Measurement Noise Covariance Research Articles

Adaptive quaternion particle filter using generalized likelihood ratio test for aircraft attitude estimation in the presence of anomalous measurement

An adaptive quaternion particle filter (QPF) based on the generalized likelihood ratio test (GLRT) is proposed for aircraft attitude estimation in the presence of an anomalous measurement. The framework of the QPF is employed to guarantee quaternion normalization. To cope with an anomalous measurement when interference occurs, the proposed algorithm uses the GLRT to detect an anomalous measurement and determine the interference source. An adaptation scheme is used to tune the measurement noise covariance matrix after the interference source has been determined so that the algorithm can remain robust against interference. Numerical simulations are carried out to evaluate the performance of the proposed algorithm and compare it with the QPF algorithm. The results show that the proposed algorithm outperforms the standard one in attitude estimation accuracy under anomalous measurement conditions.

Multiple fading factors-based strong tracking variational Bayesian adaptive Kalman filter

If the system model or the statistical characteristics of noise are inaccurate, the past measurements will directly affect the accuracy of current state estimation or even lead to filtering divergence. To overcome above difficulties, a multiple fading factors-based strong tracking variational Bayesian adaptive Kalman filter is proposed. Firstly, the inverse Wishart distribution is adopted to model the measurement noise covariance matrix. Secondly, the remodified measurement noise covariance matrix and the innovation covariance matrix estimated by exponential weighting method are employed to construct the scalar fading factor. Next, the multiple fading factors are calculated to correct the predicted error covariance matrix. Finally, the local optimal estimations of measurement noise covariance matrix and state are obtained by variational Bayesian approach. The target tracking simulations verify that the proposed algorithm has better tracking ability for the predicted error covariance matrix and the measurement noise covariance matrix compared with the existing filters.

Strong Tracking PHD Filter Based on Variational Bayesian with Inaccurate Process and Measurement Noise Covariance.

Assuming that the measurement and process noise covariances are known, the probability hypothesis density (PHD) filter is effective in real-time multi-target tracking; however, noise covariance is often unknown and time-varying for an actual scene. To solve this problem, a strong tracking PHD filter based on Variational Bayes (VB) approximation is proposed in this paper. The measurement noise covariance is described in the linear system by the inverse Wishart (IW) distribution. Then, the fading factor in the strong tracking principle uses the optimal measurement noise covariance at the previous moment to control the state prediction covariance in real-time. The Gaussian IW (GIW) joint distribution adopts the VB approximation to jointly return the measurement noise covariance and the target state covariance. The simulation results show that, compared with the traditional Gaussian mixture PHD (GM-PHD) and the VB-adaptive PHD, the proposed algorithm has higher tracking accuracy and stronger robustness in a more reasonable calculation time.

An Adaptive Kalman Filter With Inaccurate Noise Covariances in the Presence of Outliers

In this article, a novel variational Bayesian (VB) adaptive Kalman filter with inaccurate nominal process and measurement noise covariances (PMNC) in the presence of outliers is proposed. The probability density functions of state transition and measurement likelihood are modeled as Gaussian–Gamma mixture distributions. The VB inference is used to perform the state and PMNC simultaneously. Simulations show that the effectiveness of the proposed method with inaccurate noise covariances in the presence of outliers environments.

Adaptive Extended Kalman Filter Based Dynamic Equivalent Method of PMSG Wind Farm Cluster

In order to reduce the dimension of wind farm model and improve the simulation efficiency under the premise of ensuring the accuracy, this article proposes a dynamic equivalent method for permanent magnet synchronous generator (PMSG) based wind farm cluster utilizing the adaptive extended Kalman filters. Combining the dynamic model of PMSG, the equivalent wind turbine parameters that need to be identified are incorporated into the extended state variables, and an online parameters identification method based on extended Kalman filter (EKF) theory is put forward. To eliminate the influence of random noise on the accuracy of identification, the adaptive technology is introduced into EKF to estimate the process and measurement noise covariance in real time through the Sage–Husa estimator. Thus, a wind farm cluster equivalent model is obtained. Finally, the effectiveness and robustness of the proposed method are verified by time-domain simulation and frequency-domain simulation in IEEE 39-bus system.

Pulse-width modulation direct torque control induction motor drive with Kalman filter

The paper deals with application of Kalman filter in induction motor drive using pulse-width modulation direct torque control (PWM-DTC). In the first part, the conventional PWM-DTC drive is described and Kalman filter is utilized to filter components of stator current vector those are assumed to be disturbed by white noise. The second part contains simulation results that are obtained in different cases of load torque, process and measurement noise covariances. The integral time absolute error (ITAE) performance index, undershoot, ripple of important quantities are used to compare the conventional drive structure and proposed drive structure with Kalman filter. The simulation results confirm the expected dynamic response of the proposed structure.

Adaptive Central Difference Kalman Filter With Unknown Measurement Noise Covariance and Its Application to Airborne POS

Position and Orientation system (POS), a loosely integrated inertial navigation system (INS) and global positioning system (GPS), can provide high-accuracy motion information for the airborne remote sensing loads, which plays a crucial role in airborne remote sensing imaging. However, the airborne POS often suffers from the harsh environment, such as aircraft maneuver mode and other external disturbance, which will lead to measurement noise unknown and further affects the accuracy of motion parameters. In this paper, an adaptive central difference Kalman filter method based on expectation maximization algorithm is proposed, which can estimate measurement noise adaptively and further improve the performance of POS. A flight experiment is conducted and the results show that the proposed method achieves higher-accuracy motion information by compared with the traditional CDKF method and covariance matching.

Vehicle State Estimation Based on Unscented Kalman Filtering and a Genetic-particle Swarm Algorithm

Vehicle state and parameter estimation has gradually become an important way to soft-sense some variables that are difficult to measure directly using general sensors. In the traditional Kalman filtering algorithm, the selection of the process noise covariance matrix and the measurement noise covariance matrix will directly affect the filtering accuracy of the algorithm. In order to improve the filtering accuracy of the filter algorithm to obtain the optimal solution, based on a 7-DOF nonlinear vehicle dynamics model and the Magic formula tire model, a hybrid algorithm containing an unscented Kalman filter (UKF) and a genetic-particle swarm algorithm (genetic-particle swarm UKF) is used to estimate several vehicle key states. Compared with traditional estimator based on UKF and the unscented particle filter (UPF), the simulation and real vehicle test results show that the proposed estimator based on the genetic-particle swarm UKF algorithm has higher accuracy and less computation requirements than the UKF estimator. And also, the proposed hybrid algorithm has superiority on the convergence speed of the optimization than the UPF algorithm. The results of a real-vehicle experiment demonstrate that the proposed hybrid algorithm can be used effectively for solving the vehicle-state estimation problem.

Maximum Likelihood-Based Measurement Noise Covariance Estimation Using Sequential Quadratic Programming for Cubature Kalman Filter Applied in INS/BDS Integration

With the completion of the Beidou-3 system (BDS) in China, INS/BDS integration will become a promising navigation and positioning strategy. However, due to the nonlinear propagation characteristic of INS error and inevitable involvement of inaccurate measurement noise statistics, it is difficult to achieve the optimal solution through the INS/BDS integration. This paper proposes a method of cubature Kalman filter (CKF) with the measurement noise covariance estimation by using the maximum likelihood principle to solve the abovementioned problem. It establishes an estimation model for measurement noise covariance according to the maximum likelihood principle, and then, its estimation is calculated by utilizing the sequential quadratic programming. The estimated measurement noise covariance will be fed back to the procedure of CKF to improve its adaptability. Simulation and comparison analysis verify that the proposed method can accurately estimate measurement noise covariance to effectively restrain its influence on navigation solution, leading to improved navigation performance for the INS/BDS integration.

Variational Bayesian Adaptive Unscented Kalman Filter for RSSI-based Indoor Localization

Most existing localization schemes necessitate a priori statistical characteristic of measurement noise, which may be unrealistic in practical applications. This paper investigates the variational Bayesian adaptive unscented Kalman filtering (VBAUKF) for received signal strength indication (RSSI) based indoor localization under inaccurate process and measurement noise covariance matrices. First, an inaccurate and slowly varying measurement noise covariance matrix can be estimated by choosing appropriate conjugate prior distribution for an indoor localization model with inaccurate process and measurement noise covariance matrices. By choosing inverse Wishart priors distribution, the state, predicted error and measurement noise covariance matrices are inferred on each time separately. Second, a parameter optimization algorithm is designed to minimize the localization error of VBAUKF until it less than the threshold set in advance. Finally, experimental validation is presented to demonstrate the accuracy and effectiveness of the proposed filtering method for indoor localization.

Adaptive Error-State Kalman Filter for Attitude Determination on a Moving Platform

This article presents a loosely coupled visual/inertial hybrid system for relative attitude determination on a moving platform. The inertial measurements are accomplished by two gyroscopes, of which the slave gyroscope removes the redundant motion of the platform from the total motion sensed by the master gyroscope. To correct integration drift error and compensate for the gyroscope biases, we fuse the inertial and visual measurements fused together through the error-state Kalman filter (ESKF). Furthermore, an improved ESKF is proposed by utilizing the variational Bayesian (VB) inference to adaptively estimate the process and measurement noise covariance. To realize direct estimation of the process noise covariance, a latent variable is introduced and inferred together with the noise covariances and error-state. The practical experimental setup is built up and experiments of two different motion trajectories are conducted. The ESKF, the cubature Kalman filter (CKF), the extended Kalman filter (EKF), the proposed filter, and the other two adaptive filters are implemented for comparison to verify the effectiveness of the proposed filter. The results demonstrate the proposed filter show superiority in reducing both the root mean square error (RMSE) and maximum error (ME) and improving the filter consistency.

Adaptive Recursive Decentralized Cooperative Localization for Multirobot Systems With Time-Varying Measurement Accuracy

Decentralized cooperative localization (DCL) is a promising method to determine accurate multirobot poses (i.e., positions and orientations) for robot teams operating in an environment without absolute navigation information. Existing DCL methods often use fixed measurement noise covariance matrices for multirobot pose estimation; however, their performance degrades when the measurement noise covariance matrices are time-varying. To address this problem, in this article, a novel adaptive recursive DCL method is proposed for multi-robot systems with time-varying measurement accuracy. Each robot estimates its pose and measurement noise covariance matrices simultaneously in a decentralized manner based on the constructed hierarchical Gaussian models using the variational Bayesian approach. Simulation and experimental results show that the proposed method has improved cooperative localization accuracy and estimation consistency but slightly heavier computational load than the existing recursive DCL method.

Kalman Filtering With Adaptive Step Size Using a Covariance-Based Criterion

In Kalman filtering (KF), a tradeoff exists when selecting the filter step size. Generally, a smaller step size improves the estimation accuracy, yet with the cost of a high computational load. To mitigate this tradeoff influence on performance, a criterion that acts as a guideline for a reasonable choice of the step size is proposed. This criterion is based on the predictor-corrector error covariance matrices of the discrete KF. In addition, this criterion is elaborated to an adaptive algorithm, for the case of the time-varying measurement noise covariance. Two simulation examples and a field experiment using a quadcopter are presented and analyzed to show the benefits of the proposed approach.

Attitude Estimation Using Low-Cost MARG Sensors With Disturbances Reduction

Attitude information obtained from low-cost magnetic, angular rate, and gravity (MARG) sensors is prone to be deteriorated by disturbances such as external acceleration and magnetic anomaly in operational environments. To address the problem, a robust attitude estimation algorithm using low-cost MARG sensors is proposed. An error state Kalman filter (ESKF) is used for data fusing, in which the attitude errors are interpreted as a small rotation vector, and the gyro bias variation is also estimated. The nominal state and the error state are propagated with unit quaternion and rotation vector, respectively. An attitude correction is followed which combines the nominal and error parts by quaternion multiplication. The robustness of the proposed algorithm is embodied in resisting accuracy degradation of the attitude estimation caused by both external acceleration and magnetic anomalies. While external accelerations and magnetic disturbances are detected online, the accuracy reduction in attitude estimation is prevented by adaptively adjusting the related measurement noise covariance matrix. Besides, a two-step measurement update strategy is designed to guarantee that the roll and pitch update is separated from the yaw update. Various rotation and land vehicle dynamic tests have been conducted to validate the effectiveness and robustness of the proposed algorithm.

On the Adaptivity of Unscented Particle Filter for GNSS/INS Tightly-Integrated Navigation Unit in Urban Environment

Tight integration algorithms fusing Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) have become popular in many high-accuracy positioning and navigation applications. Despite their reliability, common integration architectures can still run into accuracy drops under challenging navigation settings. The growing computational power of low-cost, embedded systems has allowed for the exploitation of several advanced Bayesian state estimation algorithms, such as the Particle Filter (PF) and its hybrid variants, e.g. Unscented Particle Filter (UPF). Although sophisticated, these architectures are not immune from multipath scattering and Non-Line-of-Sight (NLOS) signal receptions, which frequently corrupt satellite measurements and jeopardise GNSS/INS solutions. Hence, a certain level of modelling adaptivity should be granted to avoid severe drifts in the estimated states. Given these premises, the paper presents a novel Adaptive Unscented Particle Filter (AUPF) architecture leveraging two cascading stages to cope with disruptive, biased GNSS input observables in harsh conditions. A INS-based signal processing block is implemented upstream of a Redundant Measurement Noise Covariance Estimation (RMNCE) stage to strengthen the adaptation of observables’ statistics and improve the state estimation. An experimental assessment is provided for the proposed robust AUPF that demonstrates a 10 % average reduction of the horizontal position error above the 75-th percentile. In addition, a comparative analysis both with previous adaptive architectures and a plain UPF is carried out to highlight the improved performance of the proposed methodology.

Robust Attitude Estimation Using IMU-Only Measurements

This article proposes two novel covariance-tuning methods to form a robust Kalman filter (RKF) algorithm for attitude (i.e., roll and pitch) estimation using the measurements of only an inertial measurement unit (IMU). KF-based and complementary filtering (CF)-based approaches are the two common methods for solving the attitude estimation problem. Efficiency and optimality of the KF-based attitude filters are correlated with appropriate tuning of the covariance matrices. Manual tuning process is a difficult and time-consuming task. Specifically, the IMU-only attitude estimation filters are prone to the external accelerations unless their covariances are adapted to gain robustness. The proposed algorithms provide an adaptive method for tuning the measurement noise covariance such that they can accurately estimate the attitude in the two axes. The first method relies on a single tuning factor, whereas the second one tunes the covariance with different (multiple) factors for each measurement axis. The proposed methodologies are tested and compared with other existing filtering algorithms in the literature under different dynamical conditions and using real-world experimental datasets in order to validate their effectiveness. Results show that highly dynamic scenarios, especially the multiple tuning factor strategy, can increase the attitude estimation accuracy more than two-times compared to the competitive algorithms.

Parameter identification and state-of-charge prediction of decommissioned lithium batteries

Aiming at the problem that different temperatures and working modes affect the parameter identification and state of charge (SOC) estimation of decommissioned lithium batteries, a new method based on the second-order RC equivalent circuit model combined with the recursive least square method (RLS) is proposed to introduce the forgetting factor, and combined with the extended Kalman filter algorithm (EKF) to realize the method of online parameter identification of decommissioned lithium batteries and the optimal estimation of SOC. In order to solve the problem of obtaining the optimal solution of the error covariance matrix and the measurement noise covariance matrix in EKF, the particle swarm optimization algorithm (PSO) is used to optimize online to further improve the SOC prediction accuracy. The results show that the joint optimization algorithm can accurately identify the parameters and SOC values of retired lithium batteries, which is helpful to realize the echelon utilization of retired lithium batteries.

Adaptively Robust Square-Root Cubature Kalman Filter Based on Amending

To solve the problem of decreased filtering accuracy and even filter divergence for the case that the model errors and measurement outliers exist simultaneously, an adaptively robust square-root cubature Kalman filter (SRCKF) based on amending is proposed in this paper. Based on the error analysis, the judgment criterion and the amending criterion related to the innovation are set. Then the filter could overcome the influence of the measurement outliers with the robust amendment of the measurement noise covariance matrix based on the principle of the innovation covariance matching. To further deal with model errors, the new method of the adaptive amendment of the predicted state based on the innovation is developed and combined. Finally, the proposed algorithm can balance the effect of the prior predicted value and the posterior feedback measurement value on the filtering process and reduce the state estimation error. The simulation results show that the proposed algorithm can effectively suppress the negative impact of the model errors and the measurement outliers and can obtain better estimation performance and obviously decreasing running time compared with the adaptively robust unscented Kalman filter (ARUKF) and the robust multiple fading factors cubature Kalman filter (RMCKF).

Time-Delay-Based Target Localization in Wireless Sensor Network With Unknown Noise Covariance

This letter addresses the problem of target localization based on the time-delay (TD) measurements in a wireless sensor network (WSN) with a noncooperative illuminator of opportunity (IO), without assuming the prior knowledge of measurement noise covariance (MNC). The joint likelihood of target position and noise variances are built, based on which the target position and MNC can naturally be estimated by maximizing the joint likelihood. However, the resulting maximum likelihood (ML) problem is intractable due to its nonconvexity and nonlinearity. In order to overcome such difficulty, an alternately iterative optimization strategy is proposed in our approach. The approximate weighted least-squares solution and closed-form shrinkage estimator are introduced into the alternative estimation steps for the target location and MNC, respectively. In simulation experiments with 40 TD measurements, the performance of the proposed method, performing without knowledge of MNC, achieves about 8 dB average improvement over the traditional method without the MNC. Its performance is also close to that of the algorithms and Cramer–Rao lower bound (CRLB) working with known MNC, thus verifying the effectiveness of proposed approach.

Multi-Fading Factor and Updated Monitoring Strategy Adaptive Kalman Filter-Based Variational Bayesian.

Aiming at the problem that the performance of adaptive Kalman filter estimation will be affected when the statistical characteristics of the process and measurement of the noise matrices are inaccurate and time-varying in the linear Gaussian state-space model, an algorithm of multi-fading factor and an updated monitoring strategy adaptive Kalman filter-based variational Bayesian is proposed. Inverse Wishart distribution is selected as the measurement noise model and the system state vector and measurement noise covariance matrix are estimated with the variational Bayesian method. The process noise covariance matrix is estimated by the maximum a posteriori principle, and the updated monitoring strategy with adjustment factors is used to maintain the positive semi-definite of the updated matrix. The above optimal estimation results are introduced as time-varying parameters into the multiple fading factors to improve the estimation accuracy of the one-step state predicted covariance matrix. The application of the proposed algorithm in target tracking is simulated. The results show that compared with the current filters, the proposed filtering algorithm has better accuracy and convergence performance, and realizes the simultaneous estimation of inaccurate time-varying process and measurement noise covariance matrices.