZWDX: a global zenith wet delay forecasting model using XGBoost

Tropospheric delays play a crucial role for Global Navigation Satellite Systems (GNSS). They are a major error source in GNSS positioning and, at the same time, also a variable of interest in GNSS meteorology. Regardless of whether the delay shall be eliminated or inverted to atmospheric parameters, and no matter how this is done, it is of utmost importance to accurately determine tropospheric delays. In this study, we present a global zenith wet delay (ZWD) model, called ZWDX, that offers accurate spatial and temporal ZWD predictions at any desired location on Earth. ZWDX is based on the XGBoost algorithm and uses ZWDs measured at over 19,000 GNSS stations as reference. The inputs of ZWDX are the geographical location, observation time, and specific humidity at nine atmospheric pressure levels. For our study, we train the model on the years 2010 to 2021 and then test it for the year 2022. While ZWDX is trained to predict ZWD values based on specific humidity values from the ERA5 reanalysis, we show that it also delivers good predictions when applied to HRES specific humidity forecasts, making it suitable for (short-term) ZWD forecasting. The ZWDX model predictions are evaluated at 2500 globally distributed, spatio-temporally independent GNSS stations, with forecasting horizons ranging from 0 h to 48 h, and achieve root mean squared errors (RMSE) between 10.1 mm and 16.2 mm. To independently evaluate ZWDX’s performance and to demonstrate its potential for a real-world downstream task, we use its predictions as a-priori values for a precise point positioning (PPP) analysis and compare the results with those obtained using ZWD values from VMF1 or VMF3. We find that the highest accuracy and fastest convergence are indeed achieved with ZWDX.Graphical

A modified spatiotemporal nonlocal thermoelasticity theory with higher-order phase delays for a viscoelastic micropolar medium exposed to short-pulse laser excitation

At the microscale and nanoscale, materials exhibit size-dependent behaviors that classical models cannot capture. This analysis introduces a size-dependent higher-order thermoelastic heat conduction model, incorporating spatial and temporal nonlocal effects in a micropolar visco-thermoelastic medium subjected to laser pulse heat flux. The two-phase delay model, featuring higher-order temporal derivatives, captures the complex interactions among mechanical, thermal, and viscous properties in materials where size effects are significant. By including phase lag, the model effectively addresses non-Fourier heat conduction in short-duration laser pulse scenarios. It accurately predicts temperature distribution, stress response, and microrotation effects in microscale and nanoscale materials. The study visually represents how factors such as micropolarity, higher-order effects, phase delay, nonlocal index, and viscosity influence the size-dependent mechanical behavior of the half-space structure. The numerical results highlight the importance of size-dependent phenomena in nanostructures, revealing deviations from classical predictions due to nonlocal interactions. Overall, the proposed spatiotemporal nonlocal homogenization model serves as a valuable tool for analyzing the complex mechanical and thermal characteristics of nanomaterials.

"It's his cheerfulness that gives me hope": A qualitative analysis of access to pediatric cancer care in Northern Tanzania.

Pediatric cancer is a significant and growing burden in low- and middle-income countries. The objective of this project was to describe the factors influencing access to pediatric cancer care in Northern Tanzania using the Three Delays Model. This was a cross-sectional qualitative study conducted between June and August 2023 at Kilimanjaro Christian Medical Centre (KCMC). Using purposive sampling methods, caregivers of children obtaining pediatric cancer care at KCMC were approached for participation in in-depth interviews (IDIs) and a demographic survey. All IDIs were facilitated in Swahili by a bilingual research coordinator. Analysis utilized inductive and deductive coding approaches to identify dominant themes and sub-themes impacting access to pediatric oncology care. Data collection concluded once saturation was achieved at 13 IDIs, defined as the absence of new codes after three consecutive interviews. Participants reported significant financial barriers to accessing pediatric cancer care along the entire care continuum. In the first delay, themes included waiting for symptoms to resolve and the identification of initial symptoms. The most substantial delays occurred in delay 2, including health infrastructure at mid-level facilities, misdiagnoses, the referral system, travel, and traditional medicine. Participants did not describe delays after arrival to KCMC and rather offered perspective on their child's cancer diagnosis, their concerns while obtaining care, and their hopes for the future. Financial support provided by the Tanzanian government was the only facilitator noted by participants. We suggest targeted interventions including 1) empowerment of CHWs and local traditional healers to advocate for earlier care seeking behavior, 2) implementation of clinical structures and training at intermediary medical centers aimed at earlier referral to a treatment facility, 3) incorporation of support and education initiatives for families of children with a cancer diagnosis. Lastly, national health plans should include pediatric cancer care.

Timeliness of lung cancer care and area-level determinants in Victoria: A Bayesian spatio-temporal analysis.

It has been reported that the timeliness of lung cancer care varies significantly across different regions. According to the Victorian Lung Cancer Registry (VLCR) report, the timeliness of lung cancer care in Victoria has changed over time. Therefore, we aimed to quantify the extent of these spatial inequalities over time and to identify area-level determinants contributing to these changes. The study analysed lung cancer cases reported to the VLCR between 2011 and 2022. Bayesian spatio-temporal Conditional Autoregressive (CAR) models were fitted, incorporating spatial random effects, temporal random effects, as well as spatio-temporal interactions. The best-performing model was selected using the Deviance Information Criterion (DIC). For the final best-fit model, the adjusted Relative Risks (aRR) and their 95% Credible Interval (CrI) were reported. Over half (51.24%) of lung cancer patients experienced treatment delays, while approximately one-third (30.98%) encountered diagnostic delays. Moderate spatio-temporal variations were observed in both delayed diagnosis and treatment. In the final best-fit model for treatment delay, an increase in the percentage of smokers was significantly associated with a higher risk of treatment delay (RR = 2.13, 95% CrI: 1.13, 4.20). Identifying high-risk areas provides useful information for policymakers, helping in the reduction of delays in lung cancer diagnosis and treatment. This study has revealed spatio-temporal inequalities in diagnostic and treatment delays, providing valuable insights for identifying areas that should be prioritized to ensure timely care for lung cancer.

RT-SVM: Channel modeling and analysis for indoor terahertz communication scenarios

Considering the increasing demands for wireless communication networks and information system applications, the wireless sector must meet the pressing requirement for high-speed technological advances. The terahertz (THz) frequency band, spanning 0.3 to 10 THz, is of significant interest in current technological innovations and academic research in telecommunications. The THz frequency band has unique properties, including high time-resolving power (femtosecond) and low absorption. This paper proposes a THz propagation ultra-wideband (UWB) channel model and coding scheme for indoor environments starting from 0.3 THz. First, we investigated the propagation path loss model by considering the effects of transmitter dimensions, molecular absorption, and attenuation as functions of frequency and distance. We developed models for power propagation delay, multiple input multiple output (MIMO) systems and discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM) response channels. Using the standard Saleh-Valenzuela model combined with Ray-tracing (RT-SVM), we studied the transmission of THz signals in indoor scenarios. We introduced physical parameters relevant to the THz indoor channel, such as line-of-sight (LoS) path loss, power distributions, temporal and spatial properties, and associations between THz multipath properties. These parameters were integrated with the RT-SVM channel model and applied to THz indoor communication. Numerical simulations demonstrate that the proposed hybrid channel model enhances THz system performance and outperforms traditional statistical and geometric-based stochastic channel models in terms of temporal and spatial dimensions, contributing to frequency loss variations.

Networked control systems induced delay modeling and stability analysis using Markov-regime-switching GARCH model

This article focuses on the stability analysis of networked control systems (NCSs). It is well-known that network-induced delays pose many control challenges due to their non-uniform and multifractal nature. With the growing integration of communication networks in control systems, the impact of time-varying and random delays on system performance becomes critical. Hence, it is essential to study their impact on the system’s stability. There are several network-induced delay modeling methods, resulting in constant, random, and probabilistic random delays, which provide the most realistic representation according to recent studies. This article introduces a new network-induced delay modeling method based on the Markov-regime-switching generalized autoregressive conditional heteroskedasticity (MRS-GARCH) process, which captures the intricate temporal dependence of random network delays. The resulting model offers a more accurate depiction of delay volatility behavior, accommodating sudden shifts between volatility regimes. Simulation results demonstrate that MRS GARCH-type modeling enables a more realistic representation of delay dynamics. We also conduct a stability analysis of NCSs modeled with the proposed method using linear matrix inequalities LMIs criteria derived from the Lyapunov-Krasovskii theorem. The simulation results show less conservatism than conventional models and provide a larger maximum allowable upper delay bound MAUDB.

Efficient slicing scheme and cache optimization strategy for structured dependent tasks in intelligent transportation scenarios

The challenges posed by structured large-scale tasks to resource-sensitive intelligent transportation systems have been acknowledged, particularly regarding the need to reduce delay and energy consumption during the caching and offloading processes. To address these challenges and improve the quality of service for vehicular users, a cloud–edge-end collaboration caching strategy (CACCSC) based on structured task content awareness was proposed in this paper. The dependencies among task fragments were modeled through fuzzy judgment criteria. In addition, a system delay model, an energy consumption model, and an edge server load balancing model were developed, along with a multi-objective optimization model that integrates system delay, energy consumption, and edge server load balancing variance. To solve this multi-objective optimization problem, an adaptive multi-objective optimization algorithm (MDE-NSGA-III) was developed, which combines an enhanced version of the Differential Evolution algorithm with improvements to the NSGA-III algorithm. Finally, it has been demonstrated through simulation experiments that when the number of users in the system reaches 35, the system delay, energy consumption, and load balancing variance of the MDE-NSGA-III optimization scheme proposed in this paper are 6.1%, 6.6%, and 25% lower than those of the NSGA-III scheme, 15.8%, 10%, and 41.7% lower than those of the NSGA-II scheme, and 62.7%, 20.7%, and 8.3% lower than those of the PeEA scheme.

Compact Analysis of the Necessity of Padé Approximation for Delayed Continuous-time Models in LQR, H-Infinity and Root Locus Control Strategies

This paper presents a comprehensive analysis of the need for the Padé approximation for continuous-time models with delays, focusing on its critical role in addressing the control challenges posed by time delays. Time delays, often referred to as dead times, transport delays or time lags, are inherent in a wide range of industrial and engineering processes. These delays introduce phase shifts that degrade control performance by reducing control bandwidth and threatening the stability of closed-loop systems. Accurate modelling and compensation of these delays is essential to maintain system stability and ensure effective control. This paper highlights the difficulties that arise when using advanced control techniques such as root locus (RL), linear quadratic regulator (LQR) and H-infinity (H_∞) control in systems with delays. Representing delays in exponential form leads to an infinite number of state problems, complicating the design and analysis of controllers in such systems. To address these challenges, the Padé approximation is proposed as an effective method for approximating time delays with rational polynomials of appropriate order. This approach allows for more accurate simulation, system analysis and controller design, thereby mitigating the problems caused by delays. The paper also provides a detailed comparative analysis between the Padé approximation and Taylor polynomials, demonstrating the superiority of the former in achieving accurate delay modelling and control performance. The results show that the use of Padé approximation not only improves the accuracy of system models, but also improves the robustness and stability of control strategies such as RL, LQR, and H_∞. These results highlight the importance of the Padé approximation as a valuable tool in the design of delay-affected control systems, offering significant advantages for both theoretical and practical applications.

Predictors of Delays in Emergency Obstetric Care among Reproductive Age Women at Tubah Health District, Cameroon

Background: Delay to timely healthcare contributes to high maternal mortality and morbidity in developing countries. The “three delay model” has been used extensively to investigate factors relating to maternal mortality. In developing countries, 1 in 16 dies, compared to one in 2800 in the developed countries due to pregnancy-related complications. This study aimed to determine the predictors of delays in Emergency Obstetric Care to contribute to a reduction in maternal and infant mortality. Methods: This was a community-based cross-sectional study. The participants were women of reproductive age selected from four villages of the Tubah Health District. Sampling was done using a multistage sampling technique in which reproductive-age women at Tubah Health District were administered a structured questionnaire. Delay was considered at three levels which included: delay in deciding to seek care (first delay), delay in reaching the health facility (second delay) and delay in receiving care at the level of the Health facility (third delay). Univariate and multivariate regressions were used to determine the predictors of delay at each level of delay. Results: Out of 420 participants, 226(53.8%) delayed in deciding to go to the Health facility and had: Maternal age (p= 0.002), Household income (p= 0.003), decision maker for obstetric care (p= 0.042) and antenatal care (p= 0.022) as significant predictors. For the second delay, 124 (29.5%) were delayed, maternal age (p=0.022) being the main predictor. 246 participants (58.6%) were delayed in receiving care at the level of the health facility and the significant predictor was low maternal age (p=0.018). Conclusion: Predictors of the first delay were: maternal age, household income, decision maker for obstetric care, and antenatal care. The main predictor of the second delay was young maternal age; for the third delay, the significant predictor was still maternal age. Young maternal was found to be a major predictor at all levels of delay.

Comparison of Click and Level-Specific CE Chirp-Stimulated Auditory Brainstem Responses in Adults with Hearing Loss.

The Claus Elberling Chirp (CE-Chirp) stimulus used in the auditory brainstem responses (ABRs) was developed to compensate for the cochlear wave delay. As a version of broadband CE-Chirp stimulus, the use of level-specific (LS) CE-Chirp stimuli, which are created with varying delay models suitable for the intensity levels at which the sound is transmitted, is becoming increasingly common. The aim of this study was to compare click ABRs with LS CE-Chirp ABR thresholds in adults with sensorineural hearing loss. The research is a cross-sectional, analytical research. Twenty-two adult patients (n = 44 ears) with bilateral sensorineural hearing loss were included in the study. Pure-tone audiometry, click ABR, and LS CE-Chirp ABR tests were performed on adult (13 males and 9 females; 42.86 ± 14.50 years) patients with bilateral sensorineural hearing loss. Click ABR and LS CE-Chirp ABR thresholds were compared in terms of proximity to behavioral hearing thresholds of 2 kHz, 4 kHz, and 2 to 4 kHz averages. Both types of ABR stimuli were able to identify with total hearing loss (n = 6). A significant difference was found between LS CE-Chirp ABR thresholds (53.81 ± 20.28 decibel normal hearing level [dB nHL]) and click ABR thresholds (58.81 ± 19.11 dB nHL) in the other ears (n = 38) with hearing loss (p = 0.00). When both ears were evaluated together and the right and left ears were evaluated separately, no difference was found between LS CE-Chirp ABR thresholds and 4 kHz hearing thresholds (p = 0.66, 0.80, and 0.69, respectively). In adults with hearing loss, the LS CE-Chirp provides ABR thresholds closer to the behavioral hearing thresholds at 2 and 4 kHz compared with the click stimulus. Notably, there was no difference between LS CE-Chirp ABR thresholds and the 4 kHz behavioral hearing thresholds. We concluded that the LS CE-Chirp can be used effectively in the estimation of behavioral hearing thresholds in adults with hearing loss.