Robust Estimation Algorithm Research Articles

Robust Multi-Model Estimation for Reliable Relative Navigation Based on Observability and Abnormity Analysis

High-precision relative positioning and navigation is a fundamental requirement for many applications such as flight formation, spacecraft docking and collision avoidance. The main purpose of this paper is to develop a robust multi-model estimation algorithm for reliable navigation when there are abnormities of measurement and motion. In order to deal with these abnormities, we propose a quantitative evaluation method of relative navigation system by introducing the degree of observability (DoO) and the degree of abnormity (DoA). In addition, we design a feedforward information fusion and a feedback information allocation method based on DoO and DoA, and thus form a multi-model robust estimation algorithm. In order to testify the effectiveness and robustness of the proposed algorithm, a practical experiment with real data sets gathered in urban areas has been carried out. The results showed that the maximum relative positioning RMSE reduction ratio can reach 75%, and the maximum relative velocity RMSE reduction ratio can reach 51% compared with EKF. Therefore, the proposed method can guarantee the accuracy and robustness of relative navigation under abnormal conditions.

A robust attitude estimation algorithm for seabed inverted ultra-short baseline

The ultra-short baseline(USBL) is fixed upside down on the seafloor to position an autonomous underwater vehicle, which is the inverted ultra-short baseline (i-USBL). Three attitude angles between the i-USBL coordinate system and the navigation coordinate system will be produced when the USBL is installed on the seabed. Significant positioning error will occur if the USBL attitude is undefined. Besides, it also affects the accuracy of attitude angles estimation that the outliers produced when using USBL. In this paper, we propose a robust singular value decomposition (RSVD) method for estimating the attitude angles. Specifically, we develop an attitude calibration model based on the i-USBL positioning mode. The USBL attitude angles is solved using singular value decomposition (SVD) according to the least squares method. The new attitude angles are used to calculate the residuals of the coordinates at each measurement point. The residuals are used to calculate the weights of each point by the IGG III weighting function. The recalculation of attitude angles is performed by using up-to-date weights and SVD. The performance of SVD, the conventional Gaussian Newton iterative method (GN), and RSVD are compared in the simulations. The simulations show that the RSVD has high calibration accuracy and robustness.

A Study of GNSS-IR Soil Moisture Inversion Algorithms Integrating Robust Estimation with Machine Learning

Soil moisture monitoring is widely used in agriculture, water resource management, and disaster prevention, which is of great significance for sustainability. The global navigation satellite system interferometric reflectometry (GNSS-IR) technology provides a supplementary method for soil moisture monitoring. However, due to the quality of the signal-to-noise ratio (SNR) measurements and the complex surface environment, inevitable outliers in multipath interference signal metrics (amplitude, frequency, and phase) were used as modeling variables to inverse GNSS-IR soil moisture. Besides, it is hard to use the univariate model to comprehensively analyze the relationship between the various factors, due to the poor fitting effect and weak generalization ability of the model. In this paper, the minimum covariance determinant (MCD) robust estimation and machine learning algorithms are adopted. The MCD robust estimation can eliminate outliers of the multipath signal metrics and machine learning algorithms, including the back propagation neural network (BPNN), Gaussian process regression (GPR), and random forest (RF), and can comprehensively establish nonlinear GNSS-IR soil moisture inversion models using multipath interference signal metrics. Moreover, the study of the modeling parameter selection for the three machine learning algorithms and the inversion results for single satellite and all satellites are also carried out to make the algorithms more generalizable. The results show that the correlation coefficients (R) and the root mean square error (RMSE) of the machine learning models for all satellite tracks are increased by 4.3~86.6% and reduced by 2.8~30%, respectively, compared with the MCD multiple regression model. The RF model with 80 decision trees and 1 node shows the clearest improvement. The total model using all satellite data has more generalization ability than the single satellite model but causes some loss of accuracy.

Indoor Occupancy Sensing via Networked Nodes (2012–2022): A Review

In the past decade, different sensing mechanisms and algorithms have been developed to detect or estimate indoor occupancy. One of the most recent advancements is using networked sensor nodes to create a more comprehensive occupancy detection system where multiple sensors can identify human presence within more expansive areas while delivering enhanced accuracy compared to a system that relies on stand-alone sensor nodes. The present work reviews the studies from 2012 to 2022 that use networked sensor nodes to detect indoor occupancy, focusing on PIR-based sensors. Methods are compared based on pivotal ADPs that play a significant role in selecting an occupancy detection system for applications such as Health and Safety or occupant comfort. These parameters include accuracy, information requirement, maximum sensor failure and minimum observation rate, and feasible detection area. We briefly describe the overview of occupancy detection criteria used by each study and introduce a metric called “sensor node deployment density” through our analysis. This metric captures the strength of network-level data filtering and fusion algorithms found in the literature. It is hinged on the fact that a robust occupancy estimation algorithm requires a minimal number of nodes to estimate occupancy. This review only focuses on the occupancy estimation models for networked sensor nodes. It thus provides a standardized insight into networked nodes’ occupancy sensing pipelines, which employ data fusion strategies, network-level machine learning algorithms, and occupancy estimation algorithms. This review thus helps determine the suitability of the reviewed methods to a standard set of application areas by analyzing their gaps.

Lithium-Ion Battery State of Charge Estimation Using Deep Neural Network

In an electric vehicle (EV), the battery management system (BMS) is crucial for managing the health and safety of the battery. The accurate estimation of battery state of charge (SOC) offers critical information about the battery’s remaining capacity. The SOC of the battery mainly depends on its non-linear internal parameters, battery chemistry, ambient temperature, aging factor etc. So, accurate SOC estimation is still a significant challenge. Many researchers have developed several model-based methods that are more complex to develop. Another approach is a data-driven based SOC estimation algorithm, which is less complex but requires more data and it may be inaccurate. In this context, this paper presents a robust and accurate SOC estimation algorithm for a Lithium-ion battery using a deep learning feed-forward neural network (DLFFNN) approach. The proposed algorithm accurately characterizes the battery’s non-linear behavior. To develop a robust SOC estimation algorithm, data is collected at different temperatures with 5% error in data (4 mV-voltage, 110 mA-current, 5∘C temperature) is added to battery datasets. The obtained results demonstrated that the performance of the proposed DLFNN is robust and accurate on different drive cycles with 1.14% Root mean squared error (RMSE), 0.66% mean absolute error (MAE), and 6.65% maximum error (MAX).

Detection of differential depressive symptom patterns in a cohort of perinatal women: an exploratory factor analysis using a robust statistics approach.

Postpartum depression can take many forms. Different symptom patterns could have divergent implications for how we screen, diagnose, and treat postpartum depression. We sought to utilise a recently developed robust estimation algorithm to automatically identify differential patterns in depressive symptoms and subsequently characterise the individuals who exhibit different patterns. Depressive symptom data (N=548) were collected from women with neuropsychiatric illnesses at two U.S. urban sites participating in a longitudinal observational study of stress across the perinatal period. Data were collected from Emory University between 1994 and 2012 and from the University of Arkansas for Medical Sciences between 2012 and 2017. We conducted an exploratory factor analysis of Beck Depression Inventory (BDI) items using a robust expectation-maximization algorithm, rather than a conventional expectation-maximization algorithm. This recently developed method enabled automatic detection of differential symptom patterns. We described differences in symptom patterns and conducted unadjusted and adjusted analyses of associations of symptom patterns with demographics and psychiatric histories. 53 (9.7%) participants were identified by the algorithm as having a different pattern of reported symptoms compared to other participants. This group had more severe symptoms across all items-especially items related to thoughts of self-harm and self-judgement-and differed in how their symptoms related to underlying psychological constructs. History of social anxiety disorder (OR: 4.0; 95% CI [1.9, 8.1]) and history of childhood trauma (for each 5-point increase, OR: 1.2; 95% CI [1.1, 1.3]) were significantly associated with this differential pattern after adjustment for other covariates. Social anxiety disorder and childhood trauma are associated with differential patterns of severe postpartum depressive symptoms, which might warrant tailored strategies for screening, diagnosis, and treatment to address these comorbid conditions. There are no funding sources to declare.

Influence of Photoplethysmogram Signal Quality on Pulse Arrival Time during Polysomnography.

Intervals of low-quality photoplethysmogram (PPG) signals might lead to significant inaccuracies in estimation of pulse arrival time (PAT) during polysomnography (PSG) studies. While PSG is considered to be a "gold standard" test for diagnosing obstructive sleep apnea (OSA), it also enables tracking apnea-related nocturnal blood pressure fluctuations correlated with PAT. Since the electrocardiogram (ECG) is recorded synchronously with the PPG during PSG, it makes sense to use the ECG signal for PPG signal-quality assessment. (1) Objective: to develop a PPG signal-quality assessment algorithm for robust PAT estimation, and investigate the influence of signal quality on PAT during various sleep stages and events such as OSA. (2) Approach: the proposed algorithm uses R and T waves from the ECG to determine approximate locations of PPG pulse onsets. The MESA database of 2055 PSG recordings was used for this study. (3) Results: the proportions of high-quality PPG were significantly lower in apnea-related oxygen desaturation (matched-pairs rc = 0.88 and rc = 0.97, compared to OSA and hypopnea, respectively, when p < 0.001) and arousal (rc = 0.93 and rc = 0.98, when p < 0.001) than in apnea events. The significantly large effect size of interquartile ranges of PAT distributions was between low- and high-quality PPG (p < 0.001, rc = 0.98), and regular and irregular pulse waves (p < 0.001, rc = 0.74), whereas a lower quality of the PPG signal was found to be associated with a higher interquartile range of PAT across all subjects. Suggested PPG signal quality-based PAT evaluation reduced deviations (e.g., rc = 0.97, rc = 0.97, rc = 0.99 in hypopnea, oxygen desaturation, and arousal stages, respectively, when p < 0.001) and allowed obtaining statistically larger differences between different sleep stages and events. (4) Significance: the implemented algorithm has the potential to increase the robustness of PAT estimation in PSG studies related to nocturnal blood pressure monitoring.

An efficient method for parameter estimation and separation of multi-component LFM signals

In this paper, an efficient and robust algorithm for fast parameter estimation and separation of multi-component LFM signals is proposed, which is suitable for processing overlapping and intersect LFM signals in the time-frequency plane. First, the key innovative idea of the algorithm is to use the fourth-order origin moment of fractional Fourier transform spectrum to formulate a reasonable search strategy for the optimal rotation order to achieve parameter estimation, and propose a step-by-step filtering technique for signals in the fractional Fourier domain achieve the signal separation we are interested in. Then, the proposed algorithm overcomes the problems of low estimation accuracy and large computational of traditional two-dimensional search and time-frequency analysis methods by virtue of good impulse characteristics and anti-noise performance. Different from existing solutions, the method avoid interference problems between multiple signals with close time-frequency distance, overlapping and cross components. Moreover, the error analysis of the linear frequency modulation signal is carried out, and the Cramer-Rao lower bound for the unbiased estimation of the parameters is derived. Finally, the simulation results demonstrate the accuracy and effectiveness of the proposed method in noisy environments by comparing with traditional methods and existing methods.

A robust method for coherent and non-coherent source number detection using a special Hankel-based covariance matrix

A robust algorithm for source number estimation based on the formation of the Hankel covariance matrix is presented. First, multiple data snapshots are taken successively from overlapped subarrays in a way similar to the forward spatial smoothing method to construct the special Hankel covariance matrix and for the total number of subarrays, these special covariance matrices are generated. Then, the average of these matrices is employed in singular value decomposition to generate the corresponding eigenvalues. Finally, the resulting eigenvalues are evaluated via the rule presented in this paper as the Moving Gradient Criterion (MGC) to estimate the number of sources by detection of the largest singular values. The greatest difference between the proposed algorithm and the other conventional methods is the form of the covariance matrix with the observed signal that can handle both non-coherent as well as fully coherent sources. Also, the proposed MGC rule adopted with this form of the covariance matrix is the strength of this work. Numerical simulations demonstrate the high superiority of the proposed approach over the competing methods such as MDL, AIC, SORTE, RAE and MSEE methods, especially in the cases of very closely spaced sources, low SNR values, low sensors number and low snapshots number.

Robust Attitude Estimation Using Magnetic and Inertial Sensors

Lightweight and low-cost magnetic and inertial sensors are commonly used for attitude estimation in a wide range of applications, from motion tracking to autonomous navigation. However, the inherent and external sensor errors and the accelerations due to the actual motion of the platform highly affect the estimation accuracy. This study proposes a robust attitude estimation algorithm that compensates the sensor errors and the external accelerations at the algorithm level. The attitude estimation filter, which is structured as a Multiplicative Extended Kalman Filter (MEKF), is modified to compensate for both the long-term and short-term measurement uncertainties. Modification is applied mainly by estimating and compensating the bias and external accelerations for long-term uncertainties and tuning the measurement noise covariance matrix for short-term uncertainties. Simulations test the proposed algorithm, and the results are compared with benchmark algorithms.

A High-speed Measurement System for Treadmill Spherical Motion in Virtual Reality for Mice and a Robust Rotation Axis Estimation Algorithm Based on Spherical Geometry

A High-speed Measurement System for Treadmill Spherical Motion in Virtual Reality for Mice and a Robust Rotation Axis Estimation Algorithm Based on Spherical Geometry

Robust Heading Estimation Algorithm for Android Smartphones

This article proposes a robust heading estimation algorithm for smartphones, which integrates the gradient descent (GD) approach and genetic algorithm (GA) to compute the heading angle of smartphones and reduce the heading error accumulation induced by the errors of sensors. In the proposed algorithm, the accelerometer, magnetometer, and gyroscope are used to estimate the heading angle. The sum of squared triaxial errors of geomagnetic strength and acceleration is regarded as the fitness of GA to improve the accuracy of heading angle and restrain the error accumulation. The angular velocity given by gyroscope is used to generate the init ial point of GA. To improve the convergence rate and local search capability of GA, a search area adjustment strategy based on GD is designed to obtain the optimal search area for each iteration of GA. Experimental results show that the proposed algorithm can achieve better heading estimation accuracy on three smartphones and four orientations, with a mean heading error of 1.577° on Mate 20 smartphone.

Robust extended state estimation for nonlinear complex networks with colored noise

In this article, a robust extended state Kalman filter estimation algorithm for nonlinear complex networks is designed, fully considering the state coupling and colored noise among system nodes. The innovative measurement information subtraction method at adjacent moments deals with colored noise, making it more in line to meet engineering requirements. The states information of system nodes is redundant, and the collected data are processed by the quantizer, which greatly reduces the impact of network bandwidth constraints. Based on the bounds of the dynamic change rate of the nonlinear function rather than the bounds of the procedure itself, the upper bound of the error covariance is obtained, and real-time gain optimization is realized. Finally, the rationality and accuracy of the estimator are verified by simulation. According to the control variable method, the effects of the quantization density and quantization level of the quantizer on the stability of system are briefly demonstrated.

Robust 6-DoF Pose Estimation under Hybrid Constraints.

To solve the problem of the insufficient accuracy and stability of the two-stage pose estimation algorithm using heatmap in the problem of occluded object pose estimation, a new robust 6-DoF pose estimation algorithm under hybrid constraints is proposed in this paper. First, a new loss function suitable for heatmap regression is formulated to improve the quality of the predicted heatmaps and increase keypoint accuracy in complex scenes. Second, the heatmap regression network is expanded and a translation regression branch is added to constrain the pose further. Finally, a robust pose optimization module is used to fuse the heatmap and translation estimates and improve the pose estimation accuracy. The proposed algorithm achieves ADD(-S) accuracy rates of 93.5% and 46.2% on the LINEMOD dataset and the Occlusion LINEMOD dataset, which are better than other state-of-the-art algorithms. Compared with the conventional two-stage heatmap-based pose estimation algorithms, the mean estimation error is greatly reduced, and the stability of pose estimation is improved. The proposed algorithm can run at a maximum speed of 22 FPS, thus constituting both a performant and efficient method.

Snow depth retrieval by using robust estimation algorithm to perform multi-SNR and multi-system fusion in GNSS-IR

Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) technology provides a new means of snow depth detection. Multi-satellite and multi-Signal-to-Noise Ratio (SNR) provide more data for daily high-precision snow depth retrieval, but also face the problem of data fusion and effective utilization. Therefore, this study proposes a robust estimation algorithm based on multi-satellite and multi-SNR fusion applied to the observations of a GNSS station in Alaska. This study uses four solutions (Savg, Smed, SRE_avg and SRE_med) to carry out multi-system fusion snow depth inversion and precision comparison research. The Savg has more obvious disadvantages, which is not suitable for snow depth assessment. The SRE_avg and SRE_med have better snow depth retrieval effects in the snowy periods. The correlation coefficient (R), root mean square error (RMSE) and mean error (ME) of the calculated snow depth using the robust estimation algorithm with respect to the nearest in-situ measurements reached 0.759, 3.7 cm and −1.4 cm, respectively. Compared with the Smed, the R is increased by 2.0 %, the RMSE corresponds to an improvement of 2.6 %. Moreover, the ME of the snow depth retrievals, as an indicator of the measurement bias, has significantly decreased by 6.7 %. The result also shows that the snow depth inversion by the robust estimation algorithm is more consistent with the in-situ measurements, further extending and advancing the optimal algorithm for snow depth retrieval.

Local response estimation of a seagoing vessel using onboard measurement data

Structural integrity management is gaining popularity because of the wide-spreading application of the digital twin concept, which is based on the fusion of the real-world measurement data and digital model used for the design. Data fusion between the measurement data and design model makes structural integrity management a feasible solution with a limited number of sensors, provided a reliable and robust local response estimation algorithm can be provided. This paper presents a methodology through which a local stress response at an arbitrary location within a seagoing vessel can be estimated using onboard measurement data. For the response transfer from the measured location A to the unmeasured location B, the relative RAO, which defines the ratio of response amplitude between location A to B, was introduced. The relative RAO concept was applied by decomposing the response spectrum at measured location A into its comprising directional components using the least square method with non-parametric modeling. The proposed method was validated using the numerically generated pseudo measurement data, where some noises were introduced artificially to imitate the actual measurement. Finally, the full-scale measurement data of the 13,000TEU container carrier was analyzed and used to verify the proposed method.

Dynamic nonlocal passive scalar subgrid-scale turbulence modeling

Extensive experimental evidence highlights that scalar turbulence exhibits anomalous diffusion and stronger intermittency levels at small scales compared to that in fluid turbulence. This renders the corresponding subgrid-scale dynamics modeling for scalar turbulence a greater challenge to date. We develop a new large eddy simulation (LES) paradigm for efficiently and dynamically nonlocal LES modeling of the scalar turbulence. To this end, we formulate the underlying nonlocal model starting from the filtered Boltzmann kinetic transport equation, where the divergence of subgrid-scale scalar fluxes emerges as a fractional-order Laplacian term in the filtered advection–diffusion model, coding the corresponding superdiffusive nature of scalar turbulence. Subsequently, we develop a robust data-driven algorithm for estimation of the fractional (noninteger) Laplacian exponent, where we, on the fly, calculate the corresponding model coefficient employing a new dynamic procedure. Our a priori tests show that our new dynamically nonlocal LES paradigm provides better agreement with the ground-truth filtered direct numerical simulation data in comparison to the conventional static and dynamic Prandtl–Smagorinsky models. Moreover, in order to analyze the numerical stability and assessing the model's performance, we carry out comprehensive a posteriori tests. They unanimously illustrate that our new model considerably outperforms other existing functional models, correctly predicting the backscattering phenomena and, at the same time, providing higher correlations at small-to-large filter sizes. We conclude that our proposed nonlocal subgrid-scale model for scalar turbulence is amenable for coarse LES and very large eddy simulation frameworks even with strong anisotropies, applicable to environmental applications.

Improved adaptively robust estimation algorithm for GNSS spoofer considering continuous observation error

Once the spoofer has controlled the navigation system of unmanned aerial vehicle (UAV), it is hard to effectively control the error convergence to meet the threshold condition only by adjusting parameters of estimation if estimation of the spoofer on UAV has continuous observation error. Aiming at this problem, the influence of the spoofer's state estimation error on spoofing effect and error convergence conditions is theoretically analyzed, and an improved adaptively robust estimation algorithm suitable for steady-state linear quadratic estimator is proposed. It enables the spoofer's estimator to reliably estimate UAV status in real time, improves the robustness of the estimator in responding to observation errors, and accelerates the convergence time of error control. Simulation experiments show that the mean value of normalized innovation squared (NIS) is reduced by 88.5%, and the convergence time of NIS value is reduced by 76.3%, the convergence time of true trajectory error of UAV is reduced by 42.3%, the convergence time of estimated trajectory error of UAV is reduced by 67.4%, the convergence time of estimated trajectory error of the spoofer is reduced by 33.7%, and the convergence time of broadcast trajectory error of the spoofer is reduced by 54.8% when the improved algorithm is used. The improved algorithm can make UAV deviate from preset trajectory to spoofing trajectory more effectively and more subtly.

Exploiting moving slope features of PPG derivatives for estimation of mean arterial pressure.

Monitoring Mean Arterial Pressure (MAP) helps calculate the arteries' flow, resistance, and pressure. It allows doctors to check how well the blood flows through our body and reaches all major organs. Photoplethysmogram technology is gaining momentum and popularity in smart wearable devices to monitor cuff-less blood pressure (BP). However, the performance reliability of the existing PPG-based BP estimation devices is still poor. Inaccuracy in estimating systolic and diastolic blood pressure leads to an overall imprecision in resultant MAP values. Hence, there is a need for robust and reliable MAP estimation algorithms. This work exploits the moving slope features of PPG contour in its first and second derivatives that directly correlate with MAP and does not require estimating systolic and diastolic blood pressure values. The proposed approach is evaluated using two different data sets (i.e., MIMIC-I and MIMIC-II) to demonstrate the robustness and reliability of the work for personalized non-invasive BP monitoring devices to estimate MAP directly. A mean absolute error of and a standard deviation of is obtained with MIMIC-II data-set using GridSearchCV random forest regressor that outperformed most of the existing related works.

A novel sampling methodology exploiting the least correlated-columns for angle of arrival estimation

Estimating Angle of Arrival (AOA) parameter from the measured data has gained much attention, particularly in the 5G-and-beyond wireless communication networks. With these communication networks, it is highly expected that the size and number of the data sets are huge and much larger than the rival traditional networks. To this end, the way of sampling and dealing with collected data in the array signal processing stage will have a significant impact on the signal estimation parameters. Thus, this manuscript proposes a novel sampling methodology to extract the collected information optimally by exploiting the least correlated and dependent columns within the measured Covariance Matrix (CM). The suggested method, Least Correlated Column Sampling (LCCS), is then adopted to implement a robust AOA estimation algorithm called Least Correlated Column Projection Matrix (LCCPM). A theoretical analysis is derived and presented to justify that the proposed technique minimizes correlations between adjacent columns and then compared with current sampling methodologies in terms of the position selection and corresponding correlation. The analytical results show that the LCCS methodology selects the least dependent columns among the rival methods. This, in turn, improves the AOA algorithm performance and enables it to localize closely-separated sources with high accuracy. To verify the theoretical claims and reveal the advantages of the suggested approach, a numerical example is given and then intensive Monte Carlo simulations are conducted over a wide range of scenarios where the proposed method performance is systemically compared with existing techniques. The obtained results show that the proposed algorithm is superior and outperforms all the preceding methodologies in terms of higher estimation resolution, lower Root Mean Square Error (RMSE), and higher Probability of Successful Detections (PSDs). The results also illustrate that the proposed method achieves higher noise immunity, less sensitivity to correlated signals, and detects a higher number of angles in comparison with conventional and recently-developed methods.