Mean Square Estimation Research Articles

Structural Optimization of 4-DOF Agricultural Robot Arm

The shortage of human labor is increasing; thus, more agricultural machinery and equipment are expected to enter the agricultural sector. One of the agricultural machinery widely studied nowadays involves robot arms. Therefore, developing robot arms is a hot issue in this field. The ideal structure of the robot arm with optimal length is currently gaining popularity and being used in many sectors, such as manufacturing and agriculture. This is closely related to the dynamic structure of agricultural areas. Therefore, this study uses the forward kinematic modeling method to design an optimal robot arm to achieve a specific coordinate in a dynamic environment. The robot in this study arm mimics the boom and arm installed on a tractor. The forward kinematic problem in this study is defined using the Denavit-Hartenberg (DH) convention method. The DH convention is commonly used to solve kinematic analysis problems of a robot arm. Simulation of kinematic modeling is performed using MATLAB software. This study studies various optimization algorithms to compare the performance of algorithms that can achieve the optimal length with minimum errors. The comparison between artificial bee colony (ABC) and particle swarm optimization (PSO) is studied. At the end of the study, the best algorithm was selected for the robot arm design with a four-degree-of-freedom (4-DOF). The best algorithm, i.e., the PSO algorithm, is evaluated by calculating mean square error (MSE of 0.00108527), root mean square error (RMSE of 0.01678), mean absolute error (MAE of 0.004286081), and end-effector position error (error of 0.080557045), where the best algorithm has the lowest value of error.

Kalman filter for radio source power and direction of arrival estimation

Images are an important source of information for spacecraft navigation. Based on an image and a known attitude, triangulation techniques (intersection or resection) are often used for positioning and navigation. In the resection problem, an observer estimate its unknown location by using angle measurements to points at known locations (i.e., landmarks), the localization performance depending on the accuracy of the angle measurements. As a contribution to resection for spacecraft navigation, we considers the dynamic image estimation problem based on radio interferometry, i.e., image of radio source power, where the measurements are sample covariance matrices (SCMs). Considering the case where several measurements are available as well as a known dynamic linear model of image evolution, a.k.a a linear state model, the minimum mean-squared error image estimator (MMSE) is given by the Kalman filter (KF) or one of its variants. However standard Kalman-like filters are not a priori suitable for the problem at hand since the measurements (i.e., SCMs) cannot be formulated analytically as a function of state parameters to be estimated (i.e., radio source power). In fact, this lack of analytical formulation can be circumvented by a statistical linear fitting allowing the SCMs to be expressed in terms of the state. This linear fitting introduces an additive residual noise, equivalent to a measurement noise, whose covariance matrix depends on the current state, a non-standard case for a measurement model. The covariance matrix of the residual noise is derived whatever the distributions of the radio sources and of the additive noise at the samples level, unveiling the contribution of their multivariate kurtosis. The proposed method is evaluated on simulated data representative of a dynamic radio interferometry framework. The results show that the proposed method is capable of effectively tracking moving radio sources in complex scenes with theoretical guaranties when the signal multivariate kurtosis is known.

Performance of Different Imputation Methods in Logistic Regression with Multicollinearity

The existence of missing values in the data, which must be taken into account, is an important issue in research. In particular, in the case of medical data, missing data can lead to a loss of trust in patient evaluation and make it impossible to classify people according to their level of health or disease. Furthermore, multicollinearity between independent variables can lead to misleading results. Therefore, the present research aims to study the efficiency of missing data imputation techniques for logistic regression with complete multicollinearity. The missing data imputation methods considered in this research were MEAN (mean imputation), MI (multiple imputation), KNN (k-nearest neighbor imputation), RF (random forest imputation), SRI (stochastic regression imputation), and BRI (Bayesian linear regression imputation). In this study, the simulation conducted was done with sample sizes of 20, 50, 100, 150, 200, 500, and 1000, as well as percentages of missing data at 10, 20, 30, and 40%. To compare efficiency, the EMSE (estimated mean square error) was used. The results showed that the RF method was most effective when the sample size was large and with a high percentage of missing data, whereas the MEAN method had the worst performance in all cases. When the sample size is small with a high proportion of missing data, KNN might be a preferable alternative for imputation. The inquiry into expanding the number of independent variables and different patterns of multicollinearity may be essential for future work.

BACK-to-MOVE: Machine learning and computer vision model automating clinical classification of non-specific low back pain for personalised management.

Low back pain (LBP) is a major global disability contributor with profound health and socio-economic implications. The predominant form is non-specific LBP (NSLBP), lacking treatable pathology. Active physical interventions tailored to individual needs and capabilities are crucial for its management. However, the intricate nature of NSLBP and complexity of clinical classification systems necessitating extensive clinical training, hinder customised treatment access. Recent advancements in machine learning and computer vision demonstrate promise in characterising NSLBP altered movement patters through wearable sensors and optical motion capture. This study aimed to develop and evaluate a machine learning model (i.e., 'BACK-to-MOVE') for NSLBP classification trained with expert clinical classification, spinal motion data from a standard video alongside patient-reported outcome measures (PROMs). Synchronised video and three-dimensional (3D) motion data was collected during forward spinal flexion from 83 NSLBP patients. Two physiotherapists independently classified them as motor control impairment (MCI) or movement impairment (MI), with conflicts resolved by a third expert. The Convolutional Neural Networks (CNNs) architecture, HigherHRNet, was chosen for effective pose estimation from video data. The model was validated against 3D motion data (subset of 62) and trained on the freely available MS-COCO dataset for feature extraction. The Back-to-Move classifier underwent fine-tuning through feed-forward neural networks using labelled examples from the training dataset. Evaluation utilised 5-fold cross-validation to assess accuracy, specificity, sensitivity, and F1 measure. Pose estimation's Mean Square Error of 0.35 degrees against 3D motion data demonstrated strong criterion validity. Back-to-Move proficiently differentiated MI and MCI classes, yielding 93.98% accuracy, 96.49% sensitivity (MI detection), 88.46% specificity (MCI detection), and an F1 measure of .957. Incorporating PROMs curtailed classifier performance (accuracy: 68.67%, sensitivity: 91.23%, specificity: 18.52%, F1: .800). This study is the first to demonstrate automated clinical classification of NSLBP using computer vision and machine learning with standard video data, achieving accuracy comparable to expert consensus. Automated classification of NSLBP based on altered movement patters video-recorded during routine clinical examination could expedite personalised NSLBP rehabilitation management, circumventing existing healthcare constraints. This advancement holds significant promise for patients and healthcare services alike.

Estimating neutrosophic finite median employing robust measures of the auxiliary variable

Our study explores neutrosophic statistics, an extension of classical and fuzzy statistics, to address the challenges of data uncertainty. By leveraging accurate measurements of an auxiliary variable, we can derive precise estimates for the unknown population median. The estimators introduced in this research are particularly useful for analysing unclear, vague data or within the neutrosophic realm. Unlike traditional methods that yield single-valued outcomes, our estimators produce ranges, suggesting where the population parameter is likely to be. We present the suggested generalised estimator's bias and mean square error within a first-order approximation framework. The practicality and efficiency of these proposed neutrosophic estimators are demonstrated through real-world data applications and the simulated data set.

Predictive analysis of concrete slump using a stochastic search-consolidated neural network

Attaining a dependable measurement of concrete slump is crucial as it is a valuable indication of concrete workability. On the other hand, complexities associated with costly traditional approaches have driven engineers to use indirect efficient models such as metaheuristic-based machine learning for approximating the slump. While the literature shows promising application of some metaheuristic techniques for this purpose, the large variety of these algorithms calls for evaluating the most capable ones to keep the solution updated. Stochastic fractal search (SFS) is one of the most powerful optimization algorithms in the literature that has not received appropriate attention in analyzing concrete mechanical parameters. In the present research, a multi-layer perceptron neural network (NN-MLP), is enhanced using the SFS. The proposed SFS-NN-MLP model aims to predict the slump based on the amount of ingredients in the mixture, as well as the curing age of specimens. Accuracy assessment revealed that the proposed model can deal with the assigned task with excellent accuracy. It indicates that the SFS could properly tune the parameters required for training the NN-MLP, and consequently, the trained network could reliably calculate the slump of specimens that were not analyzed before. For comparative validation, the SFS was replaced with two similar optimizers, namely elephant herding optimization algorithm (EHO) and slime mould algorithm (SMA). Based on the calculated mean square errors of 5.6526, 6.1129, and 7.3561 along with mean absolute errors of 4.6657, 5.0078, and 6.3066, as well as the percentage-Pearson correlation coefficients of 78.06 %, 73.95 %, and 58.11 %, respectively for the SFS-NN-MLP, EHO–NN–MLP, and SMA–NN–MLP, it was shown that the SFS-NN-MLP is the most accurate predictor. Hereupon, the SFS-NN-MLP model is recommended to be effectively used for obtaining a cost-efficient approximation of concrete slump in real-world projects.

Representation-Learning-Based CNN for Intelligent Attack Localization and Recovery of Cyber-Physical Power Systems.

Enabled by the advances in communication networks, computational units, and control systems, cyber-physical power systems (CPPSs) are anticipated to be complex and smart systems in which a large amount of data are generated, exchanged, and processed for various purposes. Due to these strong interactions, CPPSs will introduce new security vulnerabilities. To ensure secure operation and control of CPPSs, it is essential to detect the locations of the attacked measurements and remove the state bias caused by malicious cyber-attacks such as false data inject attack, jamming attack, denial of service attack, or hybrid attack. Accordingly, this article makes the first contribution concerning the representation-learning-based convolutional neural network (RL-CNN) for intelligent attack localization and system recovery of CPPSs. In the proposed method, the cyber-attacks' locational detection problem is formulated as a multilabel classification problem for CPPSs. An RL-CNN is originally adopted as the multilabel classifier to explore and exploit the implicit information of measurements. By comparing with previous multilabel classifiers, the RL-CNN improves the performance of attack localization for complex CPPSs. Then, to automatically filter out the cyber-attacks for system recovery, a mean-squared estimator is used to handle the difficulty in state estimation with the removal of contaminated measurements. In this scheme, prior knowledge of the system state is obtained based on the outputs of the stochastic power flow or historical measurements. The extensive simulation results in three IEEE bus systems show that the proposed method is able to provide high accuracy for attack localization and perform automatic attack filtering for system recovery under various cyber-attacks.

Event-Based Remote State Estimation for Nonlinear Systems: A Box Particle Filtering Method.

This article is concerned with the problem of event-based remote state estimation for nonlinear/non-Gaussian systems on a wireless network with limited bandwidth. To reduce unnecessary data transmissions, a novel event-triggering mechanism is developed by using the least-square technique. Based on this, an event-triggered box particle filtering scheme is designed to realize the minimum mean-squared error estimation at the remote estimator end, in which the posterior probability density functions are calculated separately according to the information of the event-triggered indicator to avoid the problem of excessive estimation error. Different from the existing approaches, the proposed algorithm does not depend on any Gaussian assumptions and reduces the computational complexity under the premise of ensuring the estimation performance. Finally, two simulation examples are performed to demonstrate the validity of the proposed algorithm.

Estimating Lung Volume Capacity from X-ray Images Using Deep Learning

Estimating lung volume capacity is crucial in clinical medicine, especially in disease diagnostics. However, the existing estimation methods are complex and expensive, which require experts to handle and consequently are more error-prone and time-consuming. Thus, developing an automatic measurement system without a human operator that is less prone to human error and, thus, more accurate has always been a prerequisite. The limitation of radiation dose and various medical conditions in technologies like computed tomography was also the primary concern in the past. Although qualitative prediction of lung volume may be a trivial task, designing clinically relevant and automated methods that effectively incorporate imaging data is a challenging problem. This paper proposes a novel multi-tasking-based automatic lung volume estimation method using deep learning that jointly learns segmentation and regression of volume estimation. The two networks, namely, segmentation and regression networks, are sequentially operated with some shared layers. The segmentation network segments the X-ray images, whose output is regressed by the regression network to determine the final lung volume. Besides, the dataset used in the proposed method is collected from three different secondary sources. The experimental results show that the proposed multi-tasking approach performs better than the individual networks. Further analysis of the multi-tasking approach with two different networks, namely, UNet and HRNet, shows that the network with HRNet performs better than the network with UNet with less volume estimation mean square error of 0.0010.

Discrepancy of rational points in simple algebraic groups

The aim of the present paper is to derive effective discrepancy estimates for the distribution of rational points on general semisimple algebraic group varieties, in general families of subsets and at arbitrarily small scales. We establish mean-square, almost sure and uniform estimates for the discrepancy with explicit error bounds. We also prove an analogue of W. Schmidt's theorem, which establishes effective almost sure asymptotic counting of rational solutions to Diophantine inequalities in the Euclidean space. We formulate and prove a version of it for rational points on the group variety, with an effective bound which in some instances can be expected to be the best possible.

Estimation of Reliability under Conditional Stress - Strength Setup based on Weibull Distribution

The Weibull distribution has been extensively studied and applied across various fields due to its versatility in modeling a wide range of phenomena, especially in reliability engineering, survival analysis, and lifetime modeling. The concept of Rl a,b , which represents a system's reliability in a conditional stress-strength setup, was proposed by Sabre and Khorshidian (2021). In this research, the problem of estimating reliability of the component is considered when strength variable X and stress variable Y follow independent Weibull distributions with common shapes and different scale parameters under conditional stress-strength setup. The maximum likelihood estimator, asymptotic confidence interval, Bootstrap estimators, Boot-p estimators, and Bayes estimator under-squared error loss function with associated highest posterior density interval are constructed for conditional stress-strength reliability. Simulation study is conducted to estimate mean square error (MSE) of estimator of conditional stress-strength reliability. The real data analysis is also carried out.

MSE FINDR: A Shiny R Application to Estimate Mean Square Error Using Treatment Means and Post Hoc Test Results.

Research synthesis methods such as meta-analysis rely primarily on appropriate summary statistics (i.e., means and variance) of a response of interest for implementation to draw general conclusions from a body of research. A commonly encountered problem arises when a measure of variability of a response across a study is not explicitly provided in the summary statistics of primary studies. Typically, these otherwise credible studies are omitted in research synthesis, leading to potential small-study effects and loss of statistical power. We present MSE FINDR, a user-friendly Shiny R application for estimating the mean square error (i.e., within-study residual variance, [Formula: see text]) for continuous outcomes from analysis of variance (ANOVA)-type studies, with specific experimental designs and treatment structures (Latin square, completely randomized, randomized complete block, two-way factorial, and split-plot designs). MSE FINDR accomplishes this by using commonly reported information on treatment means, significance level (α), number of replicates, and post hoc mean separation tests (Fisher's least significant difference [LSD], Tukey's honest significant difference [HSD], Bonferroni, Šidák, and Scheffé). Users upload a CSV file containing the relevant information reported in the study and specify the experimental design and post hoc test that was applied in the analysis of the underlying data. MSE FINDR then proceeds to recover [Formula: see text] based on user-provided study information. The recovered within-study variance can be downloaded and exported as a CSV file. Simulations of trials with a variable number of treatments and treatment effects showed that the MSE FINDR-recovered [Formula: see text] was an accurate predictor of the actual ANOVA [Formula: see text] for one-way experimental designs when summary statistics (i.e., means, variance, and post hoc results) were available for the single factor. Similarly, [Formula: see text] recovered by the application accurately predicted the actual [Formula: see text] for two-way experimental designs when summary statistics were available for both factors and the sub-plot factor in split-plot designs, irrespective of the post hoc mean separation test. The MSE FINDR Shiny application, documentation, and an accompanying tutorial are hosted at https://garnica.shinyapps.io/MSE_FindR/ and https://github.com/vcgarnica/MSE_FindR/. With this tool, researchers can now easily estimate the within-study variance absent in published reports that nonetheless provide appropriate summary statistics, thus enabling the inclusion of such studies that would have otherwise been excluded in meta-analyses involving estimates of effect sizes based on a continuous response.

Bias-free estimation of the covariance function and the power spectral density from data with missing samples including extended data gaps

Nonparametric estimation of the covariance function and the power spectral density of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Several common methods are tested for their systematic and random errors under the condition of variations in the distribution of the missing samples. In addition to random and independent outliers, the influence of longer and hence correlated data gaps on the performance of the various estimators is also investigated. The aim is to construct a bias-free estimation routine for the covariance function and the power spectral density from stationary stochastic processes under the condition of missing samples with an optimum use of the available information in terms of low estimation variance and mean square error, and that independent of the spectral composition of the data gaps. The proposed procedure is a combination of three methods that allow bias-free estimation of the desired statistical functions with efficient use of the available information: weighted averaging over valid samples, derivation of the covariance estimate for the entire data set and restriction of the domain of the covariance function in a post-processing step, and appropriate correction of the covariance estimate after removal of the estimated mean value. The procedures abstain from interpolation of missing samples as well as block subdivision. Spectral estimates are obtained from covariance functions and vice versa using Wiener–Khinchin’s theorem.

Stochastic Modeling of Partially Stirred Reactor (PaSR) for the Investigation of the Turbulence-Chemistry Interaction for the Ammonia-Air Combustion

The Partially Stirred Reactor (PaSR) model is carried out for the ammonia-air combustion system by means of stochastic modeling, namely by solving the transport equation for the joint Probability Density Function (PDF). The turbulent mixing is accounted for by the Linear Mean-Square Estimation (LMSE) mixing model. Notwithstanding the simplified nature of the PaSR modeling, the transported-PDF method enables capturing the effect of mixing frequency on the combustion system, especially the NOx emission. Since the chemical source term is in a closed form in the transported-PDF method, it allows us to apply different chemical mechanisms to explore, whether the set of elementary reactions that are identified as important for the prediction of NOx in the PaSR model is sensitive to the choice of chemical mechanisms. Furthermore, the effect of the residence time in the PaSR model has also been studied, and compared with those in the Perfectly Stirred Reactor (PSR) model (infinite large mixing frequency). Moreover, since the ammonia under oxygen enrichment shows some similar combustion behaviors in terms of e.g. laminar burning velocity as the ammonia under hydrogen enrichment, how large the difference of thermo-kinetic states (e.g. temperature and NOx emission) predicted by PaSR models and in laminar premixed flame configuration is also investigated. A further discussion focuses on the effect of thermal radiation, where the radiative heat loss roles in the prediction of NOx for the turbulent simulation is examined. By using the optically thin approximation model, it is shown that the thermal radiation exhibits little effect on the considered combustion systems within a typical turbulent time-scale.

DeepBayes—An estimator for parameter estimation in stochastic nonlinear dynamical models

Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods employ maximum likelihood or Bayesian estimation. However, these methods suffer from some limitations, most notably the substantial computational time for inference coupled with limited flexibility in application. In this work, we propose DeepBayes estimators that leverage the power of deep recurrent neural networks. The method consists of first training a recurrent neural network to minimize the mean-squared estimation error over a set of synthetically generated data using models drawn from the model set of interest. The a priori trained estimator can then be used directly for inference by evaluating the network with the estimation data. The deep recurrent neural network architectures can be trained offline and ensure significant time savings during inference. We experiment with two popular recurrent neural networks — long short term memory network (LSTM) and gated recurrent unit (GRU). We demonstrate the applicability of our proposed method on different example models and perform detailed comparisons with state-of-the-art approaches. We also provide a study on a real-world nonlinear benchmark problem. The experimental evaluations show that the proposed approach is asymptotically as good as the Bayes estimator.

Bayesian Learning-Assisted Joint Frequency Tracking and Channel Estimation for OFDM Systems

Orthogonal frequency division multiplexing (OFDM) is very sensitive to the carrier frequency offset (CFO). The CFO estimation precision heavily makes impacts on the OFDM performance. In this paper, a new Bayesian learning-assisted joint CFO tracking and channel impulse response estimation is proposed. The proposed algorithm is modified from a Bayesian learning-assisted estimation (BLAE) algorithm in the literature. The BLAE is expectation-maximization (EM)-based and displays the estimator mean square error (MSE) lower than the Cramer-Rao bound (CRB) when the CFO value is near zero. However, its MSE value may increase quickly as the CFO value goes away from zero. Hence, the CFO estimator of the BLAE is replaced to solve the problem.

Multi-Sensor Fusion Boolean Bayesian Filtering for Stochastic Boolean Networks.

Stochastic Boolean networks (SBNs) take process noise into account, so it is better to fit the actual situation and has a wider application background than Boolean networks (BNs). However, the presence of noise influences us to estimate the real state of the system. To minimize the inaccuracies caused by the presence of noise, an optimal state estimation problem is studied in this article. The multi-sensor fusion Boolean Bayesian filtering is proposed and a recursive algorithm is provided to calculate the prior and posterior belief of system state by fusing multi-sensor measurements based on the algebraic form of the SBN and Bayesian law. Then, the optimal state estimator is obtained, which minimizes the mean-square estimation error. Finally, a simulation example is carried out to demonstrate the performance of the proposed methodology. It has been shown through the simulation experiment that it increases the confidence level of the state estimation and improves the estimation performance using multi-sensor fusion compared with using single sensor.

Mean-square convergent continuous state estimation of randomly switched linear systems with unobservable subsystems and stochastic output noises

This paper studies mean-square (MS) convergent observers for estimating continuous states of randomly switched linear systems (RSLSs) with unobservable subsystems that are subject to stochastic output observation noises. When subsystems are unobservable and switching sequences are random, the classical Kalman–Bucy filters that are applied to observable sub-states are shown to be potentially divergent. It is also shown that unless the switching interval T can be selected to be sufficiently small from the outset, MS convergence may never be achieved, regardless of how the observers for the subsystems are designed. The critical threshold Tmax on T is derived for MS convergent observers to be achievable. Under the condition T<Tmax, this paper introduces design algorithms for subsystem observers to generate a globally MS convergent observer for the entire continuous state. A fundamental design tradeoff between convergence speeds and steady-state estimation errors is analyzed. This paper extends our recent new framework and algorithms for strong convergent observer design in RSLSs by including observation noises, considering multi-output systems, establishing new algorithms for MS convergence, and developing design tradeoff analysis. Examples and a practical case study are presented to illustrate the design procedures, main convergence properties, and error analysis.

On Some New Exponential Ratio Estimator of Population Mean in Two Phase Sampling

In this paper, we suggest employing the exponential ratio estimator to estimate the mean of the study variable using a two-phase sample strategy with two modified auxiliary variables. Several researchers discussed the properties of the estimators they proposed and discovered that the estimators in their studies were relatively efficient. The estimators previously studied are listed chronologically in the appendix to this paper. In two phase sampling, the estimator's mean square errors and relative efficiencies are calculated using auxiliary variable information. To assess the properties of our proposed estimator, we noticed that it has a lower mean square error (MSE) than the classical ratio estimator and some other exponential ratio estimators. The estimator is more useful than other estimators in solving real-world issues, notably in engineering, environmental science, management, and biological sciences. The proposed estimator has been applied to real-world data sets such as BRICS, Son's Head Measurement, Number of Hospital Beds, Sale Price of Residence, Ambient Pressure (AP), and Heating Load. In survey research, our suggested estimator has also been demonstrated to be more effective.

Size-Dependent Diffusion and Dispersion of Particles in Mucin.

Mucus, composed significantly of glycosylated mucins, is a soft and rheologically complex material that lines respiratory, reproductive, and gastrointestinal tracts in mammals. Mucus may present as a gel, as a highly viscous fluid, or as a viscoelastic fluid. Mucus acts as a barrier to the transport of harmful microbes and inhaled atmospheric pollutants to underlying cellular tissue. Studies on mucin gels have provided critical insights into the chemistry of the gels, their swelling kinetics, and the diffusion and permeability of molecular constituents such as water. The transport and dispersion of micron and sub-micron particles in mucin gels and solutions, however, differs from the motion of small molecules since the much larger tracers may interact with microstructure of the mucin network. Here, using brightfield and fluorescence microscopy, high-speed particle tracking, and passive microrheology, we study the thermally driven stochastic movement of 0.5-5.0 μm tracer particles in 10% mucin solutions at neutral pH, and in 10% mucin mixed with industrially relevant dust; specifically, unmodified limestone rock dust, modified limestone, and crystalline silica. Particle trajectories are used to calculate mean square displacements and the displacement probability distributions; these are then used to assess tracer diffusion and transport. Complex moduli are concomitantly extracted using established microrheology techniques. We find that under the conditions analyzed, the reconstituted mucin behaves as a weak viscoelastic fluid rather than as a viscoelastic gel. For small- to moderately sized tracers with a diameter of lessthan 2 μm, we find that effective diffusion coefficients follow the classical Stokes-Einstein relationship. Tracer diffusivity in dust-laden mucin is surprisingly larger than in bare mucin. Probability distributions of mean squared displacements suggest that heterogeneity, transient trapping, and electrostatic interactions impact dispersion and overall transport, especially for larger tracers. Our results motivate further exploration of physiochemical and rheological mechanisms mediating particle transport in mucin solutions and gels.