Optimal Kalman Filter Research Articles

Research on improving the ranging accuracy of ships with stereo vision through Kalman filter optimization.

The real-time and accurate detection and ranging of ships play a pivotal role in ensuring navigation safety, this study aims to enhance the navigation safety and environmental perception capabilities of inland waterway vessels. In the ship detection stage, addressing challenges such as large parameters, high computational complexity, and poor real-time performance in existing ship detection models, this paper proposes the MS-YOLOv5s ship target detection algorithm. This algorithm, based on YOLOv5s, utilizes the lightweight MobileNetV3-Small network to replace the original YOLOv5s feature extraction backbone network, thereby improving the detection speed. The results indicate that the parameter size of the MS-YOLOv5s model is 3.55M, only 50.49% of YOLOv5s. Achieving a detection rate of 50.28 FPS, the precision is 96.80%, and the mAP is 98.40%, striking a balance between high accuracy and low computational demand. In the depth estimation stage, influenced by the environment, leading to unstable measurement data, this paper proposes a binocular Kalman filter fusion ranging algorithm. The standard deviation of the ranging results is minimized to 6.032μm, which is one order of magnitude smaller than traditional ranging algorithms, significantly enhancing the robustness of the measurement results. Within a distance of 20m from the ship target, the error can be controlled within 3%, showcasing the applicability of the method proposed in this paper in complex inland waterway environments contributes to the enhancement of ships' environmental perception capabilities and navigation safety, holding positive implications for the development of intelligent vessels.

Regional Comparison of Performance between EnKF and EnOI in the North Pacific

Abstract The North Pacific is divided into different regions based on ocean currents and sea surface temperature (SST) distribution. Data assimilation is a useful tool for generating accurate ocean estimates because of the limited availability of observational data. This study compared the performances of two data assimilation methods, ensemble optimal interpolation (EnOI) and ensemble Kalman filter (EnKF), in various North Pacific subregions using an ocean model configured with the Regional Ocean Modeling System (ROMS). Both methods assimilated spaceborne SST observations, and the simulation results varied by subregion. The study found that EnKF and EnOI methods performed better than the control model in all regions when compared against satellite SST. EnOI reproduced SST as well as EnKF and required fewer computational resources. However, EnOI performed worse than the control model at sea surface height (SSH) in the equatorial region, while EnKF’s performance improved. This was due to the crushed mean state in the EnOI, which used long-term historical data as an ensemble member. El Niño–Southern Oscillation at the equator drove substantial interannual variability that crushed the ensemble mean of SSH in the EnOI. It is crucial to use a suitable assimilation method for the target area, considering the regional properties of ocean variables. Otherwise, the performance of the assimilated model may be even worse than that of the control model. While EnKF is better suited for regions with high variability in ocean variables, EnOI requires fewer computational resources. Thus, it is crucial to use a suitable assimilation method for accurately predicting and understanding the dynamics of the North Pacific.

Inverse estimation of heat flux and temperature field for a nonlinear heat transfer system using step-renewed two-stage Kalman filter

Inverse estimation of the thermal input and states is a useful tool for the monitoring of a thermal system. Nonlinear heat transfer is a quite common issue in this kind of problem. As the thermal properties are temperature-dependent, it is difficult to inversely estimate the input and temperature field. To deal with this problem, a step-renewed scheme is adopted into the weighted optimal two-stage Kalman filter (WOTSKF), forming step-renewed WOTSKF (SR-WOTSKF). This strategy is a marching method, without solving the Jacobian matrix in extended Kalman filter. The feasibility of dealing with the nonlinear inverse heat transfer problem is implemented by comparing WOTSKF and SR-WOTSKF. Then, the weighting factor, initial guess of the input heat flux and measurement noise are changed to investigate their effects on the simultaneous estimation results of heat flux and temperature field. It is found that when the weighting factor is 0.95, the relative error of the estimated heat flux using SR-WOTSKF is approximately 2.73% which is much lower than that using WOTSKF. Results using SR-WOTSKF demonstrate that the estimation results are independent of the initial guess and the estimated heat flux can track the exact one in a short period. An incorrect initial guess causes the initial estimation error of the temperature and heat flux and it makes no sense to following period. When the standard deviations of the measurement noise are adopted as 0.01, 0.10, 0.50 and 1.00, the mean relative error of the heat flux is 2.73%, 4.79%, 7.71% and 9.43%, demonstrating the strong robustness of SR-WOTSKF to resist the measurement noise.

Agricultural products industry chain construction based on multiple regression analysis on the innovation of rural management mode

Abstract This paper constructs a multiple regression analysis model of the agricultural industry chain with rural environment and economic management and estimates the model parameters using the least squares method. The linear correlation between the variables is analyzed based on the variance expansion coefficient, standardization coefficient, complex correlation coefficient and other indicators, and the regression problem is analyzed for significance. Then the antidifferential Kalman filter optimization method of least squares and the threshold denoising optimization method based on wavelet decomposition and reconstruction transformation are introduced to optimize the model parameters to improve the model performance. Finally, the impact of agricultural industry chain construction on the rural environment and economic management is analyzed based on the model. The correlation coefficients between the three dimensions of agricultural product industry chain management and the performance of rural economic management are 0.318, 0.468, 0.416, and the correlation coefficients between them and the performance of rural environmental management are 0.297, 0.528, and 0.529, respectively, which indicates that rural agricultural product industry chain construction can promote rural management.

Recurrent Neural Networks Are Universal Approximators With Stochastic Inputs.

In this article, we investigate the approximation ability of recurrent neural networks (RNNs) with stochastic inputs in state space model form. More explicitly, we prove that open dynamical systems with stochastic inputs can be well-approximated by a special class of RNNs under some natural assumptions, and the asymptotic approximation error has also been delicately analyzed as time goes to infinity. In addition, as an important application of this result, we construct an RNN-based filter and prove that it can well-approximate finite dimensional filters which include Kalman filter (KF) and Beneš filter as special cases. The efficiency of RNN-based filter has also been verified by two numerical experiments compared with optimal KF.

Reduction of the Influence of Interfering Signals on the Longitudinal Control of UAVs with Fixed Wing

The presented study offers a comprehensive insight in design and application of the Kalman filters for improvement of control efficiency of small unmanned aerial vehicles with fixed wing. The presented control scheme of the UAV includes its model, a servo drive model, and an optimal proportional-integral-derivative (PID) controller for the selected flight speed. Subsequently, process noise and measurement noise components were introduced into the whole constructed UAV model. The process noise was formed by disturbances caused by horizontal and vertical airflow in the atmosphere. The measurement noise contained deterministic and stochastic errors of the inertial measurement unit (IMU) UAV sensors and engine noise. The obtained results showed that the designed optimal Kalman filter was able to eliminate the influence of interfering signals from the control process and increased the phase safety, controllability, and stability of UAV control as a lean design can be applied in real-time control systems like Pixhawk PX4.

H∞‐FIR filtering of disturbed systems using LMI under measurement and initial errors

SummaryFinite impulse response (FIR) filtering is known to be more robust than Kalman filtering. In this article, we derive a discrete convolution‐based ‐FIR observer for disturbed systems under measurement and initial errors. The gain for the ‐FIR observer is obtained numerically by solving a linear matrix inequality (LMI). Since the LMI has a term that is quadratic with respect to the filter gain, we modify and constrain LMI by introducing an additional variable and proving a theorem. It is shown numerically and experimentally that for disturbed systems operating under measurement and initial errors, the developed ‐FIR observer surpasses the optimal FIR and Kalman filters in accuracy and has almost the same robustness as a robust unbiased FIR filter.

Identification and Error Analysis of Lithium-Ion Battery Oriented to Cloud Data Application Scenario

The label-less characteristics of real vehicle data make engineering modeling and capacity identification of lithium-ion batteries face great challenges. Different from ideal laboratory data, the raw data collected from vehicle driving cycles have a great adverse impact on effective modeling and capacity identification of lithium-ion batteries due to the randomness and unpredictability of vehicle driving conditions, sampling frequency, sampling resolution, data loss, and other factors. Therefore, data cleaning and optimization is processed and the capacity of a battery pack is identified subsequently in combination with the improved two-point method. The current available capacity is obtained by a Fuzzy Kalman filter optimization capacity estimation curve, making use of the charging and discharging data segments. This algorithm is integrated into a new energy big data cloud platform. The results show that the identification algorithm of capacity is applied successfully from academic to engineering fields by charge and discharge mutual verification, and that life expectancy meets the engineering requirements.

A Distributed Implementation of Steady-State Kalman Filter

This paper studies the distributed state estimation in sensor network, where <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$m$</tex></formula> sensors are deployed to infer the <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$n$</tex></formula> -dimensional state of a Linear Time-Invariant (LTI) Gaussian system. By a lossless decomposition of the optimal steady-state Kalman filter, we show that the problem of distributed estimation can be reformulated as that of the synchronization of homogeneous linear systems. Based on such decomposition, a distributed estimator is proposed, where each sensor node runs a local filter using only its own measurement, alongside with a consensus algorithm to fuse the local estimate of every node. We prove that the average of estimates from all sensors coincides with the optimal Kalman estimate, and under certain condition on the graph Laplacian matrix and the system matrix, the consensus error is bounded and the asymptotic error covariance is derived. As a result, the distributed estimator is stable for each single node. We further show that the proposed algorithm has a low message complexity of min( <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$m$</tex></formula> , <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$n$</tex></formula> n). Numerical examples are provided in the end to illustrate the efficiency of the proposed algorithm.

MIMU Optimal Redundant Structure and Signal Fusion Algorithm Based on a Non-Orthogonal MEMS Inertial Sensor Array.

A micro-inertial measurement unit (MIMU) is usually used to sense the angular rate and acceleration of the flight carrier. In this study, multiple MEMS gyroscopes were used to form a spatial non-orthogonal array to construct a redundant MIMU system, and an optimal Kalman filter (KF) algorithm was established by a steady-state KF gain to combine array signals to improve the MIMU's accuracy. The noise correlation was used to optimize the geometric layout of the non-orthogonal array and reveal the mechanisms of influence of correlation and geometric layout on MIMU's performance improvement. Additionally, two different conical configuration structures of a non-orthogonal array for 4,5,6,8-gyro were designed and analyzed. Finally, a redundant 4-MIMU system was designed to verify the proposed structure and KF algorithm. The results demonstrate that the input signal rate can be accurately estimated and that the gyro's error can also be effectively reduced through fusion of non-orthogonal array. The results for the 4-MIMU system illustrate that the gyro's ARW and RRW noise can be decreased by factors of about 3.5 and 2.5, respectively. In particular, the estimated errors (1σ) on the axes of Xb, Yb and Zb were 4.9, 4.6 and 2.9 times lower than that of the single gyroscope.

Simultaneous estimation of heat flux and temperature field using optimal two-stage Kalman filters

Inverse estimation of unknown input heat flux and temperature field plays an important role in thermal state monitoring. Optimal two-stage Kalman filter (OTSKF) is introduced into the inverse estimation of thermal state in this work. To further improve its performance, a new method weighted optimal two-stage Kalman filter (WOTSKF) algorithm is developed, in which a forgetting factor is used to modify OTSKF. The estimation performances of OTSKF and WOTSKF are compared in a two-dimensional heat transfer system. They are employed to estimate the state with heat flux of temporal, spatial, and spatiotemporal variation. Additionally, the effects of forgetting factor and measurement noises on the estimation accuracy of heat flux and temperature are investigated. Though decreasing the forgetting factor can improve the tracking ability and estimation accuracy of WOTSKF, it should not be too low due to the reason that low α causes fluctuation of estimation results. When the standard deviation of measurement noises σr increases from 0.05 to 2.00, the mean relative error of estimated heat flux ηq using OTSKF rises from 4.03% to 10.67% and it climbs from 2.76% to 7.07% using WOTSKF. That demonstrates proposed WOTSKF has stronger robustness than OTSKF.

Adaptive Kalman filter based on integer ambiguity validation in moving base RTK

In high-precision dynamic positioning, it is necessary to ensure the positioning accuracy and reliability of the navigation system, especially for safety–critical applications, such as intelligent vehicle navigation. In the face of a complex observation environment, when the global navigation satellite system (GNSS) uses carrier phase observations for high-precision relative positioning, ambiguity resolution will be affected, and it is difficult to estimate all ambiguities. In addition, when the GNSS signal quality and measurement noise level are difficult to predict in an environment with many occlusions, the received satellite observations are prone to very large errors, resulting in apparent deviations in the positioning solution. However, traditional positioning algorithms assume that the measurement noise is constant, which is unrealistic. This will cause incorrect ambiguity resolution, lead to meter-level positioning errors, reduce the reliability of the system, and increase the integrity risk of the system. We proposed an innovative adaptive Kalman filter based on integer ambiguity validation (IAVAKF) to improve the efficiency of ambiguity resolution (AR) and positioning accuracy. The partial ambiguity resolution (PAR) method is applied to solve the integer ambiguities. Then, the accuracy of the fixed ambiguity is verified by the ambiguity success rate. Taking the ambiguity success rate as a dynamic adjustment factor, the measurement noise matrix and variance–covariance matrix of the state estimation is adaptively adjusted at each time interval in the Kalman filter to provide a smoothing effect for filtering. The optimal Kalman filter gain matrix is obtained to improve positioning accuracy and reliability. As a result, the static and dynamic vehicle experiments show that the positioning accuracy of the proposed IAVAKF is improved by 26% compared with the KF. Through the IAVAKF, a more realistic PL can be obtained and applied to evaluate the integrity of the navigation system in the position domain. It can reduce the false alarm rate by 2.45% and 1.85% in the horizontal and vertical directions, respectively.

The development and evaluation of a combined initial alignment algorithm for strapdown inertial navigation system

This paper proposes a combined initial alignment algorithm for strapdown inertial navigation system, in which the initial alignment is carried out in two stages during the process of preflight preparations while the aircraft is not moving. This method of initial alignment has the advantages of being conducted based on the Earth’s equatorial (Greenwich) coordinate system, which is also used by the aircraft onboard navigation system. In the first stage, the coarse initial alignment is carried out, and this is done according to the orientation parameters using the vector matching method. Then, in the second stage, a fine procedure is carried out, which may be looked at as an integrated system implemented using optimal Kalman filter. In this case, the initial parameters of orientation and navigation are refined, as well as the systematic errors of the inertial sensors are estimated and corrected. The simulation results show that the required level of initial alignment accuracy could be achieved by applying coarse and fine initial alignment procedures not sequentially but in a combination.

АДАПТИВНЕ ОЦІНЮВАННЯ ПАРАМЕТРІВ РУХУ ПОВІТРЯНОГО СУДНА У РЕЖИМІ ДОТРИМАННЯ ЗАДАНОЇ ПОСАДКОВОЇ ТРАЄКТОРІЇ

The creation of a large number of new aircraft types and their intensive operation have led to an increase in air traffic. Guaranteeing the required level of safety requires continuous improvement of air traffic organization and control systems. This stimulates the modernization of existing and the creation of new types of radio equipment. In this work, the object of study is the processes of converting information signals in the goniometric channel of the radio landing system, and its goal is to achieve increased accuracy of angular measurements and their reliability by methods of secondary signal processing based on the basic principles of the theory of optimal linear discrete Kalman filter. It is shown that one of the possible ways to achieve this goal can be the use of a polymodel model of aircraft motion, supplemented by interacting logic of a stochastic type, as an effective, relatively simple resource-saving tool for overcoming a priori uncertainty of conditions and flight regime. Considerations are given regarding the adequacy of the mathematical model types used to describe a fixed aircraft approach trajectory. The issues of approximation of nonlinear dependences in the goniometric channel of the landing radar in the process of changing the coordinate system are considered. A technique for performing a computational experiment using the Monte Carlo method using the computing environment of the LabView modeling system is presented. The obtained results prove the effectiveness of the polymodel method for constructing a filter adapted to the needs of the aircraft landing process. The absence of discrepancies regarding the regulated standards for the accuracy of measuring the angular coordinates of the aircraft confirm this fact.

M-estimation based Robust Approach for Hybrid Dynamic State Estimation in Power Systems

Background: The state estimation (SE) process in power systems estimates bus voltage magnitude and phase angles vital for operating the system securely and reliably. The power systems state estimation problem has been extensively solved through a weighted least squares (WLS) based static approach that fails to track the system dynamics. Furthermore, those approaches are not inherently robust against outliers, yielding a separate bad data processing (BDP) technique. Popular Dynamic state estimation (DSE) schemes which mainly employ nonlinear Kalman filters like Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), also suffer from providing a reasonable estimation of states in the presence of bad data. Although several generalized maximum (GM) likelihood- based DSE approaches are robust against outliers, they are mainly based on nonlinear Kalman filters, which yield an iterative process. Therefore, this article focuses on developing a robust DSE approach that gives a good estimation of states against outliers in a single iteration. Objective: This article aims to propose a robust hybrid non-iterative DSE approach that gives robust SE results in the presence of bad data. Methods: The proposed novel robust hybrid DSE (NRHDSE) approach combines the robust Mestimation with the original novel hybrid DSE (NHDSE) approach. The proposed scheme implements a suitable linear relationship between integrated hybrid measurements and complex states. The proposed method uses a linear measurement model and thus employs an optimal linear Kalman filter to correct or estimate states. Results: The efficacy of the proposed approach has been demonstrated by applying it on IEEE 57, 118 bus test systems and one more extensive 246 Indian utility bus system, namely, Northern Regional Power Grid (NRPG), and after that comparing it with the original NHDSE, and DSE methods based on traditional EKF and M-estimation based robust version of EKF (REKF). The simulation result demonstrates the superiority of the proposed approach. Conclusions: Obtained results clearly show the superiority of the proposed approach.

An Efficient Estimation Method for Dynamic Systems in the Presence of Inaccurate Noise Statistics

The uncertainty of noise statistics in dynamic systems is one of the most important issues in engineering applications, and significantly affects the performance of state estimation. The optimal Bayesian Kalman filter (OBKF) is an important approach to solve this problem, as it is optimal over the posterior distribution of unknown noise parameters. However, it is not suitable for online estimation because the posterior distribution of unknown noise parameters at each time is derived from its prior distribution by incorporating the whole measurement sequence, which is computationally expensive. Additionally, when the system is subjected to large disturbances, its response is slow and the estimation accuracy deteriorates. To solve the problem, we improve the OBKF mainly in two aspects. The first is the calculation of the posterior distribution of unknown noise parameters. We derive it from the posterior distribution at a previous time rather than the prior distribution at the initial time. Instead of the whole measurement sequence, only the nearest fixed number of measurements are used to update the posterior distribution of unknown noise parameters. Using the sliding window technique reduces the computational complexity of the OBKF and enhances its robustness to jump noise. The second aspect is the estimation of unknown noise parameters. The posterior distribution of an unknown noise parameter is represented by a large number of samples by the Markov chain Monte Carlo approach. In the OBKF, all samples are equivalent and the noise parameter is estimated by averaging the samples. In our approach, the weights of samples, which are proportional to their likelihood function values, are taken into account to improve the estimation accuracy of the noise parameter. Finally, simulation results show the effectiveness of the proposed method.

How Peripheral Vestibular Damage Affects Velocity Storage: a Causative Explanation.

Velocity storage is a centrally-mediated mechanism that processes peripheral vestibular inputs. One prominent aspect of velocity storage is its effect on dynamic responses to yaw rotation. Specifically, when normal human subjects are accelerated to constant angular yaw velocity, horizontal eye movements and perceived angular velocity decay exponentially with a time constant circa 15-30s, even though the input from the vestibular periphery decays much faster (~ 6s). Peripheral vestibular damage causes a time constant reduction, which is useful for clinical diagnoses, but a mechanistic explanation for the relationship between vestibular damage and changes in these behavioral dynamics is lacking. It has been hypothesized that Bayesian optimization determines ideal velocity storage dynamics based on statistics of vestibular noise and experienced motion. Specifically, while a longer time constant would make the central estimate of angular head velocity closer to actual head motion, it may also result in the accumulation of neural noise which simultaneously degrades precision. Thus, the brain may balance these two effects by determining the time constant that optimizes behavior. We applied a Bayesian optimal Kalman filter to determine the ideal velocity storage time constant for unilateral damage. Predicted time constants were substantially lower than normal and similar to patients. Building on our past work showing that Bayesian optimization explains age-related changes in velocity storage, we also modeled interactions between age-related hair cell loss and peripheral damage. These results provide a plausible mechanistic explanation for changes in velocity storage after peripheral damage. Results also suggested that even after peripheral damage, noise originating in the periphery or early central processing may remain relevant in neurocomputations. Overall, our findings support the hypothesis that the brain optimizes velocity storage based on the vestibular signal-to-noise ratio.

Distributed Filtering for Multi-sensor Systems with Missing Data

This paper studies distributed estimation problems for multi-sensor systems with missing data. Missing data may occur during sensor measuring or data exchanging among sensor nodes due to unreliability of communication links or external disturbances. Missing data include random missing measurements of sensor itself and random missing estimates of neighbor nodes. Three distributed Kalman filter (DKF) algorithms with the Kalman-like form are designed for each sensor node. When it is available whether a datum is missing or not at each time, an optimal DKF (ODKF) dependent on the knowledge of missing data is presented, where filter gains and covariance matrices require online computing. To reduce online computational cost, a suboptimal DKF (SDKF) is presented, where filter gains and covariance matrices dependent on missing probabilities can be computed offline. When it is unavailable whether a datum is missing or not, a probability-based DKF (PDKF) dependent on missing probabilities is presented. For each DKF algorithm, an optimal Kalman filter gain for measurements of sensor itself and different optimal consensus filter gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense, respectively. Mean boundedness of covariance matrix of the proposed ODKF is analyzed. Stability and steady-state properties of the proposed SDKF and PDKF are analyzed. Also, the performance of three DKF algorithms is compared. Simulation examples demonstrate effectiveness of the proposed algorithms.

Promising Wing Vibration Measurement System Using MEMS IMUS and Kalman Filter Correction

Nowadays, there is still a need for the development of a high-precision vibration measurement system for aircraft wings. By analyzing the wing vibration characteristics a lot of aviation studies could be conducted, including the wing health monitoring, the fluttering phenomenon and so on. This paper presents preliminary results of the research carried out toward building a promising system designed to measure vibration parameters of aircraft wing. Comparing it with the existing analogue systems, the proposed system features the use of approaches that are traditional for solving orientation and navigation problems for vibration measurements. The paper presents the basic structure of the system, the fundamentals of its operation, the mathematical errors models of its main components, the correction algorithms using optimal Kalman filter. Finally, the initial simulation results of system operation are shown, demonstrating the expected accuracy characteristics of the system, which confirms its effectiveness and the prospects of the chosen direction of research.

Aging state prediction for supercapacitors based on heuristic kalman filter optimization extreme learning machine

With the advancement of wind energy, solar energy, and other new energy industries, the demand for energy storage systems are worth increasing. Supercapacitors gradually stand out among many energy storage components due to their advantages of high power density, fast charging and discharging speed, and long life. Predicting the capacity of supercapacitors from historical data is a highly non-linear problem, subject to various external and environmental factors. In this work, we propose an optimized forecasting model-an extreme learning machine (ELM) model coupled with the heuristic Kalman filter (HKF) algorithm to forecast the capacity of supercapacitors. ELM is preferred over traditional neural networks mainly due to its fast computational speed, which allows efficient capacity forecasting in real-time. Our HKF-ELM model performed significantly better than other data-driven models models that are commonly used in forecasting life of supercapacitors. The performance of the proposed HKF-ELM model was also compared with traditional ELM, Kalman filtering model, ELM optimized by the particle swarm optimization (PSO-ELM) and Kalman filter extreme learning machine models (KA-ELM). Different performance metrics, i.e., Root Mean Squared Error (RMSE), Mean Square Error (MSE) and R2 determination coefficient were used for the comparison of the selected models. The aging life of supercapacitors in different environments were also performed using the proposed approach. The results revealed that the proposed approach is superior to traditional data-driven models in terms of prediction aging life of supercapacitors and it can be applied in real-time to predict state of health (SOH) based on the previous charge and discharge data of supercapacitors. In particular, considering RMSE of forecasting, the proposed HKF-ELM model performed 77.62% better than the traditional ELM model, 77.46% better than the PSO-ELM model, 87.40% better than the traditional Kalman filter model, 82.51% better than the KA-ELM model in forecasting aging life of supercapacitors. The novelty of the proposed approach lies in the way the fast computational speed of ELMs has been combined with the accuracy gained by tuning hyperparameters using HKF. Fewer setting parameters, lower time cost and higher prediction accuracy have been need in our methodology compared to available models. Our work presents an original way of performing aging life of supercapacitors forecasting in real-time in industry with highly accurate results which are much better than pre-existing life forecasting models.