Adaptive Kalman Filter Approach Research Articles

Adaptive Kalman filter with LSTM network assistance for abnormal measurements

A classic state estimation method, the Kalman filter integrates prior information, system dynamics models, and measurement data to achieve posterior state estimations. However, measurements often encounter various unknown disturbances, leading to abnormal or inaccurate measurements and subsequently impacting the performance of Kalman filtering. In response to this challenge, this paper introduces a novel adaptive Kalman filter approach aided by posterior state estimations using the Long short-term memory (LSTM) networks. The proposed method begins by utilizing prior residuals to construct a chi-square distribution model, which facilitates the detection of abnormal measurements within data. Upon identifying abnormal measurements, an LSTM network is employed to generate alternative predictive measurements, replacing the original inaccurate measurement. This approach enhances the model’s capability to handle complex relationship and measurement uncertainties and improves filtering estimation accuracy. A noise covariance adjustment method is introduced in extreme cases where alternative predictive measurements alone are insufficient for filter requirements. This method mitigates the adverse effects of abnormal measurements on posterior estimation. Throughout the entire adaptive assistance process involving the LSTM network, deep learning maintains a stable structure of the filter while enhancing adaptability. This strategy ensures the filter’s resilience in dynamic environments with unknown factors by providing predicted measurements conforming to the chi-square distribution and corresponding measurement noise covariance. Ultimately, the efficacy of the proposed algorithm is validated through simulations and experiments involving vehicle positioning with inertial sensors.

A Fusion Adaptive Cubature Kalman Filter Approach for False Data Injection Attack Detection of DC Microgrids

With the widespread application of information technology in microgrids, microgrids are evolving into a class of power cyber–physical systems (CPSs) that are deeply integrated with physical and information systems. Due to the high dependence of microgrids’ distributed cooperative control on real-time communication and system state information, they are increasingly susceptible to false data injection attacks (FDIAs). To deal with this issue, in this paper, a novel false data injection attack detection method for direct-current microgrids (DC MGs) was proposed, based on fusion adaptive cubature Kalman filter (FACKF) approach. Firstly, a DC MG model with false data injection attack is established, and the system under attack is analyzed. Subsequently, an FACKF approach is proposed to detect attacks, capable of accurately identifying the attacks on the DC MG and determining the measurement units injected with false data. Finally, simulation validations were conducted under various DC MG model conditions. The extensive simulation results demonstrate that the proposed method surpasses traditional CKF detection methods in accuracy and effectiveness across different conditions.

State of health estimation of lithium-ion battery using dual adaptive unscented Kalman filter and Coulomb counting approach

Several charging and discharging processes of lithium-ion batteries (LIBs) can lead to a battery fading and degradation effect. This may cause sudden faults, leakages, and explosions. As a result, it is highly important to estimate the state of health (SoH) of the battery to avoid any battery problems. This article proposes a novel hybrid dual adaptive unscented Kalman filter (DAUKF)-Coulomb counting approach (CCA) to efficiently state of charge (SoC) and SoH estimation of LIBs. The Gazelle optimization algorithm (GOA) is utilized in identifying LIB model parameters under various SoC conditions. It is used for minimizing the integral squared error between measured and estimated battery voltages. The battery model includes loading, fading, and various dynamic conditions. The GOA-based model has better results than other models by >8 %. The proposed hybrid DAUKF-CCA is compared with the dual adaptive extended Kalman filter (DAEKF)-CCA and other multiple algorithms. The fitness function consists of integral squared error between estimated and measured SoC of LIBs. The simulation results of the DAUKF-CCA are verified by a comparison with the measurement results performed using commercial Panasonic LiBs. The SoC results using the DAUKF-CCA are very close to the measurement results and the error is <1 %. The proposed DAUKF-CCA can ensure that the SoC and SoH estimation of LIBs is efficiently achieved.

An integrated adaptive Kalman filter for improving the reliability of navigation systems

Abstract Integrated GPS/INS using Kalman filter is the best technique for improving navigation accuracy. Assuming that the covariance matrices are known and constant, a conventional Kalman filter (CKF) is usually used, however, when they are unknown and time-varying, several adaptive estimation approaches have to be developed to estimate the statistical information of the measurement (R), process (Q), and state (P) covariance matrices. In many situations, blunders/faults in the measurement model and/or sudden changes in the dynamic model may occur during the navigation period. Therefore, the CKF, as well as the adaptive Kalman filter (AKF) will exhibit abnormal behavior and may lead the filter to be suboptimal or even diverge. In this study, the Sage-Husa adaptive Kalman filter (SHAKF) and innovation-based adaptive Kalman filter (IAKF) approaches are employed for adapting the measurement covariance matrix(R). In the case of abrupt changes in the dynamic model, the state covariance matrix (P) is adapted using the strong tracking filter (STF). The performance of these adaptive approaches is evaluated before and after simulating a fault of different sizes in the measurement and dynamic models. The results show that with a large window width, the SHAKF outperforms the CKF and IAKF. However, when the system encounters any fault either in the measurement or dynamic model, the SHAKF loses its optimality and diverges. The sensitivity of the SHAKF to the fault is because the R matrix accumulates with the propagation of the recursive noise estimator. On the other hand, the IAKF and STF provide better performance than both the CKF and SHAKF because the gain matrix is adaptively adjusted to mitigate the influence of the fault, and therefore, they behave normally when a fault of any size occurs in the measurement and/or dynamic model.

Brake Pressure Estimation of the Integrated Braking System Considering Vehicle Dynamics

The integrated braking control system (IBC) has become one of the most popular brake-by-wire (BBW) solutions due to its compactness and versatility. Accurate monitoring of wheel cylinder pressure in real time is the basis for brake pressure control, and pressure estimation is a low-cost and reliable method. However, the IBC is an electromechanical hydraulic coupling system that has significant nonlinear behaviors; moreover, vehicle dynamics also have a critical impact on the accuracy of pressure estimation. To solve this problem, this paper proposes a novel adaptive extended Kalman filter (EKF) approach that combines a hydraulic model and a single-wheel model. This novel strategy has better estimation than the hydraulic model when the pressure is accurately estimated by the single-wheel model, while when the single-wheel model is not accurate, the EKF degrades to the hydraulic model. Finally, vehicle experimental data under high- and low-mu braking are collected. The pressure estimation error of the EKF is within 0.4 MPa in the low-mu road and 2 MPa in the high-mu road. It is proven that the proposed pressure estimation strategy is highly effective.

An adaptive unscented Kalman filter approach to secure state estimation for wireless sensor networks

AbstractWireless sensor networks are vulnerable to false data injection attacks, which may mislead the state estimation. To solve this problem, this paper presents a chi‐square test‐based adaptive secure state estimation (CTASSE) algorithm for state estimation and attack detection. Taking advantage of Kalman filters, attack signal together with process noise or measurement noise are described as total white Gaussian noise with uncertain covariance matrix. The chi‐square test method is used in the adaptation of the total noise covariance and attack detection. Then, a standard adaptive unscented Kalman filter (UKF) is used for the state estimation. Finally, simulation results show that the proposed CTASSE algorithm performs better than other UKFs in state estimation and is also effective in real‐time attack detection.

A gas migration law study of a large-scale 3D physical similarity simulation with an adaptive Kalman filter algorithm

PurposeIn this study, a physical similarity simulation plays a significant role in the study of crack evolution and the gas migration mechanism. A sensor is deployed inside a comparable artificial rock formation to assure the accuracy of the experiment results. During the building of the simulated rock formation, a huge volume of acidic gas is released, causing numerous sensor measurement mistakes. Additionally, the gas concentration estimation approach is subject to uncertainty because of the complex rock formation environment. As a result, the purpose of this study is to introduce an adaptive Kalman filter approach to reduce observation noise, increase the accuracy of the gas concentration estimation model and, finally, determine the gas migration law.Design/methodology/approachFirst, based on the process of gas floatation-diffusion and seepage, the gas migration model is established according to Fick’s second law, and a simplified modeling method using diffusion flux instead of gas concentration is presented. Second, an adaptive Kalman filter algorithm is introduced to establish a gas concentration estimation model, taking into account the model uncertainty and the unknown measurement noise. Finally, according to a large-scale physical similarity simulation platform, a thorough experiment about gas migration is carried out to extract gas concentration variation data with certain ventilation techniques and to create a gas chart of the time-changing trend.FindingsThis approach is used to determine the changing process of gas distribution for a certain ventilation mode. The results match the rock fissure distribution condition derived from the microseismic monitoring data, proving the effectiveness of the approach.Originality/valueFor the first time in large-scale three-dimensional physical similarity simulations, the adaptive Kalman filter data processing method based on the inverse Wishart probability density function is used to solve the problem of an inaccurate process and measurement noise, laying the groundwork for studying the gas migration law and determining the gas migration mechanism.

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.

An adaptive central difference Kalman filter approach for state of charge estimation by fractional order model of lithium-ion battery

The key issue of the model-based state of charge estimation approach is the accuracy of the battery model. In this paper, a fractional order model is built to simulate the electrochemistry dynamics of lithium-ion battery, whose model parameters are identified by adaptive genetic algorithm. Based on the computation simplification of central difference algorithm, an adaptive central difference Kalman filter by fractional order model is designed to estimate the state of charge. The designed approach is modelled by simulink and translated into C code, and then embedded in the battery management system for the validation by two dynamic cycles. Comparing experiments adopt two approaches, i.e. the central difference Kalman filter by fractional order model, the adaptive central difference Kalman filter by Thevenin model. Experimental results indicate that the designed approach has the better accuracy and robustness, and also show that fractional order model is more accurate than Thevenin model. With respect ot the ability to deal with noise, the robustness of the designed approach is verified by adding artificial noise. Experimental results show that the proposed approach has the best robustness to noise. Therefore, the proposed approach is a good candidate for the state of charge estimation in engineering practice.

AKF-SR: Adaptive Kalman filtering-based successor representation

To understand animals’ behavior in finding relations between similar tasks and adapting themselves to changes in the tasks, it is necessary to know how the brain generalizes the learned knowledge from a previous task to unseen tasks. Recent studies in neuroscience suggest that Successor Representation (SR)-based models provide adaptation to changes in the goal locations or reward function faster than model-free algorithms, together with lower computational cost compared to that of model-based algorithms. However, it is not known how such representation might help animals to manage uncertainty in their decision making. Existing methods for the SR learning based on standard temporal difference methods (e.g., deep neural network-based algorithms) do not capture uncertainty about the estimated SR. In order to address this issue, the paper presents a Kalman filter-based SR framework, referred to as Adaptive Kalman Filtering-based Successor Representation (AKF–SR). First, Kalman temporal difference approach, which is a combination of Kalman filter and the temporal difference method, is used within the AKF–SR framework to cast the SR learning procedure into a filtering problem to benefit from uncertainty estimation of the SR, and also decreases in memory requirement and sensitivity to model’s parameters in comparison to deep neural network-based algorithms. An adaptive Kalman filtering approach is then applied within the proposed AKF–SR framework in order to tune the measurement noise covariance and measurement mapping function of Kalman filter as the most important parameters affecting the filter’s performance. Moreover, an active learning method that exploits the estimated uncertainty of the SR to form the behaviour policy leading to more visits to less certain values is proposed to improve the overall performance of an agent in terms of received rewards while interacting with its environment. Experimental results based on three reinforcement learning environments illustrate the efficacy of the proposed AKF–SR framework over state-of-the-art frameworks in terms of cumulative reward, reliability, time and computational cost, and speed of convergence to changes in the reward function.

A two‐stage method for bus passenger load prediction using automatic passenger counting data

In high-frequency transit, providing real-time crowding information (RTCI) is a potential way to promote passenger satisfaction and reduce negative crowding externalities, by assisting passengers in choosing less crowded vehicles. To make RTCI convincing and reliable, it is necessary to provide predictive RTCI, in which bus passenger load (BPL) prediction is the primary problem. This paper proposes a novel two-stage BPL prediction method using automatic passenger counting (APC) data. The first stage is to predict short-term passenger flows at stops based on an adaptive Kalman filter approach. Using the outputs from the first stage as well as other variables directly from APC data, the second stage is to predict BPL based on a support vector regression algorithm. Several methods from the existing literature are used as benchmarks to test the relative performance of the proposed method. An empirical study on bus line 1 in Suzhou, China shows that the proposed method outperforms all the benchmarks, and shows significant superiority over other methods for stops with sharp increases in BPL and for multi-step ahead prediction. This study contributes to the limited literature on BPL prediction and lays the foundation for providing accurate and reliable predictive RTCI in the future.

Adaptive extended Kalman filtering strategies for spacecraft formation relative navigation

The relative navigation problem for spacecraft formation flying missions in near-Earth orbit is addressed here through the design of two unique adaptive extended Kalman filter algorithms. The adaptive filters are capable of updating the internal noise characteristics of the Kalman filter in real time, and are viable in all orbit scenarios, including elliptical orbits subjected to perturbations. The first adaptive Kalman filter approach uses maximum likelihood estimation techniques to derive analytical adaptations laws, which are then improved through the novel inclusion of an intrinsic smoothing routine. The second approach uses an embedded fuzzy logic system based on a covariance-matching analysis of the filter residuals, where the fuzzy system has been specifically designed for the spacecraft navigation problem at hand. Numerical simulations of two spacecraft formations demonstrate that the proposed adaptive navigation algorithms are appreciably more robust to filter initialization errors, dynamics modelling deficiencies, and measurement noises than the standard Kalman filter.

GNSS velocimeter by adaptively combining carrier phase and Doppler measurements

In order to use a stand-alone global navigation satellite system (GNSS) receiver to determine the stable instantaneous velocity, a new hybrid GNSS velocimetry approach combining carrier phase and Doppler measurements is proposed. This is a data fusion problem. The problem is expressed as a state-space model, in which the deviation between the average velocity determined by the time difference carrier phase approach and the instantaneous velocity is represented by the uncertainty of the state model. In kinematic applications, this uncertainty is often variant and hard to be known in advance, a predefined process noise level of the state model is often not sufficiently accurate in the whole working time. Here, an adaptive Kalman filtering approach is employed to fix this problem. To verify the proposed approach, one static experiment and two dynamic experiments with different sampling intervals are performed, separately. All results demonstrate the validity and stability of the proposed approach.

Starting point selection approach for power system model validation using event playback

Model validation is an essential task to determine whether a model can accurately describe the actual behaviours of a power system. Currently, major commercial software tools are equipped with an ‘event playback’ function to validate dynamic models using testing data from phasor measurement units (PMUs). Due to their limited bandwidth and low sampling rates, PMUs cannot capture the fast-transient dynamics. As such, the playback function using the conventional approach may mistakenly invalidate an accurate model during the high-frequency responses. To overcome the deficiency, a batch state estimation approach is proposed in this study to improve the performance of the ‘event playback’ function by focusing on low-frequency responses in model validation. The proposed approach consists of three major steps. First, a multi-model adaptive Kalman filter approach is used to estimate the dynamic states of the system. Second, the singular spectrum analysis (SSA) is used to detect the fault clearance time. Finally, the estimated states after the fault are used as the initial states of the ‘event playback’ to validate the dynamic model during the low-frequency responses. The analytical basis of the proposed method is also provided by showing the existence and uniqueness of the trajectory of the underlying model. The effectiveness of the proposed approach is demonstrated using the PSS/E.

Learning reference governor for cycle-to-cycle combustion control with misfire avoidance in spark-ignition engines at high exhaust gas recirculation–diluted conditions

Cycle-to-cycle feedback control is employed to achieve optimal combustion phasing while maintaining high levels of exhaust gas recirculation by adjusting the spark advance and the exhaust gas recirculation valve position. The control development is based on a control-oriented model that captures the effects of throttle position, exhaust gas recirculation valve position, and spark timing on the combustion phasing. Under the assumption that in-cylinder pressure information is available, an adaptive extended Kalman filter approach is used to estimate the exhaust gas recirculation rate into the intake manifold based on combustion phasing measurements. The estimation algorithm is adaptive since the cycle-to-cycle combustion variability (output covariance) is not known a priori and changes with operating conditions. A linear quadratic regulator controller is designed to maintain optimal combustion phasing while maximizing exhaust gas recirculation levels during load transients coming from throttle tip-in and tip-out commands from the driver. During throttle tip-outs, however, a combination of a high exhaust gas recirculation rate and an overly advanced spark, product of the dynamic response of the system, generates a sequence of misfire events. In this work, an explicit reference governor is used as an add-on scheme to the closed-loop system in order to avoid the violation of the misfire limit. The reference governor is enhanced with model-free learning which enables it to avoid misfires after a learning phase. Experimental results are reported which illustrate the potential of the proposed control strategy for achieving an optimal combustion process during highly diluted conditions for improving fuel efficiency.

Dual Deep Neural Network Based Adaptive Filter for Estimating Absolute Longitudinal Speed of Vehicles

This study employs a dual deep neural network (D-DNN) to accurately estimate the absolute longitudinal speed of a vehicle. Accuracy in speed estimation is crucial for vehicle safety, because longitudinal speed is a common parameter employed as a state variable in active safety systems such as anti-lock braking system and traction control system. In this study, DNNs are applied to determine the gain of an adaptive filter to estimate vehicle speed. The used data consists of longitudinal acceleration, wheel speed, filter gain, and estimated vehicle speed. The data generated from Carsim software are collected and preprocessed using a Simulink model. To acquire data with numerous wheel slip patterns, various acceleration and deceleration conditions are applied to four different road conditions. Though, it is challenging to achieve a single DNN model that is optimally cope with the various driving situations. Thus, we adopt two DNN models that were individually trained in low and high acceleration regions. The dual DNN model results in error reductions of 74% and 65%, compared with a single DNN and classical adaptive Kalman filter approaches, respectively.

A Kalman-Based Approach With EM Optimization for Respiratory Motion Modeling in Medical Imaging

Respiratory motion degrades quantitative and qualitative analysis of medical images. Estimation and, hence, correction of motion commonly uses static correspondence models between an external surrogate signal and internal motion. This paper presents a patient specific respiratory motion model with the ability to adapt in the presence of irregular motion via a Kalman filter with expectation maximization for parameter estimation. The adaptive approach introduces generalizability allowing the model to account for a broader variety of motion. This may be required in the presence of irregular breathing and with different sensors monitoring the external surrogate signal. The motion model framework utilizing an adaptive Kalman filter approach is tested on dynamic magnetic resonance imaging data of nine volunteers and compared to a state-of-the-art static total least squares approach. Results demonstrate the framework is capable of reducing motion to the order of ${p} ) more effective in the presence of irregular motion, assessed using the ${F}$ -test for model comparison. Utilizing the total sum of squares of estimated vector field error from the calculated ground truth, we observe approximately a fifty percent reduction in root mean square error and thirty percent reduction in standard deviation utilizing the Kalman model (EKF) in comparison to a static counterpart.

Experiments on State and Unmeasured-Parameter Estimation of Two Degree-of-Freedom System for Precise Control Based on JAUKF

We herein present system parameter estimation using the joint adaptive unscented Kalman filter and state estimation approach for a two degree-of-freedom (2-DOF) mechanical system. The unscented Kalman filter (UKF) is applied broadly in diverse engineering fields to estimate the state of the dynamic system and improve the control precision by reducing measurement noise. One aspect of parameter identification is that unmeasured parameter estimation is important in designing and maintaining the system performance with a suitable controller. This is because changes in the system parameters estimated will occur owing to external shock and deterioration in operation. State estimation has been studied thoroughly and developed widely, but not in terms of parameter estimation. Parameter estimation is important because system parameters can be altered owing to wear and tear, large disturbance, or exposure to extreme temperatures. It is difficult to disassemble and measure the parameter when it changes; hence, computational estimation is a solution. The proposed method simultaneously estimates the states as well as the parameters of custom-made 2-DOF mechanical system that is a nonlinear dynamical system. The adaptive rules in the estimation process are considered based on the moving average window method to address the effects of unexpected noise in the sensor measurements. The experimental results are analyzed to demonstrate the effectiveness of the proposed method for estimating the states and parameters. This method demonstrates better performance compared to using the joint-UKF in terms of convergence time, accuracy, and robustness to noise.

A Novel Open Circuit Voltage Based State of Charge Estimation for Lithium-Ion Battery by Multi-Innovation Kalman Filter

Accurate state of charge (SOC) estimation is a fundamental guarantee for effective development of lithium-ion power battery in electric vehicles. To improve the SOC estimation precision and robustness, a novel model-based estimation approach has been proposed. Fully giving consideration to the effect of measurement errors, the dynamic external electrical property of lithium-ion battery is approximated by a controlled auto-regressive and moving average (controlled ARMA)-based equivalent circuit model. An improved adaptive extended Kalman filter approach is developed for SOC estimation based on the multi-innovation principle. Meanwhile, the different weighting factor is added into each innovation to reduce cumulative influence of historical interference. Since the flat characteristic in OCV-SOC fitting curve enlarges the OCV-based SOC estimation error, a feedforward compensation method is introduced to reduce OCV identification error to improve OCV-based SOC estimation. The simulation and experimental results verify the validity of the proposed methodology over other estimation methods. Besides, simulated current noise is added to the condition data to prove the high precision and strong robustness of the proposed algorithm.

Real-Time Prediction of Seasonal Heteroscedasticity in Vehicular Traffic Flow Series

Over the past decade, traffic heteroscedasticity has been investigated with the primary purpose of generating prediction intervals around point forecasts constructed usually by short-term traffic condition level forecasting models. However, despite considerable advancements, complete traffic patterns, in particular the seasonal effect, have not been adequately handled. Recently, an offline seasonal adjustment factor plus GARCH model was proposed in Shi et al. 2014 to model the seasonal heteroscedasticity in traffic flow series. However, this offline model cannot meet the real-time processing requirement proposed by real-world transportation management and control applications. Therefore, an online seasonal adjustment factors plus adaptive Kalman filter (OSAF+AKF) approach is proposed in this paper to predict in real time the seasonal heteroscedasticity in traffic flow series. In this approach, OSAF and AKF are combined within a cascading framework, and four types of online seasonal adjustment factors are developed considering the seasonal patterns in traffic flow series. Empirical results using real-world station-by-station traffic flow series showed that the proposed approach can generate workable prediction intervals in real time, indicating the acceptability of the proposed approach. In addition, compared with the offline model, the proposed online approach showed improved adaptability when traffic is highly volatile. These findings are important for developing real-time intelligent transportation system applications.