Sensor Bias Research Articles

Sensor Bias Fault Diagnosis for a Class of Nonlinear Uncertain Hybrid Systems

This paper presents a sensor bias fault diagnosis approach for a class of hybrid systems with nonlinear uncertain discrete-time dynamics, measurement noise, and autonomous and controlled mode transitions. The proposed approach uses an observer based on a modified hybrid automaton framework and a fault detection scheme that employs a filtering method tighter mode-dependent thresholds for the detection of sensor faults (even with small magnitude). An autonomous guard events identification (AGEI) module is also developed and linked with both the fault detection scheme and the hybrid observer to eliminate any false alarms due to autonomous mode transitions and allow effective mode estimation. Finally, an adaptive sensor fault estimation scheme is included, which is activated once a fault is detected to isolate and estimate the sensor bias fault magnitude.

State estimation for a locally unobservable parameter-varying system: one gradient-based and one switched solutions

This work is motivated by a case study of a mechanical system where a sensor bias yields loose of observability for certain values of time-varying parameters. Two solutions are proposed: a nonlinear gradient-based observer that requires the persistency of excitation of the system trajectories and a switched observer that imposes an average dwell-time requirement. For both observers, asymptotic convergence of the estimates is proven. The theoretical results are supported by illustrative numerical simulations.

Fusion identification and estimation of multisensor multichannel AR signals with missing measurements and sensor biases

This paper studies the problem of fusion identification and estimation for multisensor multichannel autoregressive (AR) signals with unknown missing measurement rates, model parameters (MPs), sensor biases and measurement noise variances. Optimal local filters, cross-covariance matrices (CCMs), and a distributed fusion filter for AR signal are presented when the system model is accurately known, respectively. A self-tuning (ST) fusion filter is presented when MPs of AR signal, sensor biases, missing measurement rates and measurement noise variances in the system model are unknown. First, MPs of AR signal and sensor biases are identified by using a multi-dimensional recursive extended least squares (MRELS) algorithm. Further, distributed fusion estimates of MPs of AR signal are obtained by using a matrix-weighted optimal fusion estimation algorithm in the sense of linear unbiased minimum variance (LUMV). Then, receiving measurement rates and measurement noise variances are identified by correlation functions. Finally, substituting the identified parameters into the proposed optimal filtering algorithms, a matrix-weighted self-tuning (ST) fusion filtering algorithm is obtained. An example verifies the effectiveness of algorithms.

DETECTION OF FORWARD PROPULSION USING A SINGLE ACCELEROMETER DURING WALKING IN OLDER POPULATION

In the geriatric population, diminished ankle joint moment and weak plantar flexor can contribute to inadequate forward propulsion and negatively impact gait performance, which can lead to poor energetic efficiency. Detection of propulsion phase can help identify gait normality and guide rehabilitation therapy to improve functional performance. Current methods have limited application in daily life and unsuitable for continuous monitoring. In this study, we aim to develop algorithms based on a single sensor attached to the shin to accurately detect propulsion phase. Six elderly (age: 73 years, BMI: 30.4) were recruited. Participants walked at their normal pace while wearing a plantar pressure system and an accelerometer on the shin. The pressure data was used to define the beginning of the propulsion phase when the pressure switched from the heel to the forefoot. A wavelet algorithm was developed to automatically detect the start and end points of propulsion phase using an accelerometer. The Bland-Altman method was used to evaluate the agreement between these methods. Pearson’s Coefficient was used to quantify the correlation. Based on the Bland-Altman analysis, A high agreement was obtained between the proposed method using accelerometer and pressure sensor (bias =9 ms, precision = 30 ms). Both algorithms are significantly correlated (r = 0.85, p<0.05). This study presents an innovative algorithm to automatically detect the propulsion phase for older adults during walking. Using wearable could facilitate the capture of propulsion phase during living activity, which might provide more insights into the mechanism of walking during rehabilitation therapy.

Adaptive bias and attitude observer on the special orthogonal group for true-north gyrocompass systems: Theory and preliminary results

This article reports an adaptive sensor bias observer and attitude observer operating directly on for true-north gyrocompass systems that utilize six-degree-of-freedom inertial measurement units (IMUs) with three-axis accelerometers and three-axis angular rate gyroscopes (without magnetometers). Most present-day low-cost robotic vehicles employ attitude estimation systems that employ microelectromechanical system (MEMS) magnetometers, angular rate gyros, and accelerometers to estimate magnetic attitude (roll, pitch, and magnetic heading) with limited heading accuracy. Present-day MEMS gyros are not sensitive enough to dynamically detect the Earth’s rotation, and thus cannot be used to estimate true-north geodetic heading. Relying on magnetic compasses can be problematic for vehicles that operate in environments with magnetic anomalies and those requiring high-accuracy navigation as the limited accuracy ( error) of magnetic compasses is typically the largest error source in underwater vehicle navigation systems. Moreover, magnetic compasses need to undergo time-consuming recalibration for hard-iron and soft-iron errors every time a vehicle is reconfigured with a new instrument or other payload, as very frequently occurs on oceanographic marine vehicles. In contrast, the gyrocompass system reported herein utilizes fiber optic gyroscope (FOG) IMU angular rate gyro and MEMS accelerometer measurements (without magnetometers) to dynamically estimate the instrument’s time-varying true-north attitude (roll, pitch, and geodetic heading) in real-time while the instrument is subject to a priori unknown rotations. This gyrocompass system is immune to magnetic anomalies and does not require recalibration every time a new payload is added to or removed from the vehicle. Stability proofs for the reported bias and attitude observers, preliminary simulations, and a full-scale vehicle trial are reported that suggest the viability of the true-north gyrocompass system to provide dynamic real-time true-north heading, pitch, and roll utilizing a comparatively low-cost FOG IMU.

Exactly Decoupled Kalman Filtering for Multitarget State Estimation With Sensor Bias

The problem of multisensor multitarget state estimation in the presence of constant but unknown sensor biases is investigated. The classical approach to this problem is to augment the state vector to include the states of all the targets and the sensor biases, and then implement an augmented state Kalman filter (ASKF). In this paper, we propose a novel decoupled Kalman filtering algorithm. The decoupled Kalman filtering first processes each target in a separate branch, namely the single-target Kalman filtering branch, where the single-target states and the sensor biases are estimated. Then the bias estimate is refined by fusing the former bias estimates across all the single-target Kalman filtering branches. Finally, the refined bias estimate is fed back to each single-target Kalman filtering branch to improve the target state estimation. We prove that the proposed decoupled Kalman filtering is exactly equivalent to the ASKF in terms of the estimation results under a usual initial condition. The equivalence is also confirmed via the numerical example. Moreover, we further validate the proposed algorithm using the field experimental data of a multistatic passive radar.

Radar/ESM anti‐bias track association algorithm based on track distance vector detection

To address radar/ESM track association problem in the presence of sensor biases and different targets reported by different sensors, an anti-bias track association algorithm based on track distance vectors detection is proposed according to the statistical characteristics of Gaussian random vectors. The state estimation decomposition equation is first derived in MPC. The track distance vectors are obtained by the real state cancellation method. Second, in order to eliminate most non-homologous target tracks, the rough association is performed according to the features of the azimuthal rate and inverse-time-to-go (ITG). Finally, the track-to-track association of radar and ESM is extracted based on track distance vectors chi-square distribution. The effectiveness of the proposed algorithm are verified by Monte–Carlo simulation experiments in the presence of sensor biases, targets densities, and detection probabilities.

Development and application of hardware-in-the-loop simulation for the HVAC systems

The hardware-in-the-loop (HIL) employs the real controller and true signal transmission, which is efficient to test control algorithms for the situation that is inconvenient to conduct experiments. The design method of hardware-in-the-loop is presented for buildings, in which the HVAC system is simulated while the control system including controllers, A/D and D/A modules are real. The controllers embedded with control algorithms are integrated with the simulation of HVAC system. The HVAC HIL test platform is constructed so as to evaluate the candidate control strategies. The feature of HVAC HIL test platform is compared with the pure TRNSYS based simulation. The comparison tests show that pure simulation doesn’t match the true control process while the HIL platform does and provides the credible control response. With real signal transmission and controllers, the control algorithms can be tested authentically. Moreover, the fault detection and diagnosis (FDD) models using basic and improved principal component analysis (PCA) are evaluated in HVAC HIL platform. Through HIL tests, the unobservable application problem of basic PCA model is discovered. An improved wavelet-PCA model is developed, which has the satisfied efficiency to detect the various biases of sensors.

Sensor Bias Estimation for Track-to-Track Association

In this letter, we propose a heuristic method to address sensor bias estimation to improve track-to-track association accuracy. A novel multi-parameter cost function is derived from rigid transformation function and it is minimized by the covariance matrix adaptation evolution strategies algorithm. The proposed method is compared to other recognized methods under various simulation scenarios. The comparison results confirm that our approach accurately estimates sensor biases, provides higher correct association probability with low computational load compared to the competitor methods, and also it is robust to high missed and false track rates.

Underwater Position and Attitude Estimation Using Acoustic, Inertial, and Depth Measurements

This article considers the problem of constructing an observer for estimating position, velocity, attitude, underwater wave speed, rate sensor bias, and accelerometer bias that has both proven stability and close-to-optimal performance with respect to noise. The observer takes pseudorange, pseudorange difference, depth, and inertial measurements as input, and has a cascade structure for which the equilibrium point is proven to be locally exponentially stable due to the singularities in the attitude representation. The design of the observer is based on the exogenous Kalman filter principle, in which estimators with proven stability provide a linearization point for a linearized Kalman filter, to achieve both proven stability and close-to-optimal noise properties. Experimental validation is provided, with ground truth values generated by a camera positioning system with millimeter accuracy. The observer is compared to an extended Kalman filter and to a nonimplementable linearized Kalman filter using the true state as the linearization point, and the estimation error is almost identical to the linearized Kalman filter using the true state as a linearization point.

The Interannual Calibration and Global Nighttime Light Fluctuation Assessment Based on Pixel-Level Linear Regression Analysis

The Operational Linescan System (OLS) carried by the National Defense Meteorological Satellite Program (DMSP) can capture the weak visible radiation emitted from earth at night and produce a series of annual cloudless nighttime light (NTL) images, effectively supporting multi-scale, long-term human activities and urbanization process research. However, the interannual instability and sensor bias of NTL time series products greatly limit further studies of lighting data in time series with OLS. Several calibration models for OLS have been proposed to implement interannual corrections to improve the continuity and consistency of time series NTL products; however, due to the subjective factors intervention and insufficient automation in the calibration process, the interannual correction study of NTL time series images is still worth being developed further. Therefore, to avoid the involvement of subjective factors and to optimize the Pseudo-Invariant Features (PIF) identification, an interannual calibration model Pixel-based PIF (PBPIF) is proposed, which identifies PIF by pixel fluctuation characteristics. Results show that a PBPIF-based model can reduce subjective interference and improve the degree of automation during the NTL interannual calibration process. The calibration performance evaluation based on Total Sum of Lights (TSOL) and Sum of the Normalized Difference Index (SNDI) shows that compared to the traditional PIF-based (tPIF-based) and Ridgeline Sampling Regression based (RSR-based) models, the PBPIF-based one achieves better performance in reducing NTL interannual turbulence and minimizing the deviation between sensors. In addition, based on the corrected NTL time series products, pixel-level linear regression analysis is implemented to maximize the potential of the NTL resolution to produce global Light Intensity Change Coefficient (LICC). The results of global LICC can be widely applied to the detailed study of the characteristics of economic development and urbanization.

Proposal of a Geometric Calibration Method Using Sparse Recovery to Remove Linear Array Push-Broom Sensor Bias.

The rational function model (RFM) is widely used in the most advanced Earth observation satellites, replacing the rigorous imaging model. The RFM method achieves the desired calibration performance when image distortion is caused by long-period errors. However, the calibration performance of the RFM method deteriorates when short-period errors—such as attitude jitter error—are present, and the insufficient and uneven ground control points (GCPs) can also lower the calibration precision of the RFM method. Hence, this paper proposes a geometric calibration method using sparse recovery to remove the linear array push-broom sensor bias. The most important issue regarding this method is that the errors related to the imaging process are approximated to the equivalent bias angles. By using the sparse recovery method, the number and distribution of GCPs needed are greatly reduced. Meanwhile, the proposed method effectively removes short-period errors by recognizing periodic wavy patterns in the first step of the process. The image data from Earth Observing 1 (EO-1) and the Advanced Land Observing Satellite (ALOS) are used as experimental data for the verification of the calibration performance of the proposed method. The experimental results indicate that the proposed method is effective for the sensor calibration of both satellites.

Can Energy Storage Pack Hybridization Improve the Best Theoretically-Achievable Battery State Estimation Accuracy?

This article examines the degree to which the creation of a series hybrid ultracapacitor-battery string can improve achievable battery state estimation accuracy. The article is motivated by the existence of fundamental information-theoretic limits on the degree to which one can use input/output current/voltage data to estimate a battery's internal states (e.g., state of charge, state of health, etc.). Previous literature quantifies these limits rigorously using Fisher information theory [1] – [5]. One conclusion of this quantification is that it is particularly difficult to obtain accurate battery state estimates during phase transition processes, such as the phase transition that occurs in lithium iron phosphate electrodes during charge/discharge. The problematic effect, in this context, is the very small dV/dQ slope, or effective electrical elastance, of the battery. Poor battery elastance complicates battery state estimation accuracy by directly contributing to the worsening of the best-achievable battery state estimation accuracy. The literature already shows this through the use of Fisher information analysis which shows the dependence of the best-achievable battery state estimation accuracy and the effective battery elastance. Building on the above literature, the key conjecture motivating this article is that the creation of hybrid series ultracapacitor-battery strings can improve battery state estimation accuracy substantially by furnishing a significant dV/dQ system behavior. We derive this conclusion analytically, using Fisher information analysis. Then consider estimating the lithium-ion battery state of charge using input current and output battery voltage, where the current measurement is biased and the voltage sensor has zero-mean, random, Gaussian noise. By comparison between the Cramer-Rao lower bound of both the battery-only and ultracapacitor-battery hybrid, we demonstrate improvements in theoretically-achievable initial charge accuracy as well as current bias, and in turn improve the battery SOC estimation. This conclusion is validated using a Monte Carlo simulation study. Performing least square method to estimate both initial charge in the battery and current sensor bias to achieve point clouds with and without an ultracapacitor in series, as shown in Figure 1a. One can conclude that there is: (i) a dependence between the estimated current bias and initial charge; (ii) a large condition number of the Fisher information metric which is reflected in the thin shape of the cloud ellipse; (iii) significant decrease in the estimation error after adding a series ultracapacitor into the system. Finally, the article presents an experimental ultracapacitor-battery validation study, as shown in Figure 1b. The full experiment setup includes a system of three parallel 400F ultracapacitors in series with a single 0.6Ah LFP cell. Experimental data is used to solve the optimization problem of minimizing the mean squared error of physical and simulation system outputs with respect to estimated initial charge and current bias. Results show clear improvement on the estimation accuracy. Figure 1. (a) Monte Carlo simulation results comparison (above) (b) Experiment setup structure (below) This article answers the title question by providing quantifiable evidence of improved state estimation through theory, simulation and experiment. Figure 1

Modeling of multi-sensor tightly aided BDS triple-frequency precise point positioning and initial assessments

The BeiDou global navigation satellite system (BDS), which is the first satellite navigation system that provides triple-frequency signals on B1, B2, and B3 for civil applications, has been applied widely around the Asian-Pacifica region. The current BDS precise point positioning (PPP) approaches are mainly based on the B1&B2 dual-frequency observations. To make full use of BDS’ triple-frequency observations, the motion sensors measurements, and the platform motion information, this paper proposes an inertial sensor, odometer, and heading measurement tightly aided BDS triple-frequency PPP model. In this model, inertial sensor biases, odometer scale factor, residuals of slant ionospheric delays, and inter-frequency code biases are estimated simultaneously in a unique extended Kalman filter. The Rauch-Tung-Striebel (RTS) smoother is further adopted to reduce the solution's noises and enhance the stability and relative measuring accuracy. To evaluate the capability of this method, a set of triple-frequency BDS raw observations, inertial measurements, odometer data, and heading measurements collected by a customized hardware system on Lanzhou-Urumqi high speed railway track in China, are processed and analyzed. Results illustrated that both positioning accuracy and cycle slip detection capability are upgraded significantly by applying B3 frequency observations in BDS PPP. About 13–55% position accuracy enhancements from B3 observations, inertial sensors, and RTS smoother, and over 70% heading improvements from the aids of heading measurements can be obtained. Moreover, such multi-sensor tight integration system can directly provide millimeter-level positioning accuracy in term of repeatability and provide sub-millimeter-level accuracy indirectly by transforming attitude solutions into distance solutions. Such accuracy is much higher than the state-of-art GNSS and such method presents potential capability in 3D geometry measuring.

Simultaneous spatiotemporal bias and state estimation for asynchronous multi‐sensor system

Elimination of spatiotemporal bias of asynchronous multiple sensors is the foundation of accurate multi-sensor data fusion. In this article, a sequential processing simultaneous spatiotemporal bias and state estimation algorithm for asynchronous multi-sensor system is proposed. The spatiotemporal bias is combined with target state to obtain an augmented state vector, and the augmented state model is formulated. For asynchronous multi-sensor with known but different sampling periods, a sequential processing method is proposed to handle the multiple measurements. The relationship of sensor measurements, target state and spatiotemporal bias is analysed, and the corresponding measurement model is formulated. A novel algorithm, in which the unscented Kalman filter is used to handle the nonlinearity between the augmented measurement and state vectors, is proposed to jointly estimate the spatiotemporal bias and target state. Simulation results verify the effectiveness of the proposed algorithm.

An Adaptive Approach to Real-Time Estimation of Vehicle Sideslip, Road Bank Angles, and Sensor Bias

Robust estimation of vehicle sideslip angle is essential for stability control applications. However, the direct measurement of sideslip angle is expensive for production vehicles. This paper presents a novel sideslip estimation algorithm which relies only on sensors available on passenger and commercial vehicles. The proposed method uses both kinematics and dynamics vehicle models to construct extended Kalman filter observers. The estimate relies on the results provided from the dynamics model observer where the tire cornering stiffness parameters are updated using the information provided from the kinematics model observer. The stability property of the proposed algorithm is discussed and proven. Finally, multiple experimental tests are conducted to verify its performance in practice. The results show that the proposed approach provides smooth and accurate sideslip angle estimation. In addition, our novel algorithm provides reliable estimates of bank angles and lateral acceleration sensor bias.

Field Sensor Bias Calibration With Angular-Rate Sensors: Theory and Experimental Evaluation With Application to Magnetometer Calibration

Field sensors, such as magnetometers and accelerometers, are widely used sensors for attitude estimation, yet their accuracy is limited by sensor measurement bias. This paper reports a novel methodology for estimating the sensor bias of three-axis field sensors. Our approach employs three-axis angular velocity measurements from an angular-rate gyroscope to estimate the three-axis field sensor measurement bias that, when properly calibrated, can significantly improve attitude estimation. We report three methods implementing this approach based on batch linear least squares, real-time Kalman filter, and real-time adaptive identification. Assuming the field is constant, our methods impose less restrictive conditions for the movements of the instrument required for calibration than previously reported methods, do not require a priori knowledge of the field (e.g., the magnitude of the local magnetic field) or the attitude of the instrument, and also ensure convergence for the estimated parameters. The proposed methods are evaluated and compared with the previously reported methods with numerical simulation and in a comparative laboratory and field experimental evaluation with the sensors onboard an underwater robot vehicle. Finally, as an application example of the magnetometer bias calibration, the proposed methods are used to improve the estimation of the position of an underwater vehicle in Monterey Bay at 2800 in depth.

Sensor Bias Estimation Based on Ridge Least Trimmed Squares

A robust sensor bias estimation approach, named as the ridge least trimmed squares (RLTS), is proposed. Combing the advantages of ridge regression and least trimmed squares, RLTS can solve the sensor bias estimation problem with the presence of misassociations and ill-conditioning. Simulation results verify the effectiveness of the proposed approach.

Fault detection and isolation in batteries power electronics and chargers

This paper focuses on the residual-based fault detection and isolation (FDI) in batteries power electronics and chargers. Currently, isolation of multiple faults is performed by generating a bank of residuals, one residual signal for each fault. It is shown that, with a combination of different residual evaluation functions, various battery and electronics faults, including battery short/open circuit, sensor biases, input voltage drop, and switches short/open circuit, can be detected and isolated by using the magnitude and slope of a residual signal or its norm that is generated from the battery voltage. In this paper, the constant-current constant-voltage (CCCV) battery chargers based on buck and boost converters are studied. The FDI systems with observer- and historical-based residual generation methods are designed and simulation results are discussed.

Development of a charge pump for sensor biasing in a Serial Powering scheme for the ATLAS pixel detector upgrade

CMOS monolithic pixel detector technology is one of the options considered for the outer layer of an upgraded ATLAS pixel detector in 2026. In this upgrade pixel detector modules will be powered in series by a constant current source to reduce power losses and material budget. On-chip shunt regulators generate the local 1.8 V supply voltage from the input current to provide power to the integrated circuits. The sensor bias for monolithic sensors is often limited and not sufficiently large to allow a common bias for all sensors in the serial powering chain. In this paper, we give an introduction to the serial powering strategy for CMOS detectors with emphasis on the design and simulation results of a regulated charge pump circuit for sensor biasing. Two prototypes operating with a pumping frequency of 640 MHz, one with 6-stages and one with 19-stages, were designed and fabricated in a modified TowerJazz 0.18 μm CMOS imaging technology to provide negative bias down to − 6 V and − 20 V, respectively. Simulation results demonstrate good performance of the charge pump circuit which could be used to bias the CMOS sensor.