Fading Kalman Filter Research Articles

Dynamic load altering attack detection based on adaptive fading Kalman filter in smart grid

AbstractThis paper mainly studies a detection method of dynamic load altering attacks (D‐LAAs) in smart grids. First, communication factors are considered, and a smart grid discrete system model under D‐LAA attack is established. Second, for closed‐loop D‐LAAs, an adaptive fading Kalman filter (AFKF) is designed to estimate the states of smart grids with Gaussian noise in real time, and a Euclidean distance ratio detection algorithm based on AFKF is proposed to detect D‐LAAs. Moreover, the proposed detection algorithm can identify D‐LAAs even in the presence of noise in the measurement data, significantly enhancing the speed of attack detection. Finally, take a smart grid with three generators and six buses as an example. Its feasibility and effectiveness of the Euclidean distance ratio detection algorithm are verified by simulations. The simulations are carried out through the real‐time hardware‐in‐the‐loop simulation platform, which is mainly composed of StarSim and multi‐tasking devices.

Research on automatic early warning of UAV attitude abnormal state based on MEMS sensor

The Unmanned Aerial Vehicle's (UAV) attitude control is crucial to the success of the mission. On the basis of this, the paper suggests a paradigm for autonomous early warning of improper UAV attitude based on MEMS sensors. To obtain early warning of anomalous UAV attitude, the model solves UAV attitude using the quaternion approach and employs a fading Kalman filter to correct for MEMS gyroscope inaccuracy. The simulation test demonstrates that in the static state, the errors of the drone's pitch angle and roll angle are within 0.2°, and the heading angle error is about 0.5°. In the high manoeuvring state, the errors of the UAV's pitch angle and roll angle are all within 0.5°, and the mean value of the heading angle error is also controlled within 2°. The experiment achieves high-precision automated warning of aberrant attitude by filtering the fading Kalman filter to correct the random error of the UAV gyroscope. It also increases the precision with which human motion is measured. The suggested approach promotes the growth of the UAV sector.

A Lag Compensation-Enhanced Adaptive Quasi-Fading Kalman Filter for Sensorless Control of Synchronous Reluctance Motor

A novel position estimation strategy based on lag compensation-assisted adaptive quasi-fading Kalman filter (LC-AQFKF) is proposed for synchronous reluctance motor (SynRM) sensorless drive in this article. In LC-QFKF, the quasi-fading factor is derived to avoid the harsh assumptions of conventional adaptive fading Kalman filter, and accessibility of the method is improved while ensuring the estimation accuracy. The computational efficiency of LC-AQFKF is promoted by introducing the quasi-fading factor into the prediction error covariance matrix. Moreover, the frequency characteristic of AQFKF-based active back electromotive force observer is analyzed, and the phase lag problem in high-speed situations caused by the low-pass filtering property of AQFKF is overcome. In this way, the estimation accuracy of the rotor position is significantly enhanced. Besides, the double dynamic position compensation method is put forward to strengthen the position estimation performance of sensorless SynRM drive under dynamic conditions. The effectiveness of the proposed scheme is validated at a 1.5 kW SynRM drive.

An Adaptive Fusion Attitude and Heading Measurement Method of MEMS/GNSS Based on Covariance Matching.

Aimed at the problem of filter divergence caused by unknown noise statistical characteristics or variable noise characteristics in an MEMS/GNSS integrated navigation system in a dynamic environment, on the basis of revealing the parameter adjustment logic of covariance matching adaptive technology, a fusion adaptive filtering scheme combining innovation-based adaptive estimation (IAE) and the adaptive fading Kalman filter (AFKF) is proposed. By setting two system tuning parameters, for the process noise covariance adaptation loop and the measurement noise covariance adaptation loop, covariance matching is sped up and achieves an effective suppression of filter divergence. The vehicle-mounted experimental results show that the mean square error of the combined attitude error obtained based on the fusion filtering method proposed in this paper is better than 0.5°, and the mean square error of the heading error is better than 1.5°. The results can provide technical support for the continuous extraction of low-cost attitude information from mobile platforms.

Distributionally Robust State Estimation for Linear Systems Subject to Uncertainty and Outlier

Parameter uncertainties and measurement outliers unavoidably exist in a real linear system. Such uncertainties and outliers make the true joint state-measurement distributions (induced by the true system model) deviate from the nominal ones (induced by the nominal system model) so that the performance of the optimal state estimator designed for the nominal model becomes unsatisfactory or even unacceptable in practice. The challenges are to quantitatively describe the uncertainties in the model and the outliers in the measurements, and then robustify the estimator in a right way. This article studies a distributionally robust state estimation framework for linear systems subject to parameter uncertainties and measurement outliers. It utilizes a family of distributions near the nominal one to implicitly describe the uncertainties and outliers, and the robust state estimation in the worst case is made over the least-favorable distribution. The advantages of the presented framework include: 1) it only uses a few scalars to parameterize the method and does not require the structural information of uncertainties; 2) it generalizes several classical filters (e.g., the fading Kalman filter, risk-sensitive Kalman filter, relative-entropy Kalman filter, outlier-insensitive Kalman filters) into a unified framework. We show that the distributionally robust state estimation problem can be reformulated into a linear semi-definite program and in some special cases it can be analytically solved. Comprehensive comparisons with existing state estimation frameworks that are insensitive to parameter uncertainties and measurement outliers are also conducted.

Dynamic load-altering attack detection based on adaptive fading Kalman filter in power systems

This paper presents an effective and feasible method for detecting dynamic load-altering attacks (D-LAAs) in a smart grid. First, a smart grid discrete system model is established in view of D-LAAs. Second, an adaptive fading Kalman filter (AFKF) is designed for estimating the state of the smart grid. The AFKF can completely filter out the Gaussian noise of the power system, and obtain a more accurate state change curve (including consideration of the attack). A Euclidean distance ratio detection algorithm based on the AFKF is proposed for detecting D-LAAs. Amplifying imperceptible D-LAAs through the new Euclidean distance ratio improves the D-LAA detection sensitivity, especially for very weak D-LAA attacks. Finally, the feasibility and effectiveness of the Euclidean distance ratio detection algorithm are verified based on simulations.

Novel interacting multiple model filter for uncertain target tracking systems based on weighted Kullback–Leibler divergence

Interacting multiple model (IMM) filter is a classical method to track targets in hybrid situations. However, it can exhibit divergence when the models are correlated or the system suffers from uncertainties. The generalized covariance intersection method based on the weighted Kullback–Leibler (K–L) divergence can solve the divergence problem of correlated estimates. A novel interacting multiple model (NIMM) filter is presented that combines two different algorithms, the adaptive fading Kalman filter and the maximum correntropy Kalman filter, based on the model interacting with the weighted K-L divergence to address the uncertainty problems of the system. The NIMM filter algorithm is designed and the stability and accuracy are analyzed. The simulation results demonstrate that the proposed filter can effectively improve the accuracy under different uncertainty conditions for classical examples and ballistic trajectory tracking scenarios.

Dynamic Visual Tracking for Robot Manipulator Using Adaptive Fading Kalman Filter

This paper focuses on the problem of visual tracking of a moving target with the temporary occlusion of image feature, a dynamic visual tracking control system for robot manipulator is developed by using adaptive fading Kalman filter (AFKF). The estimation of the residual covariance is used to compute the forgetting factor to automatically adjust the weight of the image observation data for improving the visual state estimation accuracy. When the target features are occluded, the prediction of missing observation sequence are generated by using the predicted compensation noise and preorder observation sequence to determine the forgetting factor for estimating the missing visual states. Then, a parameter adaptive law with projection error compensation is designed to realize the visual tracking with uncertain camera parameters. Finally, the trajectory tracking experiments based on a real robot platform is carried out to verify the performance of the proposed state estimator and tracking controller. The results show that the proposed method can accurately realize the visual tracking with the occluded trajectory and inaccurate camera parameters, which improves the flexibility of dynamic visual tracking of robot manipulator.

A Novel Adaptive Fading Kalman Filter-Based Approach to Time-Varying Brain Spectral/Connectivity Analyses of Event-Related EEG Signals

This paper proposes a novel adaptive fading Kalman filter (AF-KF)-based approach to time-varying brain spectral and functional connectivity analyses of event-related multi-channel electroencephalogram (EEG) signals. By modeling the EEG signals as a time-varying (TV) multivariate autoregressive (MVAR) process, a new AF-KF with variable number of measurements (AF-KF-VNM) is proposed for estimating the spectra of the EEG signals and identifying their functional connectivity. The proposed AF-KF-VNM algorithm uses a new adaptive fading method to adaptively update the model parameters of the KF for improved state estimation and utilizes multiple measurements for better adaptation to the nonstationary signal observations. Experimental results on a simulated data for modeling the TV directed interactions in multivariate neural data show that the proposed AF-KF-VNM method yields better tracking performance than other approaches tested. The proposed algorithm is then integrated into a novel methodology for combined functional Magnetic Resonance Imaging (fMRI) activation maps and EEG spectrum analyses for quantifying the differences in spectrum contents and information flows between the target and standard conditions in a visual oddball paradigm. The results and findings show that the proposed methodology agrees well with the literature and is capable of revealing significant frequency components and information flow involved as well as their time variations.

Modeling Analysis on Improving Cylinder Balance in A Gasoline Engine Using Electromagnetic Valve Train

For the multi-cylinder gasoline engine, the consistency among cylinders is an important index to affect the engine emission and the engine power. In this paper, an individual cylinder air-fuel ratio (A/F) control method for a fourcylinder camless engine with the electromagnetic valve train (EMVT) was proposed to reduce the imbalance of engine torque. An individual cylinder A/F estimation algorithm with a single universal exhaust gas oxygen (UEGO) sensor based on fading Kalman filtering was introduced. Four proportional-integral feedback controllers were built to regulate the individual A/F by adjusting the intake valve closing (IVC) timing of each cylinder independently based on the EMVT. The effectiveness of the proposed estimation and control approach was validated by co-simulation of GT-Power and Simulink. The results showed that the proposed estimation method could accurately estimate the individual cylinder A/F, and the maximum estimation error under steady state condition was less than 1 %. With the feedback control, both the individual A/F imbalance and the cylinderto- cylinder torque generation imbalance were decreased.

Model-based topography estimation in trolling mode atomic force microscopy

In this study, a novel approach based on a modified Kalman filter algorithm is presented to directly estimate and measure the surface topography of samples by trolling mode atomic force microscopy. Trolling mode atomic force microscopy was introduced as an atomic force microscopy alternative to overcome imaging problems in liquid environments by reducing the liquid-resonator interaction forces. In conventional imaging techniques, the time to reach the steady state periodic motion of the oscillating probe restricts scanning speed. To overcome this limitation, we propose a novel imaging technique for trolling mode atomic force microscopy based on the system dynamics model and using the adaptive fading Kalman filter with forgetting factor. In this approach, the sample height is estimated directly without the need for any closed loop controller. As a result, the scanning speed is improved significantly, and topography is obtained more accurately compared to the conventional imaging method. Moreover, the effects of process noise, scanning speed, and parameter uncertainties on the performance of proposed approach are investigated.

Hierarchical Fault-Tolerant Control using Model Predictive Control for Wind Turbine Pitch Actuator Faults

Wind energy is one of the fastest growing energy sources in the world. It is expected that by the end of 2022 the installed capacity will exceed 250 GW thanks to the supply of large scale wind turbines in Europe. However, there are still challenging problems with wind turbines. In particular, off-shore and large-scale wind turbines are required to tackle the issue of maintainability and availability because they are installed in harsh off-shore environments, which may also prevent engineers from accessing the site for immediate repair works. Fault-tolerant control techniques have been widely exploited to overcome this issue. This paper proposes a novel fault-tolerant control strategy for wind turbines. The proposed strategy has a hierarchical structure, consisting of a pitch controller and a wind turbine controller, with parameter estimations using the adaptive fading Kalman filter technique. The pitch controller compensates any fault with a pitching actuator, while the wind turbine controller computes the optimal reference command for pitching behavior so that the effect of the fault with a pitch actuator can be minimized. The performance of the proposed approach is demonstrated through a set of simulations with a wind turbine benchmark model.

LED chip accurate positioning control based on visual servo using dual rate adaptive fading Kalman filter

In this paper, to improve the positioning accuracy of LED chip, a dual rate adaptive fading Kalman filter algorithm with delay compensation is proposed and applied to the LED chip visual servo positioning system. Firstly, a structure of dual rate Kalman filter is introduced to the visual servo control system, which compensate the visual information delay and realize the accurate time sequential coordination of encoder and visual feedback. Then, considering the inaccuracy of system mathematical model, the adaptive forgetting factor is added to the iterative process of above algorithm, and the impact of accumulated model error on system stability is consequently mitigated. Finally, the experimental results show that the proposed method obviously decreases the positioning errors of LED chip and is robust to inaccuracy and uncertainty of system model parameters.

SOC estimation with thermal and charging rate consideration using dual filter approach for lithium-ion battery

Electric vehicles are subjected to various environmental conditions in which ambient temperature variations and high power requirements are common in the duty cycle. These factors greatly impact the state of charge of the batteries. The battery management system in the electric vehicles enables batteries to operate within a safe operating window by monitoring their states and controlling the environment. One of the important states is the state of charge, and accurate information of it is necessary to extract maximum performance from batteries with safety. An equivalent circuit model was used for representing the battery dynamics, and core temperature of the battery was modeled using the algebraic equation. Ambient temperature variation was captured through internal resistance, and a current requirement variation was captured through open circuit voltage. The fading Kalman filter was used for online estimation of the state of charge. The present technique estimates the state of charge at different C rates like 0.5, 1, and 2 C at ambient temperatures like 298, 313, and 333 K. It was found that the proposed method estimates SOC with an average root mean square error of 0.358 and a maximum percentage error of 3% SOC for all the considered charging/discharging rates and temperatures.

Computationally inexpensive dual filter approach for estimation and control of SOC for the lithium-ion battery

Accurate estimation of the state of charge and its control is crucial for a battery energy management system for longer life and safety of the lithium-ion battery and depends on the accuracy of model used for capturing battery dynamics. Considering the equivalent circuit model, I used a recursive least square filter to update the parameters of the model at each sampling time. The polynomial approach is used for establishing the relationship between the open circuit voltage and state of charge. The fading Kalman filter is used for online estimation of the open circuit voltage and then, the state of charge is predicted using the developed relationship. A linear classical controller is designed and implemented. The control oriented model for designing the controller is identified using the perturbation data. To avoid nonlinear optimization of control oriented model identification, first a higher order model is identified and then the second order plus time delay model is generated. The present technique tracks the set points very well within +/−5% of the desired value in 950 and 1800 s for 30 and 70% SOC set points, respectively. The present approach requires minimal computational efforts as compared with nonlinear estimation because of analytical solutions of the essential equations.

An Adaptive Kalman Filtering Approach to Fourier Analysis for Estimating Various Chirp-Type GNSS Interference Frequencies

An adaptive Kalman filter-based frequency estimation algorithm is proposed to track the frequency of a chirp-type global navigation satellite system (GNSS) interference. The unknown interference frequency of GNSS in the received signal can be estimated by using received samples in the time domain, but the thus-obtained value can include a large amount of error caused by measurement noise and by the frequency change rate of the interference. In order to reduce the error, an adaptive fading Kalman filter that is based on the Fourier series is applied in the proposed algorithm. Furthermore, an optimal order-reduction algorithm is proposed to select the appropriate order of the Fourier series for the type of received interference. The performance of the tracking algorithm is verified by making comparisons with conventional algorithms. The proposed algorithm has better tracking performance than conventional algorithms when the jammer-to-signal ratio (J/S) is more than 30 dB, which would seriously affect the accuracy of the GNSS.

Adaptive maneuvering frequency method of current statistical model

Current statistical model U+0028 CSM U+0029 has a good performance in maneuvering target tracking. However, the fixed maneuvering frequency will deteriorate the tracking results, such as a serious dynamic delay, a slowly converging speedy and a limited precision when using Kalman filter U+0028 KF U+0029 algorithm. In this study, a new current statistical model and a new Kalman filter are proposed to improve the performance of maneuvering target tracking. The new model which employs innovation dominated subjection function to adaptively adjust maneuvering frequency has a better performance in step maneuvering target tracking, while a fluctuant phenomenon appears. As far as this problem is concerned, a new adaptive fading Kalman filter is proposed as well. In the new Kalman filter, the prediction values are amended in time by setting judgment and amendment rules, so that tracking precision and fluctuant phenomenon of the new current statistical model are improved. The results of simulation indicate the effectiveness of the new algorithm and the practical guiding significance.

Noise adaptive fading Kalman filter for free-space laser communication beacon tracking.

We proposed a prediction algorithm for laser communication pointing, acquisition, and tracking (PAT) subsystems in order to further improve PAT accuracy and reduce the effect of processing delay. In terms of this prediction algorithm, a fading Kalman filter is employed, with the observation noise obtained by the gray value distribution of the laser images. Moreover, to better fit the dynamics of a laser target, the two-stage dynamic model has been chosen as the state transition model for Kalman filtering. In addition, the two-stage dynamic model has been modified by accommodating its form to a change of time lag, thereby compensating the effect of time delay. A series of horizontal path (17 km) experiments under different atmospheric conditions were conducted in the fields. According to the experimental results, the algorithm we proposed could effectively reduce the tracking error and improve pointing accuracy.

ARMA model based adaptive unscented fading Kalman filter for reducing drift of fiber optic gyroscope

In this paper, the fiber optic gyroscope drift is modeled using an auto-regressive-moving-average (ARMA), time series model. The drift is subsequently reduced using the proposed adaptive unscented fading Kalman filter algorithm. The proposed algorithm has two cascaded stages for updating the state error and measurement noise covariance. In the first stage, the predicted state error covariance is updated using a transitive factor and in the second stage the measurement noise covariance is updated using another transitive factor. The suggested algorithm is used for reducing the drift of the FOG signal in both static and dynamic conditions at room temperature. The performance of the proposed algorithm is analysed using Allan Variance and drift for the static signal and root mean square error for the dynamic signal. The performance of the suggested algorithm is compared with the unscented Kalman filter (UKF) and a single transitive factor based adaptive UKF algorithm. The experimental results demonstrate that the proposed algorithm performs better than UKF and a single transitive factor based adaptive UKF algorithm for reducing the drift and random noise in both static as well as dynamic conditions.

AFAKF for manoeuvring target tracking based on current statistical model

The fixed maximum acceleration of current statistical model (CSM) will lead to the deterioration of Kalman filter. To improve the performance of CSM in target tracking, a new modified CSM (MCSM) and a new Kalman filter (KF) are proposed. The new model, which employs innovation dominated subjection function to adaptively adjust maximum acceleration, has a better performance in target tracking, but it is very sensitive to innovation and will lead to a fluctuant phenomenon when target manoeuvres occur. The new adaptive fading Kalman filter which is formed by amendatory KF (AKF) and adaptive fading KF can weaken the fluctuant phenomenon caused by MCSM. The principle and deducing of AKF are specifically elaborated based on probability theory. Three simulations results indicate the high performance and robustness of MCSM and MCSM-adaptive fading amendatory Kalman filter in target tracking.