Application Of Kalman Filter Research Articles

Unscented Kalman filter application for state estimation of a Qball-X4 quadrotor

In the process of controlling the quadrotor, accurate state estimation plays a crucial role. For positioning purposes, the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are employed to determine the position of moving subjects. The Qball-X4 quadrotor is a highly nonlinear object, and when combined with Gauss interference, it can compromise the accuracy of the EKF. To address these challenges, this study focuses on assessing the suitability of the UKF nonlinear filtering method for estimating the state of the Qball-X4 quadrotor. This estimation is based on measurements from the gyroscope and Global Positioning System (GPS). To simulate real-life conditions, measurement noise has been deliberately introduced into the sensors. Rigorous testing under various conditions has emphasized the superior performance of the UKF filter in estimating the state of the quadrotor. This paper presents a valuable method to enhance the accuracy and reliability of the navigation system for the Qball-X4 quadrotor.

A moment-based Kalman filtering approach for estimation in ensemble systems.

A persistent challenge in tasks involving large-scale dynamical systems, such as state estimation and error reduction, revolves around processing the collected measurements. Frequently, these data suffer from the curse of dimensionality, leading to increased computational demands in data processing methodologies. Recent scholarly investigations have underscored the utility of delineating collective states and dynamics via moment-based representations. These representations serve as a form of sufficient statistics for encapsulating collective characteristics, while simultaneously permitting the retrieval of individual data points. In this paper, we reshape the Kalman filter methodology, aiming its application in the moment domain of an ensemble system and developing the basis for moment ensemble noise filtering. The moment system is defined with respect to the normalized Legendre polynomials, and it is shown that its orthogonal basis structure introduces unique benefits for the application of Kalman filter for both i.i.d. and universal Gaussian disturbances. The proposed method thrives from the reduction in problem dimension, which is unbounded within the state-space representation, and can achieve significantly smaller values when converted to the truncated moment-space. Furthermore, the robustness of moment data toward outliers and localized inaccuracies is an additional positive aspect of this approach. The methodology is applied for an ensemble of harmonic oscillators and units following aircraft dynamics, with results showcasing a reduction in both cumulative absolute error and covariance with reduced calculation cost due to the realization of operations within the moment framework conceived.

Real-time image denoising corrupted by shot-noise

In this paper the new model for the image noise is proposed. The video data is modelled as a sequence of images corrupted by the shot-noise. Shot-noise may occur due to the defect in the device’s hardware or in the camera’s sensor. This kind of noise effects not only the current image of the video sequence but also the subsequent images, the effect decays as time passes and disappears totally after a certain time period. The shot-noise process consists of the sequence of jumps that decay gradually as time passes. The times at which the jumps occur are Poisson distributed and the hight of the jumps is normally distributed. It can be proved that under certain conditions shot-noise process tends to Gaussian process. Therefore, it was proposed to apply Kalman filter to remove the noise and to restore the corrupted sequence of images. The numerical experiments that were carried out that show the effectiveness of the proposed approach for denoising the shot-noise corrupted videos.

Numerical experiment toward simultaneous estimation of the spatiotemporal evolution of interseismic fault slips and block motions in southwest Japan

Interseismic strain around southwest Japan can be attributed to slip phenomena on the plate interface and processes inside the continental plate, such as block motions and inland fault slips. Although many crustal deformation analyses have been carried out, the simultaneous estimation of these phenomena and comprehensive discussion regarding the effect on the total strain budget remain topics to be investigated. In this study, we conducted numerical experiment to evaluate the possibility of simultaneously monitoring the spatiotemporal evolution of interseismic fault slips and block motions based on state-space modeling. We aimed to estimate fault slips and block motions using the time series of dense continuous Global Navigation Satellite System sites covering southwest Japan, encompassing 25 years from 1996 onward. We calculated synthetic block motions of the forearc region, monotonically increasing back slips on block boundary faults, and long-term slow slip events in the Tokai region, Kii Channel, and Bungo Channel. Subsequently, we generated the expected synthetic displacement time-series at GNSS stations. Applying Kalman filtering, we successfully estimated the spatiotemporal evolution of block motions, cumulative back slips, multiple slow slip events occurring in different regions. Although the contributions of fault slips and block motions showed slight trade-off, main characteristics of the slip distributions and the direction of block motions were well-recovered. We recovered slow slip events with slips of 5–10 cm or larger. We investigated the estimation uncertainty and separation precision of the unknown parameters using the covariance matrix estimated by Kalman filtering. Focusing on the structure of the non-diagonal component of the covariance matrix, we evaluated the complex effects of site and subfault locations on the estimated slip spatial distribution bias. For instance, the extent of the correlation between subfaults suggested that the three slow slip regions have different tendency of the uncertainties of slip areas, extending toward landside, seaward, or both of them. Our framework enables the comprehensive evaluation of the contributions and uncertainties of various deformation sources covering the entire subduction zone.Graphical abstract

Multiple similarity measure-based maximum correntropy criterion Kalman filter with adaptive kernel width for GPS/INS integration navigation

The filter based on the maximum correntropy criterion (MCC) has low sensitivity to non-Gaussian noise, which can effectively improve the robustness of the filter. However, the uncertainty of kernel width restricted the application of the maximum correntropy criterion Kalman filter (MCCKF) in the integrated navigation system. In order to overcome the above difficulty, this paper proposes a multiple similarity measure-based maximum correntropy criterion Kalman filter with adaptive kernel width (ABMCCKF). ABMCCKF uses the MORKF framework and distinguishes the noise polluted by outliers through a designed protecting window, which also ensures that the kernel width is compatible with the noise pollution level. Through the window, ABMCCKF utilizes the optimality of both MCC and the minimum mean square error criterion (MMSE). Simulations and vehicular experiments are used to verify the effectiveness of the method. The results show that the ABMCCKF have a good performance when the optimal kernel width is uncertain.

Application of Kalman filter in wharf surface displacement of Beidou automatic monitoring

To meet the requirements for real-time dynamic monitoring of wharf surface displacement, an automatic monitoring system based on Beidou satellite navigation was constructed, and it was applied to monitor the surface displacement of a wharf in Tianjin Port. Next, the sensible system noise of the Kalman filter state equation was determined by the simulation experiment. Finally, the monitoring data were processed and analyzed by Kalman filter. The results show that the accuracy of the monitoring data can be improved by more than 30% by Kalman filtering, particularly the elevation direction accuracy can reach more than 40%. The plane and elevation accuracy can be less than 1.5mm, after the Beidou automatic monitoring data has been processed by Kalman filtering, and this meets the needs for most engineering deformation monitoring. In a word, the Beidou automatic monitoring system is characterized by continuity, real-time and high precision, and can be applied to most engineering deformation monitoring requirements.

Application of Kalman Filtering with Bayesian formulation in adaptive sampling

An extensive amount of research is emphasized on survey designs and estimation procedures related to rare and clustered characteristics of a population. Adaptive Sampling design is the most applicable probabilistic technique to estimate the mean or total of the variable of interest, bearing rarity and clustered characteristics. Since rarity is regarded as a time-dependent feature, such surveys need to be organized constantly over time. No studies so far have investigated the effect of time in the estimation context of Adaptive Sampling. This research therefore captures the need to synthesize this periodic information when conducting a survey using Adaptive Sampling design. A recursive process is employed here that improves the estimate of the population parameter from a practical perspective. “Kalman Filtering” is a well known recursive procedure to use past data. Later, statisticians were able to use that Kalman Filtering technique with the Bayesian formulation. This Bayesian approach is proposed to employ here to improve the estimation in the context of Adaptive Sampling design, utilizing the past data. A simulation study is carried out and it is concluded that the suggested approach substantially improves the estimation accuracy.

Sensitivity analysis of the hyperparameters of an ensemble Kalman filter application on a semi-distributed hydrological model for streamflow forecasting

Data Assimilation (DA) is an important step for improving prediction accuracy and real-time correction of hydrological models for operational forecasting purposes. The Ensemble Kalman filter (EnKF) is one of the most popular techniques used to address the issues of updating the model states and parameters by creating a novel set of initial conditions in real-time. This study aims at identifying optimal seasonal EnKF parametrizations to reduce the uncertainty associated with the initial conditions in a semi-distributed hydrological model of a snow-dominated catchment in Canada. Sensitivity analysis is performed to evaluate the effects of the EnKF individual hyperparameters (temperature, precipitation and inflow uncertainties) and the updating of three state variables (vadose zone, saturated zone and snowpack) on the skill of short-term (up to 9 days lead-time) forecasts. Results show that the performance of the forecasts is sensitive to the individual hyperparameters and particularly so to the temperature uncertainty, which varies between seasons. Additionally, the forecast skill is related to the choice of the state variables to be updated depending on the season. The vadose zone state variable displays higher importance and sensitivity than the other states, and the results indicate that all state variables should not be systematically updated on this catchment and with the implemented hydrological model. Finally, combining the best hyperparameter values with the optimal combination of state variables to update, insight is provided on the success of the data assimilation scheme that is evaluated on a rolling horizon using a set of seasonal rules to gain forecast performance over the span of multiple years.

Research on a High-Precision State-of-Charge Estimation Method Based on Forgetting Factor Recursive Least Squares and Adaptive Extended Kalman Filter Applied to LiFePO4 Battery

The state-of-charge (SOC) estimation accuracy is closely associated with the estimation method and the battery parameter identification performance. The battery parameter identification method based on forgetting factor recursive least squares (FFRLS) has the advantages of high parameter identification accuracy and fast dynamic response speed. On this basis, the performance of two SOC estimation methods, the extended Kalman filter (EKF) and adaptive extended Kalman filter (AEKF) are compared and studied. The results show that AEKF has better steady-state and dynamic SOC estimation performance, but the estimation accuracy and dynamic response performance are still not objective. To further improve the performance of SOC estimation, a joint SOC estimation method based on FFRLS-AEKF is proposed, and the SOC estimation experimental results with FFRLS-AEKF and AEKF are conducted. The experimental results show that the proposed joint SOC estimation method based on FFRLS-AEKF has a better steady-state and dynamic performance of SOC estimation. The maximum absolute error of the proposed algorithm is 4.97%. As the battery working time increases, the SOC estimation accuracy continues to converge to the true value, and the average absolute error is reduced to 2.5%. The proposed method and theoretical analysis are proven to be correct and feasible.

The Use of Artificial Intelligence Approaches for Performance Improvement of Low-Cost Integrated Navigation Systems.

In this paper, the authors investigate the possibility of applying artificial intelligence algorithms to the outputs of a low-cost Kalman filter-based navigation solution in order to achieve performance similar to that of high-end MEMS inertial sensors. To further improve the results of the prototype and simultaneously lighten filter requirements, different AI models are compared in this paper to determine their performance in terms of complexity and accuracy. By overcoming some known limitations (e.g., sensitivity on the dimension of input data from inertial sensors) and starting from Kalman filter applications (whose raw noise parameter estimates were obtained from a simple analysis of sensor specifications), such a solution presents an intermediate behavior compared to the current state of the art. It allows the exploitation of the power of AI models. Different Neural Network models have been taken into account and compared in terms of measurement accuracy and a number of model parameters; in particular, Dense, 1-Dimension Convolutional, and Long Short Term Memory Neural networks. As can be excepted, the higher the NN complexity, the higher the measurement accuracy; the models' performance has been assessed by means of the root-mean-square error (RMSE) between the target and predicted values of all the navigation parameters.

On the fast track: Rapid construction of stellar stream paths

ABSTRACT Stellar streams are sensitive probes of the Galactic potential. The likelihood of a stream model given stream data is often assessed using simulations. However, comparing to simulations is challenging when even the stream paths can be hard to quantify. Here we present a novel application of self-organizing maps and first-order Kalman filters to reconstruct a stream’s path, propagating measurement errors and data sparsity into the stream path uncertainty. The technique is Galactic-model independent, non-parametric, and works on phase-wrapped streams. With this technique, we can uniformly analyse and compare data with simulations, enabling both comparison of simulation techniques and ensemble analysis with stream tracks of many stellar streams. Our method is implemented in the public Python package TrackStream, available at https://github.com/nstarman/trackstream.

Comparison of ensemble Kalman filter application to a prediction model of soil solute transfer into surface runoff by updating different parameters

Comparison of ensemble Kalman filter application to a prediction model of soil solute transfer into surface runoff by updating different parameters

Application of kalman filter for radar target tracking.

In this paper, the principles of recursive tracking and prediction filters are used to track a single maneuvering aerial target and implemented using instantaneous noisy measurements. Kalman filter is used to estimate (predict) the system state (bearing, range, target course, and speed) as they cannot be measured directly from measurements. Furthermore, after mathematical formulation of the equations for the Kalman filter fitting the application, it was then applied and evaluated. Monte Carlo Simulation technique was applied to quantify the results and the simulation results are obtained using a python program.

Unbalance identification for a practical turbofan engine using augmented Kalman filter improved with the convergence criterion

Kalman filter has emerged as a powerful tool for unbalance identification in rotating machinery. Recently, the augmented Kalman filter combined with the finite element model has grown up and projects its potential for complex rotor systems. This paper investigates the application of the augmented Kalman filter (AKF) to a practical turbofan engine. The current study reveals that using steady-state responses as measurements can cause fluctuation in the estimated results, even divergence for some cases, while the available signals in practice are steady-state responses generally. To the authors' knowledge, this practical problem is revealed for the first time. To address the problem, the convergence criterion is employed to improve the AKF and formulates the adaptive fading augmented Kalman filter (AFAKF) proposed in this paper. Results indicate that the increase of the amplification factor, the insufficient measurement points, and the complexity of the dynamic model can all lead to the deterioration of the estimated unbalance. The proposed AFAKF method shows favorable convergence and can achieve accurate estimation with less than 5% relative errors, and the superiority over AKF in computation cost is also observed.

Streamflow simulation in poorly gauged basins with regionalised assimilation using Kalman filter

The streamflow estimation in ungauged or poorly gauged basins is a fundamental and challenging problem in hydrology, which has often been solved by transferring hydrological information from gauged basins (i.e. by regionalisation). Most studies on streamflow regionalisation focus on identifying the best methods to transfer the hydrologic model parameters and uses primarily physiographic attributes or climate information for these purposes. In the present study, the sequential data assimilation method – the Kalman filter – has been used to determine streamflow in a poorly gauged (unknown) basin to combine, in an optimal way, observations of neighbouring basins and model simulation of a given basin. The methodology is based on the concept of concatenated upstream catchments, where the aggregation of unobserved states can be estimated. The streamflow estimate is further divided between the unknown sub-catchments using linear regression on the catchments’ hydrological characteristics, which are subsequently used to approximate error statistics and operators in the Kalman filter application. The results were evaluated on 165 catchments in the Czech Republic using RMSE, MASE and MAE criteria and indicate that in 87.3% of the cases, the proposed methodology improved the accuracy of streamflow estimations by an average of 40% (in combined evaluated measurements) compared to the original simulations within the system for drought monitoring and forecasting in the Czech Republic ‘HAMR’.

Standoff detection of backscattered light based on tunable diode laser absorption spectroscopy

Standoff detection is of great significance in greenhouse gas measurement monitoring, early warning security and leak detection. Variations in topographic characteristics and distances will undoubtedly increase background noise. However, the effect of real-time changes in the angle between the sensor and the target on dynamic detection is rarely studied. In this article, a portable laser sensor is developed to retrieve gas concentration of CH4 by collecting the backscattered light from a distant non-cooperative target. The experimental results show that “2f/1f” based on wavelength-locked wavelength modulation technique can effectively suppress the background interference caused by a change in the detection angle. Increasing the sampling frequency does not achieve denoising for static detection but can lead to significant noise reduction for dynamic detection. For a modulation frequency of 4 k Hz, the mean standard deviation of the gas concentration is improved to 42.8 % and 7.04 % of that at 1 k Hz and 250 Hz, respectively. Kalman filtering can significantly improve the denoising effect for dynamic detection. The background concentration perturbation is reduced by a factor of 4.19 ∼ 4.71 after applying Kalman filtering. Combined with Kalman filtering, the minimum detection limit for Allan variance prediction can reach 20.5 ppb@ (0.15 sec) at a modulation frequency of 4 k Hz.

An experimental comparative study of adaptive sigma-point Kalman filters: Case study of a rigid–flexible four-bar linkage mechanism and a servo-hydraulic actuator

This paper investigates the application, design, and implementation of different adaptive sigma-point Kalman filters for nonlinear dynamic systems. It is a well-known fact that the performance of nonlinear Kalman filters depends on a prior knowledge of system noise statistics. In real-time applications, this knowledge is difficult and in some cases impossible to predefine. Therefore, an adaptation mechanism based on the random weighting method is proposed in this work to estimate, simultaneously, noise covariance and the state of the system. On the other hand, for real time execution, the computational efficiency of such filters should also be considered to minimize the burden on computational resources. Based on these two factors, in this paper, four different variants of the adaptive sigma-point Kalman filter are studied in detail: (I) an Adaptive Unscented Kalman filter (AUKF), (II) an Adaptive Square-root Unscented Kalman filter (ASr-UKF) with an Unscented Transformation sigma-point selection strategy, (III) an Adaptive Scaled Spherical Simplex Unscented Kalman filter (AS3UKF), and (IV) an Adaptive Square-root Scaled Spherical Simplex Unscented Kalman filter (ASr-S3UKF) with scaled spherical simplex sigma-point selection strategy. The performance of these adaptive sigma-point Kalman filters is analyzed here in depth and discussed for application to a simulated rigid–flexible four-bar linkage mechanism and a practical servo-hydraulic actuator setup under different scenarios. The simulation and the experimental results indicated that, for the cases studied in this article, the filters are competitive and present advantages and disadvantages that should be dealt with according to the requirements of the problem.

Application of particle filter to assess uncertainty for reservoir state and parameter estimation

A bimodal water saturation distribution can be found around the waterfront during water flooding in an oil reservoir, leading to subsequent non-Gaussian distribution of water saturation. Therefore, application of the Gaussian based methods may result in poor history matching and corresponding parameter estimation. For the reliability of the oil reservoir model, it is very important to ensure the realistic update of water saturation during history matching at any phase of production from oil reservoirs. This work employs particle filter (PF) for water flooding reservoir data assimilation, considering the effect of “non-Gaussianity” in water saturation distribution around the shock front during updating model state vector. This paper investigates the performance of the PF in updating state variables, particularly water saturation and efficiency to approximation of posterior probability distribution. In addition, particle perturbation is implemented by applying “ensemble covariance” in resampling stage in order to diverse particles and thereby avoid particle collapse. The methodology is presented stepwise considering a one-dimensional (1D) case first and then two-dimensional (2D) five-spot water flood problem. In both cases, state variables are updated with the application of PF and ensemble kalman filter (EnKF). With respect to history and water saturation matching, and approximation of posterior probability distribution, the performance of EnKF is comparable with PF where the non-Gaussianity is weak. However, in the presence of strong non-Gaussianity, EnKF shows four times higher error compared to PF. Furthermore, between “ensemble covariance” and typical “randomization” cases, “ensemble covariance” case shows a higher number of particles participating in resampling stage in particle perturbation. Therefore, “ensemble covariance” case leads to 5.3% and 7.5% more accurate results in estimating reservoir permeability and porosity, respectively.

Application of the Unscented Kalman Filter to Estimate the Material Properties of a Layered Half-Space

Full waveform inversion (FWI) to estimate physical properties of a system is one of the major research topics in science and engineering. This study proposes a probabilistic approach toward these solutions by applying the unscented Kalman filter (UKF). The responses of the vertical displacements of a layered half-space subjected to a harmonic vertical disk load on the surface are calculated from an estimated profile of shear-wave velocities and compared with measurements or observations. In the calculation of the dynamic responses, the thin-layer method (TLM), which is efficient for layered media, is employed. In order to improve the solutions to the considered inverse problem, regularization terms are included in the observations so that the differences in the material properties between two consecutive layers vanish. The proposed UKF method is demonstrated with a variety of FWI problems in a layered half-space. The results show that the proposed method can estimate the material properties of a layered half-space accurately.

Application of Kalman Filter to Large-scale Geospatial Data: Modeling Population Dynamics

To utilize a huge amount of observation data based on real-world events, a data assimilation process is needed to estimate the state of the system behind the observed data. The Kalman filter is a very commonly used technique in data assimilation, but it has a problem in terms of practical use from the viewpoint of processing efficiency and estimating the deterioration in precision when applied to particularly large-scale datasets. In this article, we propose a method that simultaneously addresses these problems and demonstrate its usefulness. The proposed method improves the processing efficiency and suppresses the deterioration in estimation precision by introducing correction processes focusing on the non-negative nature and sparseness of data in wavelet space. We show that the proposed method can accurately estimate population dynamics on the basis of an evaluation done using population data generated from cellular networks. In addition, the possibility of wide area abnormality detection using the proposed method is shown from a situation analysis of when Category 5 typhoon Hagibis made landfall in Japan. The proposed method has been deployed in a commercial service to estimate real-time population dynamics in Japan.