Sensor Bias Research Articles

CRLB for Estimating Time-Varying Rotational Biases in Passive Sensors

In target tracking systems involving data fusion it is common to encounter sensor measurement biases that contribute to the tracking errors. There is extensive research into estimating sensor biases, but very little research into bias estimation in the dynamic case, meaning that biases that change over time are addressed. This paper investigates the means for and necessity of estimating bias rates of change in addition to constant sensor biases to reduce the errors in the state estimates. This is explored by comparing the Cramer–Rao lower bound and root-mean-square error of simultaneous target state and bias estimates for rotational biases with three-dimensional passive sensors with roll, pitch, and yaw biases. The present work models the dynamic biases as linearly varying over time. The iterated least squares method is used for the search of the maximum likelihood estimate, and is shown to be statistically efficient via hypothesis testing.

Decentralized Information Filter with Noncommon States

This paper addresses the problem of state estimation using a decentralized estimator in the presence of sensor or node-specific local state variables that arise from heterogeneous sensor dynamics, time-varying biases, or both. The state vector at each node is divided into two sets: states common to all nodes and states describing the local sensor dynamics and bias. Each node works as an independent Kalman filter to estimate the common as well as the local states associated with it, whereas communication between the notes is restricted to just the common states. The novelty of the proposed algorithm lies in the assimilation process of the decentralized estimator, wherein the local state vectors are fused without increasing the computational or the communication-related costs. Additionally, the proposed algorithm is extended by incorporating covariance intersection to address the problem of unknown correlation between the local estimators in decentralized estimation. The algorithm is validated using numerical simulations. The error characteristics of the proposed algorithm are comparable to those of a centralized Kalman filter, and the proposed algorithm is seen to offer a substantial reduction in the costs associated with estimation.

Bias CRLB in Sine Space for a Three-Dimensional Sensor

As bias estimation methods are developed, it becomes necessary to obtain the bound on bias estimation for more complex bias and sensor models. Three-dimensional (3-D) sensors, such as radars commonly used in applications, contain both scale and additive biases in sine space which result in a nonlinear estimation problem that may have poor observability and accuracy depending on the geometry of the sensors. By converting the sine space and range measurements to Cartesian using an unbiased conversion, it is possible, via creation of pseudomeasurements, to eliminate the need to estimate the target's state thereby reducing the sensor bias estimator complexity. The present paper evaluates the Cramer–Rao lower bound (CRLB) for estimating scale and additive biases in sine space for 3-D sensors and compares it with a maximum likelihood formulation implemented via iterated least squares, which is thereby shown to be statistically efficient. Additionally, the importance of measurement diversity is investigated with respect to the CRLB.

Instant Mercury Ion Detection in Industrial Waste Water with a Microchip Using Extended Gate Field-Effect Transistors and a Portable Device.

Mercury ion selective membrane (Hg-ISM) coated extended gate Field Effect transistors (ISM-FET) were used to manifest a novel methodology for ion-selective sensors based on FET’s, creating ultra-high sensitivity (−36 mV/log [Hg2+]) and outweighing ideal Nernst sensitivity limit (−29.58 mV/log [Hg2+]) for mercury ion. This highly enhanced sensitivity compared with the ion-selective electrode (ISE) (10−7 M) has reduced the limit of detection (10−13 M) of Hg2+ concentration’s magnitude to considerable orders irrespective of the pH of the test solution. Systematical investigation was carried out by modulating sensor design and bias voltage, revealing that higher sensitivity and a lower detection limit can be attained in an adequately stronger electric field. Our sensor has a limit of detection of 10−13 M which is two orders lower than Inductively Coupled Plasma Mass Spectrometry (ICP-MS), having a limit of detection of 10−11 M. The sensitivity and detection limit do not have axiomatic changes under the presence of high concentrations of interfering ions. The technology offers economic and consumer friendly water quality monitoring options intended for homes, offices and industries.

Two‐layer online state‐of‐charge estimation of lithium‐ion battery with current sensor bias correction

Because of the harsh working condition in electrified vehicles, the measured current and voltage signals typically contain non-ignorable noises and bias, which potentially decline the accuracy of state-of-charge estimation. In this regard, the noise and bias corruption should be well addressed to maintain sufficient accuracy and robustness. This paper improves the existing methods in the literature from two aspects: (a) A novel offset-free equivalent circuit model is developed to remove the current bias; and (b) based on the offset-free equivalent circuit model, a two-layer estimator is proposed to estimate the state of charge using real-time identified model parameters. The robustness of the two-layer estimator against model uncertainties and the aging effect is further evaluated. Simulation and experimental results show that the proposed two-layer estimator can effectively attenuate the current bias and estimate the state of charge accurately with the error confined to ±4% under different levels of current bias and model uncertainties.

Changes in Accuracy of Continuous Glucose Monitoring Using Dexcom G4 Platinum Over the Course of Moderate Intensity Aerobic Exercise in Type 1 Diabetes.

Continuous glucose monitoring (CGM) systems help diabetes management in patients with type 1 diabetes (T1D) but could have lower accuracy during exercise. We aim to evaluate the dynamics of CGM accuracy during exercise in patients with T1D. Secondary analysis of data was carried out on 22 patients with T1D (glycated hemoglobin [HbA1c]: 7.3% ± 1.0%, diabetes duration: 23 ± 13 years), who did three exercise sessions (45 min at 60% VO2max on an ergocycle, 3 h postmeal) with paired Dexcom G4 Platinum, and capillary glucose values that were collected every 5 min. Dexcom accuracy was evaluated using sensor bias (SB) and absolute relative difference (ARD). For dynamics of SB analysis, data pairs following hypoglycemia correction were excluded. The analyzed data included 792 pairs (594 during 66 exercise sessions, 198 at rest before exercise). Median ARD was 8.44 (5.35-12.13)% at rest and increased to 16.77 (10.75-26.72)% during exercise (P < 0.001). During exercise, mean SB values evolved from T0 minutes = 5.95 ± 16.04 mg/dL (exercise start); T5 = 9.55 ± 16.40; T10 = 13.51 ± 18.02; T15 = 15.32 ± 20.36; T20 = 17.30 ± 18.92; T25 = 19.46 ± 17.48; T30 = 21.08 ± 19.64; T35 = 19.10 ± 20.36; T40 = 19.82 ± 20.18; and T45 = 18.02 ± 20.90 (exercise end). CGM overestimated capillary at a mean SB of 14.23 ± 16.76 mg/dL over the whole exercise session. CGM accuracy decreased during moderate aerobic exercise as previously described. However, the trend to overestimate capillary glucose was maintained at relatively stable values within 15 min of exercise initiation, which could help patients in their clinical decisions. Similar analyses would be needed for other types of exercise.

A long-term dataset of lake surface water temperature over the Tibetan Plateau derived from AVHRR 1981\u20132015

Lake surface water temperature (LSWT) is of vital importance for hydrological and meteorological studies. The LSWT ground measurements in the Tibetan Plateau (TP) were quite scarce because of its harsh environment. Thermal infrared remote sensing is a reliable way to calculate historical LSWT. In this study, we present the first and longest 35-year (1981–2015) daytime lake-averaged LSWT data of 97 large lakes (>80 km2 each) in the TP using the 4-km Advanced Very High Resolution Radiometer (AVHRR) Global Area Coverage (GAC) data. The LSWT dataset, taking advantage of observations from NOAA’s afternoon satellites, includes three time scales, i.e., daily, 8-day-averaged, and monthly-averaged. The AVHRR-derived LSWT has a similar accuracy (RMSE = 1.7 °C) to that from other data products such as MODIS (RMSE = 1.7 °C) and ARC-Lake (RMSE = 2.0 °C). An inter-comparison of different sensors indicates that for studies such as those considering long-term climate change, the relative bias of different AVHRR sensors cannot be ignored. The proposed dataset should be, to some extent, a valuable asset for better understanding the hydrologic/climatic property and its changes over the TP.

Accuracy of pulse oximeters at low oxygen saturations in children with congenital cyanotic heart disease: An observational study.

Pulse oximetry overestimates arterial oxygen saturation (SaO2 ) at less than 90% saturation in cyanotic children. The Masimo Blue sensor (Masimo Corp., Irvine, CA) is a pulse oximetry sensor developed for use in children with cyanosis. However, there remains a lack of research in actual clinical practice. We evaluated the intraoperative performance of three different pulse oximeters to measure oxyhemoglobin saturation (SpO2 ) at low saturations in pediatric patients with cyanotic heart disease and the influence of clinical variables (SaO2 , hemoglobin concentration, perfusion index, and weight) on the accuracy of the sensors. This prospective observational study compared SpO2 measured using three pulse oximeters (Masimo Blue [Masimo Corp., Irvine, CA]; Masimo LNCS, and Nellcor [Medtronic, Dublin, Ireland]) at selected SaO2 ranges (≥85%, 75%-84%, 60%-74%, and<60%). Accuracy was evaluated according to bias and Bland-Altman analysis with appropriate correction for multiple measurements. Relationships between bias and clinical variables were assessed using a generalized estimating equation. Two hundred and fifty-eight samples were analyzed. The mean overall bias (limits of agreement) of Masimo Blue, Masimo LNCS, and Nellcor sensor was -5.3 (-20.9 to 10.3%), -7.4 (-21.9 to 7.1%), and -7.4 (-22.5 to 15.1%), respectively. However, there was no difference in bias among the three sensors at SaO2 <60%. Generalized estimating equation showed that SaO2 value was associated with bias of all sensors. Perfusion index affected the bias of Blue sensor and LNCS sensor, and patients' weight was associated with bias of Nellcor sensor. Masimo blue sensor demonstrated overall lower bias compared to the other two sensors. However, the accuracy of all sensors was similarly poor at SaO2 less than 60%. Bias was influenced by SaO2 , perfusion index, and body weight.

Diagnosis of Multiple Open-Circuit Switch Faults Based on Long Short-Term Memory Network for DFIG-Based Wind Turbine Systems

Effective fault diagnosis for power electronic converters is an essential and mandatory operation to reduce failures and unscheduled shutdowns. This paper presents a data-driven fault diagnosis method, using long short-term memory (LSTM) network, to detect multiple open-circuit switch faults of the back-to-back converter in doubly fed induction generator (DFIG)-based wind turbine systems. Twelve sensor signals of the back-to-back converter for different fault types are measured. Wind speed fluctuation and sensor bias faults are considered as interference factors. The method has been evaluated in a grid-connected DFIG simulink model. Simulation results have demonstrated that, compared with least squares support vector machine (LS-SVM), back-propagation artificial neural network (BPANN) and recurrent neural network (RNN), the proposed method excavates the deep information of the fault signal with the highest diagnosis accuracy and strongest robustness with short time delay. Experimental tests undertaken on a hardware-in-the-loop testing platform further validate the effectiveness of the LSTM-based network.

Thermal variation of electric field sensor bias caused by anisotropy of LiNbO3

Electric field sensors based on LiNbO3 are attractive for use in high-intensity transient electric field measurements. However, the working bias of such sensors is easily influenced by temperature variations. Many researchers have worked to improve the thermal stability of the bias of these sensors, mostly in terms of waveguide direction selection and suppression of the pyroelectric effect. In this letter, we present an analysis of the steady-state temperature stability of an x-cut, z-propagation, straight waveguide common-path interferometer-based sensor and show that the difference between the thermo-optic coefficients of no and ne caused by the anisotropy of the LiNbO3 crystal is the main factor that affects the steady-state working bias of the electric field sensor at different working temperatures. The experimental results for the changes in the sensor bias with temperature in the steady states are in good agreement with the theoretical analysis.

Harmonization of GEOV2 fAPAR time series through MODIS data for global drought monitoring

The temporal consistency of the fAPAR GEOV2 full time series (constituted by data derived from SPOT-VGT1/2 and PROBA-V) is analyzed against the single-sensor MODIS dataset, with a particular focus on the most recent fAPAR anomalies (z-scores) produced from PROBA-V in the period 2014–2017. The intercomparison highlights a systematic overestimation of GEOV2 fAPAR z-scores when compared to MODIS fAPAR, likely related to the observed positive bias (over 90% of the domain) in the PROBA-V vs. SPOT-VGT1/2 relationship. A simple two-step harmonization procedure has been proposed to remove this discrepancy, based on two separate linear corrections of SPOT-VGT1/2 (2001–2013) and PROBA-V (2014–2017) data with respect to MODIS, followed by a time lag correction. The harmonized GEOV2 time series preserves the overall dynamic of fAPAR, while removing the sensor bias and improving the consistency with MODIS data. The fAPAR anomalies from the harmonized GEOV2 time series provide unbiased estimates of z-scores that are overall well correlated (R = 0.55 ± 0.25) with the MODIS fAPAR anomalies.

An implementation of the cubature Kalman filter for estimating trajectory parameters and air data of a hypersonic vehicle

Trajectory parameters (including the position, velocity, and attitude angles of a vehicle) and air data (consisting of the flow angles, the Mach number, and the freestream static pressure) are vital data for the analysis and evaluation process in the hypersonic flight tests. This paper describes a data fusion estimation algorithm for a flush air data sensing system/inertial navigation system/global positioning system integrated system, which is used to estimate the trajectory parameters and air data for an unpowered hypersonic vehicle. In the approach, the raw outputs of flush air data sensing system (i.e. the surface pressure measurements) are integrated with global positioning system results (the vehicle’s position and velocity) and inertial navigation system measurements (including the acceleration and the angular velocity measurements) by using a nonlinear Kalman filter algorithm. Firstly, the system state vector is defined with the trajectory parameters, the biases of the inertial sensors and the winds. Then, the system dynamic models are built based on the motion equations of an unpowered hypersonic vehicle, the inertial sensor error models and the wind model. Besides, the system measurement vector is designed with the global positioning system results and the flush air data sensing system raw outputs. Based on these works, the system state is directly estimated by using the cubature Kalman filter algorithm. After that, the air data is calculated based on the estimated values and a high-fidelity model of atmosphere. Simulation cases are implemented to assess the performance of the proposed algorithm. The results show that the proposed method could estimate the trajectory parameters and air data for hypersonic vehicle with a high precision.

Speed Estimation using Smartphone Accelerometer Data

This paper is focused on developing an algorithm to estimate vehicle speed from accelerometer data generated by an onboard smartphone. The kinetic theory tells that the integration of acceleration gives the speed of a vehicle. Thus, the integration of the acceleration values collected with the smartphone in the direction of motion would theoretically yield the speed. However, speed estimation by the integration of accelerometer data will not yield accurate results, as the accelerometer data in the direction of motion is not pure acceleration, but involves white noise, phone sensor bias, vibration, gravity component, and other effects. To account for these sources of noise and error, a calibration method that can adjust the speed at certain times or points is needed. The exact times when the vehicle stops and starts are identified and used to calibrate the estimated speed. Based on the collected sample data, the proposed method yields that the estimated speed is on average within 10 mph of the actual speed, with a lower margin at the street-level driving. This suggests that with more information to calibrate the speed, the model accuracy can be improved further.

Single Space Based Sensor Bias Estimation Using a Single Target of Opportunity

Sensor registration refers to the estimation/compensation of systematic (bias) errors, in contrast to the random errors from sensor noise. Various methods have been proposed for bias estimation of multiple optical sensors using common targets of opportunity. However, the proposed solutions required the use of multiple (two or more) optical sensors and the need to solve the data association problem arising from the fusion of measurements from multiple sensors. In order to remove these constraints, we provide in this paper a new methodology using a single exoatmospheric target of opportunity seen in a single satellite borne sensor's field of view to estimate the sensor's biases simultaneously with the state of the target. The satellite-based sensor sees the target from a changing direction as a function of its position, allowing the target in this nonlinear tracking system to be observable. The sensor provides the line of sight (LOS) measurements of azimuth and elevation to the target. Sensor pointing calibration is the key precondition for accurate tracking of a target in a space-based system. Statistical tests on the results of simulations, and the evaluation of the Cramer–Rao lower bound (CRLB) on the covariance of the bias estimates show that this method is statistically efficient.

Monitoring sedimentation of magnetorheological fluids using a vertical axis monitoring system with a low aspect ratio sensor coil**This research was conducted at the University of Maryland while the first author was a visiting student.

Adaptive energy absorbers (EAs) utilizing magnetorheological fluids (MRFs) are currently being investigated for severe impact or shock mitigation problems because magnetorheological energy absorbers can adjust stroking load to account for severity of impact and payload mass. Utilizing MRFs in such EAs requires a highly stable suspension that maintains a uniform concentration. Suspension stability of MRFs can be studied using a MRF column and an automated vertical axis inductance monitoring system (AVAIMS), where an inductance sensor is translated up and down the vertical MRF column to track the mud-line, defined as the boundary between the clarified fluid at the top of the column and the MRF below. The rate of descent of the mud-line is typically referred to as the sedimentation rate of the MRF. In this paper, a refined inductance sensor is developed that features a low aspect ratio coil to better localize rapid changes in concentration or sedimentation zone boundaries, as well as to improve symmetry of the applied magnetic field in the MRF sample enclosed by the sensor. This low aspect ratio solenoid (LARS) sensor was developed to measure the vertical distribution of the concentration of carbonyl iron particles in the MRF column. Compared with the high aspect ratio solenoid sensor used in our prior work, the results of FEM simulation and sedimentation experiments demonstrate that the LARS sensor was better able to localize rapid changes in concentration or density. Using the AVAIMS with the refined LARS sensor, a method was developed, based on the measured concentration gradient profile, to identify sedimentation zone boundaries in an MRF column, and these results were compared to our prior work using the measured concentration profile only. Sedimentation zone boundaries that are consistent with Kynch’s sedimentation theory were obtained using the concentration gradient profile method, such as monotonically descending mud-line, linearly ascending gel-line, and linearly ascending cake-line. Key metrics to characterize the time histories of the sedimentation zone boundaries are measured including mud-line descent rate, gel-line ascent rate, and cake-line ascent rate. Identification of sedimentation zone boundaries using the LARS sensor in conjunction with the concentration gradient profile method exhibited two main advantages including the direct measurement and improved localization of the large concentration change that occurs at a sedimentation zone boundary, and the elimination of sensor bias.

Runway Relative Positioning of Aircraft with IMU-Camera Data Fusion

Abstract In this article the challenge of providing precise runway relative position and orientation reference to a landing aircraft based-on monocular camera and inertial sensor data is targeted in frame of the VISION EU H2020 research project. The sensors provide image positions of the corners of the runway and the so-called vanishing point and measured angular rate and acceleration of the aircraft. Measured data is fused with an Extended Kalman Filter considering measurement noise and possible biases. The developed method was tested off-line with computer simulated data from simulation of the aircraft and the processing of artificial images. This way the image generated noise and the uncertainties in image processing are considered realistically. Inertial sensor noises and biases are generated artificially in the simulation. A large set of simulation cases was tested. The results are promising so completing instrumental landing system and GPS with the estimates can be a next step of development.

Differentiator-based velocity observer with sensor bias estimation: an inverted pendulum case study

In this paper we consider the problem of velocity estimation and stabilization for balancing an inverted pendulum equipped with a reaction wheel. A homogeneous differentiator is proposed for velocity estimation, and it is shown that a bias in sensor readings yields steady-state estimation error. The proposed observer is augmented with a reduced-order bias estimator and local asymptotic stability of the coupled observers is shown. The proposed solution is tested and compared with another approach on an experimental setup.

An iterative optimization method for estimating accelerometer bias based on gravitational apparent motion with excitation of swinging motion.

Field calibration is an important method to guarantee the accuracy of a strapdown inertial navigation system. Zero velocity update based on the zero-velocity constraint when the carrier is without translational motion is a typical system-level calibration method. In zero velocity update, there is a coupling between biases and horizontal misalignment angles. The accuracy of horizontal misalignment angles is determined by the equivalent accelerometer biases in horizontal directions, which means that improving the accuracy of horizontal angles needs accurate calibration of accelerometer biases. Meanwhile, alignment with gravitational apparent motion is widely used taking advantages of its alignment ability in a swinging condition. But it is an analytical method and cannot calibrate sensor biases and is always dealt as a coarse alignment method. In order to calibrate accelerometer biases and utilize advantages of the alignment method with gravitational motion, a method to estimate accelerometer biases based on an iterative optimization method and gravitational apparent motion is presented in this paper. First, accelerometer biases are introduced to calculate apparent acceleration and an objective function is constructed. Then, Newton's iteration is applied to iteratively optimize the parameters describing gravitational apparent motion and accelerometer biases. As revealed by the theoretical analysis and experimental results, different patterns of gravity and accelerometer biases will be generated when the carrier exhibits a swinging motion; thus, the convergence of the proposed algorithm will be ensured. After accelerometer biases are removed, initial alignment performed with the gravitational apparent motion reconstructed by the estimated parameters gives nearly zero horizontal misalignment angles.

Light Sensing Enhancement and Energy Saving Improvement in Concentric Double-MIS(p) Tunnel Diode Structure With Inner Gate Outer Sensor Operation

Double-metal–insulator–semiconductor tunnel diodes with concentric structure are able to exhibit transistor and light sensor behavior. Generally, the outer ring is used to serve as a control gate and supply additional charges to the inner sensor through coupling. However, there is not yet any discussion about the contrary situation in exchanging the conventional role of the inner device and the outer ring. In this paper, we compare two operating situations with no other variants involved. Comparing the results of them, we find that when the inner device plays as a control gate and the outer ring being a sensor (i.e., inner gate outer sensor), the asymmetric coupling effect can make the outer sensor achieve much higher light-to-dark current ratio, however, only need nearly half of the sensor bias under the same control gate bias. In addition, further calculation of total power consumption shows that there is no larger power needed behind this more sensitive performance compared with the conventional operation.

Long-Term Inertial Navigation Aided by Dynamics of Flow Field Features

A current-aided inertial navigation framework is proposed for small autonomous underwater vehicles in long-duration operations ( $>$ 1 h), where neither frequent surfacing nor consistent bottom tracking is available. We instantiate this concept through mid-depth underwater navigation. This strategy mitigates dead-reckoning uncertainty of a traditional inertial navigation system by comparing the estimate of local ambient flow velocity with preloaded ocean current maps. The proposed navigation system is implemented through a marginalized particle filter where the vehicle's states are sequentially tracked along with sensor bias and local turbulence that is not resolved by general flow prediction. The performance of the proposed approach is first analyzed through Monte Carlo simulations in two artificial background flow fields, resembling real-world ocean circulation patterns, superposed with smaller scale turbulent components with Kolmogorov energy spectrum. The current-aided navigation scheme significantly improves the dead-reckoning performance of the vehicle even when unresolved small-scale flow perturbations are present. For a 6-h navigation with an automotive-grade inertial navigation system, the current-aided navigation scheme results in positioning estimates with under 3% uncertainty per distance traveled (UDT) in a turbulent double-gyre flow field, and under 7.3% UDT in a turbulent meandering jet flow field. Further evaluation with field test data and actual ocean simulation analysis demonstrates consistent performance for a 6-h mission, positioning result with under 25% UDT for a 24-h navigation when provided direct heading measurements, and terminal positioning estimate with 16% UDT at the cost of increased uncertainty at an early stage of the navigation.