Bias Compensation Research Articles

Lithium-Ion Battery Parameters and State of Charge Joint Estimation Using Bias Compensation Least Squares and the Alternate Algorithm

For safe and efficient operation of electric vehicles (EVs), battery management system is essential. Nevertheless, a challenge lying in battery management systems is how to obtain an algorithm for state of charge (SOC) estimation that has both high accuracy and low computational cost. For this purpose, the battery parameters and SOC joint estimation algorithm based on bias compensation least squares and alternate (BCLS-ALT) algorithm are proposed in this paper. The battery model parameters are identified online using the bias compensation least squares (BCLS), while the SOC is estimated applying the alternate (ALT) algorithm, which can switch the computational logic between H-infinity filter (HIF) and ampere-hour integral (AHI) to improve the computational efficiency and accuracy. The experimental results show that the accuracy of the SOC estimated by the BCLS-ALT algorithm is the highest, and the computational efficiency is also high, with the switching threshold SOCALT being set to 25%. Despite the 20% initial error and the 10% current drift, the proposed BCLS-ALT algorithm can obtain high accuracy and robustness of SOC estimation under different ambient temperatures and dynamic load profiles.

Experimental Results and Posterior Cramér–Rao Bound Analysis of EKF-Based Radar SLAM With Odometer Bias Compensation

Radar mounted on a moving vehicle returns time-varying detections corresponding to unstable scattering points, unlike optical sensors, which produce relatively stable detections. We present an efficient extended Kalman filter-based simultaneous localization and mapping (EKF-SLAM) algorithm for radar, utilizing new techniques of clustering and sifting the time-varying detections. Velocity bias and yaw rate bias, which are inherent in any odometer are also estimated and compensated using the same EKF. For theoretical performance evaluation, the posterior Cramér-Rao bound (PCRB) for SLAM with odometer bias estimation is derived and compared with the root-mean-squared errors (RMSEs), with and without bias estimation. The simulation results show that the RMSE for SLAM with bias estimation is the closest to the PCRB. The proposed algorithm is also verified experimentally with field data. The comparison with the ground truth trajectory obtained from a differential global positioning system shows that the proposed algorithm yields an accurate trajectory estimate, even under large odometer bias. Also, the real-time capability of the proposed algorithm is verified.

Attitude dynamics aiding for three-dimensional passive target tracking of strap-down seeker based on instrumental variable Kalman filter

The accuracy of three-dimensional (3D) passive target tracking under strap-down system is usually affected by the measurement accuracy of attitude angular rate and attitude angle. In order to save the problem, a novel 3D passive target tracking method based on instrumental variable Kalman filter (IVKF) aided by the attitude dynamic is proposed. At first, the maneuvering target motion model is established based on the “current” statistical model and the filtering equation of MEMS inertial measurement unit (IMU) is also set up. Then, linearize the nonlinear state equations and replace the nonlinear measurement equations with pseudolinear equations. The 3D pseudolinear Kalman filter (PLKF) algorithm is derived according to the linear Kalman filter (KF). To counter the severe bias problems with PLKF, bias compensation and recursive instrumental variable (IV) methods are considered. In order to enhance observability of the system, a 3D motion tracking sliding-mode guidance law is deduced. Finally, some mathematical simulations were made to verify the effectiveness of the proposed method. The simulation results show the effect of the measurement accuracy and complexity of the algorithm are reduced, which proves the validity of the method.

Maximum Likelihood Iterative Algorithm for Hammerstein Systems with Hard Nonlinearities

In this paper, we consider several iterative algorithms for Hammerstein systems with hard nonlinearities. The Hammerstein system is first simplified as a polynomial identification model through the key term separation technique, and then the parameters are estimated by using the maximum likelihood (ML) based gradient-based iterative algorithm. Furthermore, an ML least squares auxiliary variable algorithm and an ML bias compensation gradient-based iterative algorithm are developed to identify the saturation system with colored noise. Simulation results are included to illustrate the effectiveness of the proposed algorithms.

An Assessment of Impact of Adaptive Notch Filters for Interference Removal on the Signal Processing Stages of a GNSS Receiver

With the fast growing diffusion of real-time high-accuracy applications based on the global navigation satellite system (GNSS), the robustness of GNSS receiver performance has become a compelling requirement. Disruptive effects can be induced to signal processing stages of GNSS receivers due to the disturbances from radio frequency interference (RFI), even leading to a complete outage of the positioning and timing service. A typical RFI threat to GNSS signals is represented by portable jammers, which transmit swept-frequency (chirp) signals in order to span the overall GNSS bandwidth. The implementation in the receivers of adaptive notch filters (ANFs) for chirp cancellation has been extensively investigated and proved to be an efficient countermeasure. However, the performance of the ANF is strongly dependent on its configuration setup. Inappropriate parameter settings of the ANF for interference removal may induce severe distortion to the correlation process. In addition, an effective mitigation will still introduce a vestigial signal distortion contributed by the residual unmitigated chirp and the ANF operation itself, being not negligible for high-accuracy solutions. This article addresses the detailed analysis for assessing the effects of interference mitigation by notch filtering. A bias compensation strategy is proposed, wherein for each pseudorandom noise, the biases due to parameter settings of the notch filter are estimated and compensated. The impact of using the ANF operation on chirp signals at the acquisition and tracking stages of GNSS receivers is analyzed. On the basis of the three proposed metrics, the effects can be quantitatively estimated to depict a complete picture of the most influential parameters of the chirp and the ANF configurations, as well as the optimal achievable performance at the acquisition and tracking stages.

Analysis and Compensation of Bias Drift for a Micromachined Spinning-rotor Gyroscope with Electrostatic Suspension.

Bias stability is one of primary characteristics of precise gyroscopes for inertial navigation. Analysis of various sources of the bias drift in a micromachined electrostatically suspended gyroscope (MESG) indicates that the bias stability is dominated by the temperature-induced drift. The analytical results of temperature drift resulting from the rotor structure and capacitive position sensing electronics are modeled and analyzed to characterize the drift mechanism of the MESG. The experimental results indicate that the bias drift is mainly composed of two components, i.e., rapidly changing temperature drift and slowly changing time drift. Both the short-term and long-term bias drift of the MESG are tested and discussed to achieve online bias compensation. Finally, a neural network based-bias compensation scheme is presented and verified experimentally with improved bias stability of the MESG.

Positioning Accuracy of the Shearer Based on a Strapdown Inertial Navigation System in Underground Coal Mining

Automation and intelligent coal mining comprise the most important fields in coal mining technology research. The key to automation and intelligent coal mining is the automated mining of the working face, and accurate positioning of the shearer is one of the most important technologies in the automated mining process. However, significant defects in non-inertial navigation system (INS)-based methods have led to low positioning accuracy. In this paper, we propose a new shearer positioning technology to further improve the positioning accuracy of the shearer and monitor the shearer position in real time. The shearer positioning system proposed is based on the strapdown inertial navigation system (SINS). We conducted shearer positioning experiments with gyroscopes, accelerometers, and other inertial navigation instruments. The experimental results are thoroughly studied on the basis of error compensation techniques such as inertial instrument zero bias compensation and Kalman filter compensation. Compared with traditional shearer positioning technology, the experimental results show that the shearer positioning system based on SINS can achieve more accurate positioning of the shearer and can accurately reflect the running characteristics of the shearer working the mining face.

Enhanced online model identification and state of charge estimation for lithium-ion battery under noise corrupted measurements by bias compensation recursive least squares

In online battery model identification by recursive least squares (RLS), the identification biases are generated by the noises in the voltage and current measurements, further resulting in the accuracy degradation of model-based state of charge (SOC) estimation. Firstly, the detailed formula derivation presents the relationship between noise variances and identification biases in least squares. Then, through the practical identification on a general battery model, the consistent results from the formulas and simulations both adequately and quantitatively verify that the model identified by RLS is biased, when either only one of voltage and current measurements or both are corrupted by noises. To further assess the noise effects on SOC and parameter estimations, a conventional co-estimation algorithm joining RLS and extended Kalman filter (EKF) is applied into the simulations and experiments especially under noise corrupted measurements, the numerical results show that the estimation accuracy degradation generated by noises is quite considerable. Hence, bias compensation RLS and EKF co-estimation algorithms are proposed to alleviate the impact of the noises. Simulation and experiment studies show that the proposed algorithms can compensate the model identification biases caused by noises and can enhance SOC estimation accuracy under noise corrupted measurements.

Robust filtering employing bias compensated M‐estimate affine‐projection‐like algorithm

This Letter presents a bias compensated M-estimate affine-projection-like algorithm for robust adaptive filtering in case of noisy input signal and impulsive noise interference. In order to mitigate the effect of bias introduced due to noisy input signal, a bias compensation vector is derived along with robust cost function minimisation employing M-estimate and accordingly the weight update learning process of the adaptive filter has been improved. In conjunction with this, a new input noise variance estimation method is introduced using the median filter. The proposed algorithm is evaluated for acoustic echo cancellation application and compared with other existing methods. Simulation results demonstrate its effectiveness in terms of enhanced convergence and better steady-state performance in case of impulsive environment and input signal contaminated with noise.

L1 Norm Penalized Bias Compensated Linear Constrained Affine Projection Algorithm

This paper presents an l1-norm penalized bias compensated linear constrained affine projection (l1-BC-CAP) algorithm for sparse system identification having linear phase aspectin the presence of noisy colored input. The motivation behind the development of the proposed algorithm is formulated on the concept of reusing the previous projections of input signal in affine projection algorithm (APA) that makes it suitable for colored input. At First, l1-CAP algorithm is derived by adding zero attraction based on l1-norm into constrained affine projection (CAP) algorithm. Then, the proposed l1-BC-CAP algorithm is derived by addinga bias compensator into the filter coefficient update equation of l1-norm constrained affine projection (l1-CAP) algorithm to alleviate the adverse consequence of input noise on the estimation performance. Hence, the resulting l1-BC-CAP algorithm excels the estimation performance when applied to linear phase sparse system in the existence of noisy colored input. Further, this work also examines the stability concept of the proposed algorithm

Bias Compensation Model for Sensor Orientation Under Weak Conditions

The high-precision geometric positioning of satellite images is the basis for the geometric processing of remote-sensing images and acquisition of various geospatial information. It is an important premise for the wide application of high-resolution remote-sensing satellite images. To correct systematic biases in rational function models (RFMs), many compensation methods for system errors inherent of RFMs have been proposed. Thus far, the bias compensation model (BCM) is the most widely accepted method under rigorous conditions, namely narrow camera field, small off-nadir angle, and small attitude error. However, research studies on the compensation effect of the BCM under weak conditions (wide camera field, large off-nadir angle, or large attitude error) are still lacking, and some researchers commented that the BCM is inapplicable under weak conditions in the absence of experiments. This letter analyzes the effect of position and attitude errors on orientation accuracy in the image space. An experiment was conducted using data from the Gaofen-1 (GF-1) wide-field-view-4 (WFV-4) sensor to compare the proposed analysis with the traditional analysis, and the results obtained using the BCM under weak conditions were found to be consistent with our analysis rather than the traditional analysis. This confirms that the BCM can also be used under weak conditions.

A Stable Adaptive Observer for Hard-Iron and Soft-Iron Bias Calibration and Compensation for Two-Axis Magnetometers: Theory and Experimental Evaluation

This letter addresses the problem of on-line estimation and compensation of the hard-iron and soft-iron biases of a 2-axis magnetometer under dynamic motion, utilizing only biased measurements from a 2-axis magnetometer. The proposed adaptive observer formulates the relation between the true magnetic field vector and the magnetometer measurements as an algebraic system where the unknown biases enter linearly. The observer is shown to be globally stable. When the magnetometer measurements are persistently exciting (PE), the system is shown to be globally asymptotically stable, and the biases are shown to converge to their true values. The estimated biases are used to provide a calibrated magnetic field direction vector which is utilized to estimate magnetic geodetic heading. The adaptive observer is evaluated in a numerical simulation and a full-scale vehicle trial. For the proposed observer: $(i)$ knowledge of the instrument attitude is not required for sensor bias estimation, $(ii)$ zero a priori knowledge of the local magnetic field vector magnitude or vector direction is needed, $(iii)$ the system is shown to be globally stable, $(iv)$ the error system is shown to be globally asymptotically stable when the measured magnetometer signal is PE. $(v)$ magnetometer hard-iron and soft-iron bias compensation is shown to dramatically improve dynamic heading estimation accuracy.

Optimization of Ring Laser Gyroscope Bias Compensation Algorithm in Variable Temperature Environment.

In a high accuracy strapdown inertial navigation system (SINS), the ring laser gyroscope’s (RLG) bias changes and the performance decreases due to factors in the RLG’s self-heating and changes in ambient temperature. Therefore, it is important to study the bias temperature drift characteristics of RLGs in high, low, and variable temperature environments. In this paper, a composite temperature calibration scheme is proposed. The composite temperature model introduces the derivative term and the temperature derivative cross-multiplier on the basis of the static model and sets the overlap regions for the piecewise least squares fitting. The results show that the composite temperature model can compensate the bias trend term well at ambient temperature, improve the fitting accuracy, and smooth the output curve. The compensation method has a small amount of calculations and flexible parameter design. The precision of the laser gyros in one SINS is improved by about 64.9%, 15.7%, and 3.6%, respectively, which has certain engineering application value.

AOA Pseudolinear Target Motion Analysis in the Presence of Sensor Location Errors

This paper presents new pseudolinear estimation algorithms for angle-of-arrival (AOA) target motion analysis when the sensor locations are not precisely known. Sensor location errors can cause significant performance degradation for the existing pseudolinear estimator (PLE) and its variants. In particular, we analytically show that, in the presence of sensor location errors, the well-known weighted instrumental variable estimator (WIVE) is no longer asymptotically unbiased due to the non-vanishing correlation between the instrumental variable matrix and the pseudolinear noise vector. To ameliorate this bias problem, a novel bias compensation method is developed for the WIVE, which is proven to be approximately efficient for a large number of measurements under the small noise assumption. In addition, a selective-angle-measurement (SAM) strategy is integrated into the bias-compensated WIVE (BCWIVE) to strengthen the correlation between the instrumental variable matrix and the measurement matrix, alleviating the performance degradation in large AOA and sensor location noises, and unfavourable geometries. The performance advantages of the proposed BCWIVE and SAM-BCWIVE over the PLE, its WIVE variants and the maximum likelihood estimator are demonstrated by way of extensive simulation examples.

Enhancing Accuracy and Numerical Stability for Repetitive Time-Varying System Identification: An Iterative Learning Approach

Time-varying system identification is an appealing but challenging research area. Existing identification algorithms are usually subject to either low estimation accuracy or bad numerical stability. These deficiencies motivate the development of an iterative learning identification algorithm in this paper. Three distinguished features of the proposed method result in the achievement of high estimation accuracy and high numerical stability: i) recursion along the iteration axis, ii) bias compensation, and iii) singular value decomposition (SVD). Firstly, an extra iteration axis associated with the original time axis is introduced in the parameter estimation process. A norm-optimal identification approach with the balance between convergence speed and noise robustness is then proposed along the iteration axis, followed by further analysis on the accuracy and the numerical stability. Secondly, in order to eliminate the estimation bias in the presence of noise and thus to improve the accuracy, a bias compensation algorithm along the iteration axis is proposed. Thirdly, a SVD-based update algorithm for the covariance matrix is developed to avoid the possible numerical instability during iterations. Numerical examples are finally provided to validate the algorithm and confirm its effectiveness.

Research on synchronous control strategy of steer-by-wire system with dual steering actuator motors

Steer-by-wire (SBW) system with dual steering actuator motors is a novel and potential type of steering system by means of hardware fault tolerant redundancy to enhance the driving safety. The basic control strategy "road feel feedback and steering angle control" has been carried out. Aiming at the non-synchronous appearance of dual steering actuator motors, dual-motor synchronous control employing differential negative feedback method has been proposed to reduce the adverse influence of "servo fight" non-synchronous issue. In addition, considering the existence of unavoidable backlash impact, dual-motor anti-backlash control adopting variable bias compensation current method has been developed to abate the negative effect caused by backlash factors for SBW system, so that the precision of steering implementation for SBW system can be enhanced. The results of simulations and hardware-in-loop experiments are analysed and then the conclusion has been drawn that the proposed control strategy is effective and feasible.

DeepMMSE: A Deep Learning Approach to MMSE-Based Noise Power Spectral Density Estimation

An accurate noise power spectral density (PSD) tracker is an indispensable component of a single-channel speech enhancement system. Bayesian-motivated minimum mean-square error (MMSE)-based noise PSD estimators have been the most prominent in recent time. However, they lack the ability to track highly non-stationary noise sources due to current methods of a priori signal-to-noise (SNR) estimation. This is caused by the underlying assumption that the noise signal changes at a slower rate than the speech signal. As a result, MMSE-based noise PSD trackers exhibit a large tracking delay and produce noise PSD estimates that require bias compensation. Motivated by this, we propose an MMSE-based noise PSD tracker that employs a temporal convolutional network (TCN) a priori SNR estimator. The proposed noise PSD tracker, called DeepMMSE makes no assumptions about the characteristics of the noise or the speech, exhibits no tracking delay, and produces an accurate estimate that requires no bias correction. Our extensive experimental investigation shows that the proposed DeepMMSE method outperforms state-of-the-art noise PSD trackers and demonstrates the ability to track abrupt changes in the noise level. Furthermore, when employed in a speech enhancement framework, the proposed DeepMMSE method is able to outperform state-of-the-art noise PSD trackers, as well as multiple deep learning approaches to speech enhancement. Availability: DeepMMSE is available at: https://github.com/anicolson/DeepXi .

Research on synchronous control strategy of steer-by-wire system with dual steering actuator motors

Steer-by-wire (SBW) system with dual steering actuator motors is a novel and potential type of steering system by means of hardware fault tolerant redundancy to enhance the driving safety. The basic strategy road feel feedback and steering angle control has been carried out. Aiming at the non-synchronous appearance of dual steering actuator motors, dual-motor synchronous employing differential negative feedback method has been proposed to reduce the adverse influence of servo fight non-synchronous issue. In addition, considering the existence of unavoidable backlash impact, dual-motor anti-backlash adopting variable bias compensation current method has been developed to abate the negative effect caused by backlash factors for SBW system, so that the precision of steering implementation for SBW system can be enhanced. The results of simulations and hardware-in-loop experiments are analysed and then the conclusion has been drawn that the proposed strategy is effective and feasible.

A New Variable Forgetting Factor-Based Bias-Compensated RLS Algorithm for Identification of FIR Systems With Input Noise and Its Hardware Implementation

This paper proposes a new variable forgetting factor QRD-based recursive least squares algorithm with bias compensation (VFF-QRRLS-BC) for system identification under input noise. A new variable forgetting factor scheme is proposed to improve its convergence speed and steady-state mean squares error. A new method for recursive estimation of the additive noise variance is also proposed for reliable bias compensation. The mean and mean-square asymptotic behaviors of the algorithm are analyzed and a self-calibration scheme is further proposed to improve the steady-state mean squares error (MSE) due to finite sample effect. Simulations show that the proposed VFF approach offers improved tracking and steady-state MSE performance over the conventional recursive least squares method and its fixed FF counterpart. A linear array architecture is proposed for the realization of this algorithm and several hardware efficient techniques are introduced to avoid the expensive cubic root and division operations required. The proposed algorithm is validated on Xilinx Zynq®-7000 AP SoC ZC702 Field Programmable Gate Array (FPGA). For a 10-tap finite impulse response (FIR) system, the implementation requires only about 11.5k slice look-up table (LUT)s, 4.5k slice registers and 50 DSP48s and it can work up to about 0.58 MHz sample rate with a 200 MHz system clock. The hardware resources are considerably lower than traditional techniques using divider and cubic root realization. The linear array architecture also serves as an attractive alternative to the systolic array in medium to low rate applications due to its reduced hardware usages.

Noise Bias Compensation for Reconstructed HDR Images in Two Layer Coding

Noise Bias Compensation for Reconstructed HDR Images in Two Layer Coding