Adaptive Filter Research Articles

Adaptive polynomial Kalman filter for nonlinear state estimation in modified AR time series with fixed coefficients

AbstractThis article presents a novel approach for adaptive nonlinear state estimation in a modified autoregressive time series with fixed coefficients, leveraging an adaptive polynomial Kalman filter (APKF). The proposed APKF dynamically adjusts the evolving system dynamics by selecting an appropriate autoregressive time‐series model corresponding to the optimal polynomial order, based on the minimum residual error. This dynamic selection enhances the robustness of the state estimation process, ensuring accurate predictions, even in the presence of varying system complexities and noise. The proposed methodology involves predicting the next state using polynomial extrapolation. Extensive simulations were conducted to validate the performance of the APKF, demonstrating its superiority in accurately estimating the true system state compared with traditional Kalman filtering methods. The root‐mean‐square error was evaluated for various combinations of standard deviations of sensor noise and process noise for different sample sizes. On average, the root‐mean‐square error value, which represents the disparity between the true sensor reading and estimate derived from the adaptive Kalman filter, was 35.31% more accurate than that of the traditional Kalman filter. The comparative analysis highlights the efficacy of the APKF, showing significant improvements in state estimation accuracy and noise resilience.

Online state of charge estimation of LiFePO4 battery based on EKF-AUKF algorithm with reference compensation for estimation results

The state of charge(SOC) is an important index in Battery Management System(BMS) for smart grids and electric vehicles, whose accuracy is affected by model and sensor errors. In this paper, an online SOC estimation method based on EKF-AUKF algorithm with reference compensation for estimation results is proposed. Firstly, a joint estimation method based on extended Kalman filter(EKF) and adaptive unscented Kalman filter(AUKF) algorithm is adopted to estimate SOC under Beijing bus dynamic stress test(BBDST) condition. The result shows that the estimation error is within 2 %. Secondly, the characteristics of EKF-AUKF algorithm under voltage and current sampling errors are analyzed over the whole SOC range. The results indicate that voltage measurement error increases SOC estimation error. Then, an online reference is built by calculating the sum of the estimation result of ampere-hour counting(AHC) method and constant deviation, and then the difference between the estimation result of EKF-AUKF algorithm and online reference can be obtained. The absolute value of the difference is used to compare with limit deviation value and compensate the SOC of EKF-AUKF method by different compensation coefficients. Finally, the effectiveness of the proposed method is verified under different operating conditions. The experimental results show that the proposed method can greatly improve the SOC estimation accuracy under large voltage error.

Multi-state Markovian-random walk adaptive filter for time-varying block sparse system identification

This paper presents a higher order multi-state Markov model for block sparsity model of a system impulse response. To capture the time-varying behavior of the system, a random walk model for temporal evolution is incorporated; resulting in a two-dimensional multi-state Markov-Random walk model across spatial and temporal domains. Additionally, a block batch data structure is utilized for the adaptive filter design. The proposed adaptive filter is aimed to find the Maximum A Posteriori (MAP) estimator of the batch time-varying impulse response. The associated optimization problem is demonstrated to be convex and efficiently solvable through the Steepest-Descent (SD) approach. Furthermore, the final recursion of the proposed adaptive filter is derived and a mean convergence analysis of the algorithm is provided. Simulation results show the effectiveness of the proposed algorithm under severe time-varying conditions of the system impulse response, where alternative algorithms may exhibit divergence or poor convergence. Synthetic experiments and real-world experiments using acoustic channel estimation further validate the superiority of the proposed algorithm.

Lithium battery state of charge estimation based on improved variable forgetting factor recursive least squares method and adaptive Kalman filter joint algorithm

As one of the core functions of the battery management system, battery state of charge (SOC) estimation is crucial to battery life and safety. As the traditional recursive least squares method cannot adapt well to complex variable current conditions, this paper proposes a SOC estimation method that combines the improved variable forgetting factor recursive least squares (IVFFRLS) and the adaptive extended Kalman filter (AEKF). First, IVFFRLS removes the rounding operation of the original algorithm to improve the sensitivity to errors and uses a genetic algorithm to optimize the upper and lower bounds of the variable forgetting factor and the sensitivity coefficient to improve the accuracy of the VFFRLS algorithm. Meanwhile, AEKF introduces a noise covariance adaptive update link based on the covariance matching method to correct the system's process noise Q and measurement noise R in real time to improve the SOC estimation accuracy. Based on the second-order RC equivalent circuit model, the method proposed in this paper has good accuracy and robustness under four different working conditions. The experimental results show that compared with traditional methods, the proposed IVFFRLS-AEKF algorithm has higher SOC estimation accuracy and better robustness.

Optimized Longitudinal and Lateral Control Strategy of Intelligent Vehicles Based on Adaptive Sliding Mode Control

To improve the tracking accuracy and robustness of the path-tracking control model for intelligent vehicles under longitudinal and lateral coupling constraints, this paper utilizes the Kalman filter algorithm to design a longitudinal and lateral coordinated control (LLCC) strategy optimized by adaptive sliding mode control (ASMC). First, a three-degree-of-freedom (3-DOF) vehicle dynamics model was established. Next, under the fuzzy adaptive Unscented Kalman filter (UKF) theory, the vehicle state parameter estimation and road adhesion coefficient (RAC) observer were designed to estimate vehicle speed (VS), yaw rate (YR), sideslip angle (SA), and RAC. Then, a layered control concept was adopted to design the path-tracking controller, with a target VS, YR, and SA as control objectives. An upper-level adaptive sliding mode controller was designed using RBF neural networks, while a lower-level tire force distribution controller was designed using distributed sequential quadratic programming (DSQP) to obtain an optimal tire driving force. Finally, the control strategy was validated using Carsim and Matlab/Simulink software under different road adhesion coefficients and speeds. The findings indicate that the optimized control strategy is capable of adaptively adjusting control parameters to accommodate various complex conditions, enhancing the tracking precision and robustness of vehicles even further.

Cycle Fluctuations in the U.S. Real GDP and National Income and Product Accounts Aggregates

This article provides a new set of empirical regularities describing the U.S. macroeconomy, focusing on business cycle fluctuations in the real GDP and eleven major aggregates from the U.S. National Income and Product Accounts (NIPAs). Patterns of the cyclical fluctuations are assessed using filtering methodologies that adapt to the properties of the series being studied. We employ a recent dataset that includes the Great Recession caused by the 2008 financial crisis and the ensuing recovery. We aim to (1) examine the lead-lag relations via cross-correlations between the aggregate cycle in the U.S. real GDP and the cyclical movements in the eleven major NIPA aggregates; (2) investigate econometrically the inter-linkage between the cyclical component of real GDP and that of each NIPA aggregate by way of the Granger-causality test; and (3) evaluate the capability or the predictive power of each NIPA aggregate to forecast real GDP growth via three forecasting models. Comparisons are made with popular nonparametric HP and Baxter-King (BK) filters. The basic conclusion from the empirical analysis is that the adaptive model-based filters have demonstrated advantages over the commonly used HP and BK filters for business cycle analysis across very diverse economic series from the U.S. national accounts, and the structural time series model using smoothed trend and cycle estimates produced more accurate forecasts than the AR(p) model that forecasts directly using the unfiltered time series.

An adaptive spatiotemporal filter for ultrasound localization microscopy based on density canopy clustering

Ultrasound Localization Microscopy (ULM) facilitates structural and hemodynamic imaging of microvessels with a resolution of tens of micrometers. In ULM, the extraction of effective microbubble signals is crucial for image quality. Singular Value Decomposition (SVD) is currently the most prevalent method for microbubble signal extraction in ULM. Most existing ULM studies employ a fixed SVD filter threshold using empirical values which will lead to imaging quality degradation due to the insufficient separation of blood signals. In this study, we propose an adaptive and non-threshold SVD filter based on canopy-density clustering, termed DCC-SVD. This filter automatically classifies the components of the SVD based on the density of their spatiotemporal features, eliminating the need for parameter selection. In in vitro tube phantom, DCC-SVD demonstrated its ability to adaptive separation of blood and bubble signal at varying microbubble concentrations and flow rates. We compared the proposed DCC-SVD method with the Block-match 3D (BM3D) filter and a classical adaptive method called spatial similarity matrix (SSM), using concentration-variable in vivo rat brain data, as well as open-source rat kidney and mouse tumor datasets. The proposed DCC-SVD improved the global spatial resolution by approximately 4 μm from 30.39 μm to 26.02 μm. It also captured vessel structure absent in images obtained by other methods and yielded a smoother vessel intensity profile, making it a promising spatiotemporal filter for ULM imaging.

Research on dynamic blood oxygen saturation measurement based on motion noise reconstruction combined with convex combination least mean square adaptive filter

The performance of a pulse oximeter based on photoelectric detection is greatly affected by motion noise (MA) in the photoplethysmographic (PPG) signal. This paper presents an algorithm for detecting motion oxygen saturation, which reconstructs a motion noise reference signal using ensemble of complete adaptive noise and empirical mode decomposition combined with multi-scale permutation entropy, and eliminates MA in the PPG signal using a convex combination least mean square adaptive filters to calculate dynamic oxygen saturation. The test results show that, under simulated walking and jogging conditions, the mean absolute error (MAE) of oxygen saturation estimated by the proposed algorithm and the reference oxygen saturation are 0.05 and 0.07, respectively, with means absolute percentage error (MAPE) of 0.05% and 0.07%, respectively. The overall Pearson correlation coefficient reaches 0.971 2. The proposed scheme effectively reduces motion artifacts in the corrupted PPG signal and is expected to be applied in portable photoelectric pulse oximeters to improve the accuracy of dynamic oxygen saturation measurement.

Design and implementation of an adaptive unscented Kalman filter with interval Type-3 fuzzy set for an attitude and heading reference system considering gyroscope bias

Low-cost microelectromechanical sensors used in attitude and heading reference systems (AHRS) suffer from unstable on–off biases, scaling errors, and nonlinearities that lead to an increase of navigation errors over time. To damp these errors and uncertainties from ultimate attitude and heading angles, the bias term of gyroscopes is augemented in under estimation state vector for high frequency feedback compensation. In this paper, an adaptive estimation algorithm to combine the strong tracking filter (STF) and interval type-3 fuzzy set (IT3FS) with an unscented Kalman filter (UKF) is proposed to deal with the large uncertainties in the microelectromechanical AHRS. The UKF, involving strong capability of dealing with nonlinearity, is limited by large instable bias uncertainty. By combining the STF to adaptively tuning of the UKF gain matrix and the IT3FS to determine the STF fading factor as well, the new IT3FS-STUKF algorithm is developed for high estimation performance against the significant uncertainties. To validate the proposed IT3FS-STUKF, real experiments are conducted with ground vehicles in urban areas, which show an improved accuracy compared to the extended Kalman filter (EKF) at reasonable computational burden.

Performance analysis of unconstrained partitioned-block frequency-domain adaptive filters in under-modeling scenarios

The unconstrained partitioned-block frequency-domain adaptive filter (PBFDAF) offers superior computational efficiency over its constrained counterpart. However, the correlation matrix governing the natural modes of the unconstrained PBFDAF is not full rank. Consequently, the mean coefficient behavior of the algorithm depends on the initialization of adaptive coefficients and the Wiener solution is non-unique. To address the above problems, a new theoretical model for the deficient-length unconstrained PBFDAF is proposed by constructing a modified filter weight vector within a system identification framework. Specifically, we analyze the transient and steady-state convergence behavior. Our analysis reveals that modified weight vector is independent of its initialization in the steady state. The deficient-length unconstrained PBFDAF converges to a unique Wiener solution, which does not match the true impulse response of the unknown plant. However, the unconstrained PBFDAF can recover more coefficients of the parameter vector of the unknown system than the constrained PBFDAF in certain cases. Also, the modified filter coefficient yields better mean square deviation (MSD) performance than previously assumed. The presented alternative performance analysis provides new insight into convergence properties of the deficient-length unconstrained PBFDAF. Simulations validate the analysis based on the proposed theoretical model.

Top oil temperature prediction at a multiple time scale for power transformers based on adaptive extended Kalman filter

Top oil temperature prediction at a multiple time scale for power transformers based on adaptive extended Kalman filter

A hybrid model for state of charge estimation of lithium-ion batteries utilizing improved adaptive extended Kalman filter and long short-term memory neural network

With lithium-ion batteries being utilized in all aspects of life, accurately estimating the state of charge (SOC) of a battery has become a key issue in battery management systems. In this paper, an improved hybrid model based on adaptive extended Kalman filter (AEKF) and improved long short-term memory (ILSTM) neural network is proposed. The proposed model is based on a second-order RC equivalent circuit model, and the dynamic forgetting factor recursive least squares (DFFRLS) and AEKF algorithms are utilized to obtain the initial SOC estimates. And the estimation error in the AEKF algorithm due to neglecting the higher order terms of the Taylor expansion equations is compensated by the improvement of the LSTM network. The results under different working conditions indicate that the SOC estimation of the hybrid model has good convergence and high system robustness. The maximum error (MAX) of this algorithm is less than 2.3 %, especially the root mean square error (RMSE) and mean absolute error (MAE) are less than 0.84 % and 0.65 %, respectively.

Dynamic Tracking Method Based on Improved DeepSORT for Electric Vehicle

The development of electric vehicles has facilitated intelligent transportation, which requires the swift and effective detection and tracking of moving vehicles. To satisfy this demand, this paper presents an enhanced DeepSORT algorithm. By selecting YOLO-SSFS as the front-end detector and incorporating a lightweight and high-precision feature training network called FasterNet, the proposed method effectively extracts vehicle appearance attributes. Besides this, the noise scale adaptive Kalman filter is implemented and the conventional cascade matching process is substituted with global join matching, thereby enhancing overall performance and tracking accuracy. Validation conducted on the VisDrone dataset demonstrates the superiority of this method compared to the original DeepSORT algorithm, exhibiting a 4.76% increase in tracking accuracy and a 3.10% improvement in tracking precision. The findings reveal the advantages of the algorithms in the domain of vehicle detection and tracking, allowing significant technological advancements in intelligent transportation systems.

Online numerical simulation method based on adaptive unscented Kalman filter for shear wall structures

Hybrid test method is an effective approach to evaluate the seismic performance of engineering structures. Particularly, online numerical simulation method (ONSM) based on unscented Kalman filter (UKF) model updating significantly improves the accuracy of the hybrid test results. However, the sensitivity of UKF to the initial values of the state vector, state covariance, and observation noise covariance may lead to the distortion of hybrid test results. To address these issues, one novel ONSM based on adaptive UKF (ONSM-AUKF) is proposed in this paper. The AUKF algorithm incorporates an adaptive variance module to maintain equilibrium. This not only reduces the sensitivity of UKF to the initial parameter settings, prevents filter divergence, but also enhances the accuracy and stability of estimation. The proposed ONSM-AUKF accurately identifies the constitutive model parameters by utilizing measured data from specimens through the AUKF algorithm, which improves the accuracy and the stability of parameter estimation. The simulation results indicate that AUKF algorithm has the capability to decrease the sensitivity of initial parameter settings, thus enhancing the stability and robustness of parameter estimation in comparison to the UKF algorithm. The experimental results validate the feasibility and effectiveness of the proposed ONSM-AUKF, as well as the advantages of the ONSM-AUKF over the ONSM-UKF. The results indicate that the proposed ONSM-AUKF may have broad application prospect in evaluating the seismic performance of various of complex engineering structures.

Research on Vehicle Stability Control Based on a Union Disturbance Observer and Improved Adaptive Unscented Kalman Filter

This paper considers external disturbances imposed on vehicle systems. Based on a vehicle dynamics model of the vehicle with three degrees of freedom (3-DOFs), a union disturbance observer (UDO) composed of a nonlinear disturbance observer (NDO) and an extended state observer (ESO) was designed to obtain external disturbances and unmodeled items. Meanwhile, an improved adaptive unscented Kalman filter (iAUKF) with anti-disturbance and anti-noise properties is proposed, based on the UDO and the unscented Kalman filter (UKF) method, to evaluate the sideslip angle of vehicle systems. Finally, a vehicle yaw stability controller was designed based on UDO and the global fast terminal sliding mode control (GFTSMC) method. The results of co-simulation demonstrated that the proposed UDO was effectively able to observe external disturbances and unmodeled items. The proposed iAUKF, which considers external disturbances, not only achieves adaptive updating and adjustment of filtering parameters under different sensor noise intensities but can also resist external disturbances, improving the estimation accuracy and robustness of the UKF. In the anti-disturbance performance test, the maximum estimation error of the sideslip angle of the iAUKF under the three working conditions was less than 0.1°, 0.02°, and 0.5°, respectively. Based on the UDO and the GFTSMC, a vehicle yaw stability controller is described, which improves the accuracy of control and the robustness of the vehicle’s stability control system and greatly strengthens the driving safety of the vehicle.

Helicopter Turboshaft Engines’ Gas Generator Rotor R.P.M. Neuro-Fuzzy On-Board Controller Development

The work is devoted to the helicopter turboshaft engines’ gas generator rotor R.P.M. neuro-fuzzy controller development, which improves control accuracy and increases the system’s stability to external disturbances and adaptability to changing operating conditions. Methods have been developed, including improvements to the automatic control system structural diagram which made it possible to obtain the system transfer function in the bandpass filter transfer function form. The work also improved the fuzzy rules base and the neuron activation function mathematical model, which significantly accelerated the neuro-fuzzy controller training process. The transfer function frequency and time characteristics analysis showed that the system effectively controlled the engine and reduced vibration. Methods for ensuring a guaranteed stability margin and the synthesis of an adaptive filter were studied, which made it possible to achieve the system’s high stability and reliability. The results showed that the developed controller provided high stability with amplitude and phase margins, effectively compensating for changes in external conditions. Experimental studies have demonstrated that the control quality improved by 2.31–2.42 times compared to previous neuro-fuzzy controllers and by 5.13–5.65 times compared to classic PID controllers. Control errors were reduced by 1.84–2.0 times and 5.28–5.97 times, respectively, confirming the developed neuro-fuzzy controller’s high efficiency and adaptability.

Large-eddy simulation of shock train in convergent-divergent nozzles with isothermal walls

ABSTRACT High-order accurate Large-eddy simulations (LES) have been carried out for compressible, turbulent flow through two bell-shaped convergent-divergent nozzles- one with a short divergent portion and the other with a longer one. An explicit filtering approach based on approximate deconvolution method is used for the LES. The nozzles have isothermal walls and circular cross-sections. The incoming flow is a turbulent, subsonic fully developed pipe flow at centreline Mach number of around 0.4 and friction Reynolds number 216. An adaptive filter is used to capture the shocks appearing in the divergent portion of the nozzles. The complicated behaviour of the mean flow, Reynolds stresses, production and pressure-strain terms of the axial Reynolds stress budget in the shock train region is shown. The broadband nature of the shock train oscillations having multiple dominant frequencies in these nozzles is observed in the present LES.

Synthesis of hardware and software for adaptive discrete high-order control systems based on a model of the desired transient process with a guaranteed degree of stability

In this work, analytical expressions for the connection between optimization criteria andsettings parameters of the adaptive PI-PID controller with variable parameters of the object andadaptive filter have been removed. A method for synthesizing a model of discrete controllersbased on given dynamic characteristics has been developed. A method has been developed forsynthesizing a model of a discrete PID controller based on given dynamic characteristics basedon the criterion of the transient process of a guaranteed level of stability. 3 figures, 0 tables, 32formulas, 19 bibliographic sources..Analytical expressions have been removed to link the optimization criteria andadjustment parameters of the adaptive PI-PID controller with the variable parameters of theobject and adaptive filter.A method for synthesizing a model of discrete controllers from specified dynamiccharacteristics has been developed. The average warehouse of output pulses at the output of anonlinear channel, which is formed at the output of such a regulator and is seen as an inertialinduced uninterrupted part, changes according to the law, which is designated as a reversetransmission the function of the lanyard of the new molded filter model at the collar of the non-linear element.A method has been developed for synthesizing a model of a discrete PID controller fromspecified dynamic characteristics based on the criterion of the required transient process of aguaranteed stability level.The modeling showed that while the parameters of the object and the adaptive filter willchange during the ASC operation, then, obviously, the optimal parameters for adjusting theadaptive PID controller will immediately change.

Closed-loop state of charge estimation of Li-ion batteries based on deep learning and robust adaptive Kalman filter

The state of charge (SOC) is among the most crucial monitoring states in battery management systems. To accurately and robustly estimate the battery SOC, a closed-loop SOC estimation method based on deep neural networks is proposed in this study. Initially, a hybrid deep learning model, TGMA, is established by combining a temporal convolutional network (TCN) with a gated recurrent unit (GRU) and incorporating a multi-head self-attention mechanism (MHA) to estimate SOC. Subsequently, to further enhance the accuracy of estimating the battery SOC and the ability to resist outliers, the pre-estimated SOC from the deep learning model TGMA is used as the noisy observation in the Kalman filter, and robust factor and noise adaptive filtering are introduced into the Kalman filter, proposing a closed-loop estimation method based on deep learning and robust adaptive Kalman filter (RAKF). Finally, through comparison with other similar methods, the proposed TGMA-RAKF method is validated to have higher accuracy, generalization, and robustness against outliers under different operating conditions and temperatures, with root mean square error, mean absolute error, and maximum absolute error all less than 1 %, 1 %, and 2.5 % respectively.

Load Effect Analysis Method of Cable-Stayed Bridge for Long-Span Track Based on Adaptive Filtering Method

Load Effect Analysis Method of Cable-Stayed Bridge for Long-Span Track Based on Adaptive Filtering Method