Proposed Kalman Filter Research Articles

Kalman Filter Using a Third-Order Tensorial Decomposition of the Impulse Response

For system identification problems associated with long-length impulse responses, the recently developed decomposition-based technique that relies on a third-order tensor (TOT) framework represents a reliable choice. It is based on a combination of three shorter filters, which merge their estimates in tandem with the Kronecker product. In this way, the global impulse response is modeled in a more efficient manner, with a significantly reduced parameter space (i.e., fewer coefficients). In this paper, we further develop a Kalman filter based on the TOT decomposition method. As compared to the recently designed recursive least-squares (RLS) counterpart, the proposed Kalman filter achieves superior performance in terms of the main criteria (e.g., tracking and accuracy). In addition, it significantly outperforms the conventional Kalman filter, while also having a lower computational complexity. Simulation results obtained in the context of echo cancellation support the theoretical framework and the related advantages.

FPGA Implementation of a Pipelined Kalman Filter for Object Tracking in Two Dimensions

In a location tracking system for a moving object, not only accuracy but also real-time processing are important factors. The Kalman filter, as a recursive function, stands out as one of the prominent algorithms for object tracking. It continuously compares measured data with predicted values based on the system characteristics in real time, and then corrects the error of the predicted values while considering the noise of both system and measured data. This paper focuses on designing a hardware-based Kalman filter for object tracking in two dimensions. Following an analysis of the Kalman filter algorithm, the blocks capable of parallel processing are identified and configured to be processed in parallel, effectively reducing data processing time. The clock speed is enhanced by using the pipeline technique. In addition, the time-sharing technique is applied to increase the utilization of hardware resources and reduce the area. Data was processed at 32-bit floating points to uphold accuracy comparable to software-implemented Kalman filters. The proposed Kalman filter architecture is designed using verilog HDL and then simulated in Synopsys VCS/Verdi. And the accuracy is verified by comparing results with a software-based Kalman filter designed using MATLAB. It was implemented using Zynq ZYNQ-7 ZC702 Programmable logic via Xilnix Vivado, and can operate at 33MHz. It takes a total of 44 clocks, or 1.32 us, to process one data. Therefore, it was confirmed that the designed Kalman filter hardware is suitable for real-time processing.

Enhancing the Quality of Fog/Mist Images by Comparing the Effectiveness of Kalman Filter and Adaptive Filter for Noise Reduction

The primary objective of this study is to enhance the precision of fog and mist noise reduction in photographsby introducing a novel Kalman filter and comparing its performance to that of an Adaptive filter. Materialsand Methods: For this investigation, the research dataset was sourced from the Kaggle database system. Usingtwenty iteration samples (ten for Group 1 and ten for Group 2), involving a total of 1240 samples, the efficacyof fog and mist noise elimination with improved accuracy was assessed. This evaluation was conductedemploying a G-power of 0.8, a 95% confidence interval, and alpha and beta values of 0.05 and 0.2,respectively. The determination of the sample size was based on the outcomes of these calculations. The novelKalman filter and the Adaptive filter, both utilizing the same number of data samples (N=10), were employedfor fog and mist noise removal from images. Notably, the Kalman filter exhibited a higher accuracy rate.Results: The novel Kalman filter showcased a success rate of 96.34%, outperforming the Adaptive filter'ssuccess rate of 93.78%. This difference in performance is statistically significant. The study's significancethreshold was set at p=.001 (p<0.05), confirming the significance of the hypothesis. This analysis was carriedout through an independent sample T-test. Conclusion: In conclusion, the proposed Kalman filter model,achieving an accuracy rate of 96.34%, demonstrates superior performance compared to the Adaptive filter,which yielded an accuracy rate of 93.78%. This comparison underscores the efficacy of the Kalman filter inthe context of image noise removal.

Online monitoring system of material moisture content based on the Kalman filter fusion algorithm in air-impingement dryer

A Kalman filter fusion algorithm was proposed, and an online monitoring system was developed for real-time monitoring of the moisture content of materials in an air-impingement dryer. The Kalman filter algorithm was used to estimate the optimal state of the original detection values of the weighting sensor and air velocity sensor. A backpropagation (BP) neural network fusion model was established, where the weight detection value, elastic substrate temperature, air velocity, and impingement distance were considered inputs and the real weight of the material was the output. The optimal topology of the BP neural network was selected, and the initial weights and thresholds of the BP neural network were optimized using a genetic algorithm. The coefficient of determination (R2) and root mean square error (RMSE) of the optimized BP neural network fusion model were 0.9995 and 4.9, respectively. The Kalman filter fusion algorithm, which can realize online monitoring of moisture content, was established using the Kalman filter algorithm and fusion model. Moreover, an online monitoring system for material moisture content was developed, validation experiments were carried out, and the R2 and RMSE of the nine sets of validation experiments were 0.9963 and 0.78, respectively. The monitoring system satisfied the requirements of material moisture content detection accuracy in the drying process. The developed monitoring system is greatly important for improving the automation level of the drying equipment for fruits and vegetables. The proposed Kalman filter fusion algorithm also provides a reference for other multifactor fusion detection.

Design of Transfer Alignment Algorithm with Velocity and Azimuth Matching for the Aircraft Having Wing Flexibility

A transfer alignment is used to initialize, align, and calibrate a SINS(Slave INS) using a MINS(Master INS) in motion. This paper presents an airborne transfer alignment with velocity and azimuth matching to estimate inertial sensor biases under the wing flexure influence. This study also considers the lever arm, time delay and relative orientation between MINS and SINS. The traditional transfer alignment only uses velocity matching. In contrast, this paper utilizes the azimuth matching to prevent divergence of the azimuth when the aircraft is stationary or quasi-stationary since the azimuth is less affected by the wing flexibility. The performance of the proposed Kalman filter is analyzed using two factors; one is the estimation performance of gyroscope and accelerometer bias and the other is comparing aircraft dynamics and attitude covariance. The performance of the proposed filter is verified using a long term flight test. The test results show that the proposed scheme can be effectively applied to various platforms that require airborne transfer alignment.

The linear-nonlinear data preprocessing based hybrid (LNDH) models for wind power forecasting

PurposeThe purpose of this paper is to propose a new linear-nonlinear data preprocessing-based hybrid model to achieve a more accurate result at a lower cost for wind power forecasting. For this purpose, a decomposed based series-parallel hybrid model (PKF-ARIMA-FMLP) is proposed which can model linear/nonlinear and certain/uncertain patterns in underlying data simultaneously.Design/methodology/approachTo design the proposed model at first, underlying data are divided into two categories of linear and nonlinear patterns by the proposed Kalman filter (PKF) technique. Then, the linear patterns are modeled by the linear-fuzzy nonlinear series (LLFN) hybrid models to detect linearity/nonlinearity and certainty/uncertainty in underlying data simultaneously. This step is also repeated for nonlinear decomposed patterns. Therefore, the nonlinear patterns are modeled by the linear-fuzzy nonlinear series (NLFN) hybrid models. Finally, the weight of each component (e.g. KF, LLFN and NLFN) is calculated by the least square algorithm, and then the results are combined in a parallel structure. Then the linear and nonlinear patterns are modeled with the lowest cost and the highest accuracy.FindingsThe effectiveness and predictive capability of the proposed model are examined and compared with its components, based models, single models, series component combination based hybrid models, parallel component combination based hybrid models and decomposed-based single model. Numerical results show that the proposed linear-nonlinear data preprocessing-based hybrid models have been able to improve the performance of single, hybrid and single decomposed based prediction methods by approximately 66.29%, 52.10% and 38.13% for predicting wind power time series in the test data, respectively.Originality/valueThe combination of single linear and nonlinear models has expanded due to the theory of the existence of linear and nonlinear patterns simultaneously in real-world data. The main idea of the linear and nonlinear hybridization method is to combine the benefits of these models to identify the linear and nonlinear patterns in the data in series, parallel or series-parallel based models by reducing the limitations of the single model that leads to higher accuracy, more comprehensiveness and less risky predictions. Although the literature shows that the combination of linear and nonlinear models can improve the prediction results by detecting most of the linear and nonlinear patterns in underlying data, the investigation of linear and nonlinear patterns before entering linear and nonlinear models can improve the performance, which in no paper this separation of patterns into two classes of linear and nonlinear is considered. So by this new data preprocessing based method, the modeling error can be reduced and higher accuracy can be achieved at a lower cost.

A new Gaussian–Student's t mixing distribution‐based Kalman filter with unknown measurement random delay rate

SummaryIn this article, a new Gaussian–Student's t mixing distribution‐based Kalman filter is presented to investigate the filtering issue for linear stochastic system with unknown measurement random delay rate and non‐stationary heavy‐tailed measurement noise. Firstly, by employing a Bernoulli distributed variable and introducing system state extension method, the form of measurement likelihood function of double measurement noise distributions is converted from the weighted sum to an exponential product. Secondly, the non‐stationary heavy‐tailed measurement noises of current time and last time are modeled as Gaussian–Student's t mixing distributions by introducing extra Bernoulli distributed variables. Thirdly, the variational Bayesian technique is utilized to jointly infer the system state, the Bernoulli distributed variables of measurement noises, distribution mixing probabilities, the intermediate random variables, the Bernoulli distributed variable of measurement delay and the unknown measurement random delay rate. Finally, the effectiveness of the proposed Kalman filter is demonstrated by a target tracking simulation experiment.

Kalman Filter for Linear Systems With Unknown Structural Parameters

This brief considers Kalman filter for linear systems with unknown structural parameters. We design a Bayesian parameter identification algorithm based on maximum likelihood (ML) criterion and expectation maximization (EM). Under the identification of structural parameter, we perform the Kalman filter to estimate the states. The Kalman filter and the parameter identification algorithm are interactive to estimate the states and the structural parameters. More specifically, first, we use EM algorithm together with Kalman smoother to estimate the structural parameters. Then, on the basis of results provided by the first step, we employ the classical Kalman filter to predict and update the states, which formulates the final proposed Kalman filter. Performance analysis and simulation results verify the presented filter.

Antenna Array-Aided Real-Time Kinematic Using Moving Base Stations

A global navigation satellite systems (GNSS) real-time kinematic (RTK) using multiple base stations is referred as an antenna array-aided RTK. This positioning method more reliably resolves carrier phase integer ambiguities by processing additional measurements provided from multiple GNSS reference stations whose antenna locations are accurately surveyed. In this study, a conventional antenna array-aided RTK is extended to improve RTK performance with multiple moving base stations. Because accurately surveyed antenna coordinates are not available, we propose an antenna array-aided Kalman filter approach to first check the sanity of the fixed integer ambiguities and baselines estimated by moving reference stations and use them as a-priori information in RTK measurement formulations. Our flight test results with three unmanned aerial vehicles confirmed that the proposed Kalman filter formulation outperformed the conventional RTK and a priori antenna array-aided RTK approaches in the aspects of positioning accuracy, time to first fix, and success probability of integer ambiguity fixes.

Practical Implementation of New Algorithm for Restricting Data Fusion in Cloud Computing with Use of Information Kalman Filtering

These days’ lots of technologies migrate from traditional systems into cloud and similar technologies; also we should note that cloud can be used for military and civilian purposes [3]. On the other hand, in such a large scale networks we should consider the reliability and powerfulness of such networks in facing with events such as high amount of users that may login to their profiles simultaneously, or for example if we have the ability to predict about what times that we would have the most crowd in network, or even users prefer to use which part of the Cloud Computing more than other parts – which software or hardware configuration. With knowing such information, we can avoid accidental crashing or hanging of the network that may be cause by logging of too much users. In this paper we propose Kalman Filter that can be used for estimating the amounts of users and software’s that run on cloud computing or other similar platforms at a certain time. After introducing this filter, at the end of paper, we talk about some potentials of this filter in cloud computing platform. In this paper we demonstrate about how we can use Kalman filter in estimating and predicting of our target, by the means of several examples on Kalman filter. Also at the end of paper we propose information filter for estimation and prediction about cloud computing resources.

A Kalman Filter for Multilinear Forms and Its Connection with Tensorial Adaptive Filters.

The Kalman filter represents a very popular signal processing tool, with a wide range of applications within many fields. Following a Bayesian framework, the Kalman filter recursively provides an optimal estimate of a set of unknown variables based on a set of noisy observations. Therefore, it fits system identification problems very well. Nevertheless, such scenarios become more challenging (in terms of the convergence and accuracy of the solution) when the parameter space becomes larger. In this context, the identification of linearly separable systems can be efficiently addressed by exploiting tensor-based decomposition techniques. Such multilinear forms can be modeled as rank-1 tensors, while the final solution is obtained by solving and combining low-dimension system identification problems related to the individual components of the tensor. Recently, the identification of multilinear forms was addressed based on the Wiener filter and most well-known adaptive algorithms. In this work, we propose a tensorial Kalman filter tailored to the identification of multilinear forms. Furthermore, we also show the connection between the proposed algorithm and other tensor-based adaptive filters. Simulation results support the theoretical findings and show the appealing performance features of the proposed Kalman filter for multilinear forms.

A Novel Kalman Filter Formulation for Improving Tracking Performance of the Extended Kernel RLS

In this paper, two contributions are presented. Firstly, a novel variant of the Kalman filter is developed and used to improve the tracking performance of the extended kernel recursive least squares algorithm (Ex-KRLS). Without resorting to the Riccati equation, the proposed formulation of the Kalman filter relies on principles of optimization and convex duality to obtain a stable quadratic form. It allows for performance and stability efficiency by minimizing the estimation error with the manipulation of a single scalar variable. Secondly, the proposed Kalman filter formulation is embedded into the Ex-KRLS-KF algorithm, an extension of the Ex-KRLS, to further improve its tracking performance. For this purpose, the state model of the proposed Ex-KRLS-KF variant is constructed in the original state space, while the hidden state is then estimated using the proposed Kalman filter formulation. The standard KRLS algorithm learns the measurement model used in hidden state estimation. We show through a comprehensive set of computer experiments that the proposed hybrid algorithm has more flexible state and noise models than competing alternative algorithms. We evaluate the proposed algorithm in two benchmarking tasks (nonlinear Rayleigh multipath channel tracking and Lorenz system modeling) and compare its performance with those provided by the state-of-the-art algorithms.

Toward Accurate Position Estimation Using Learning to Prediction Algorithm in Indoor Navigation.

Internet of Things is advancing, and the augmented role of smart navigation in automating processes is at its vanguard. Smart navigation and location tracking systems are finding increasing use in the area of the mission-critical indoor scenario, logistics, medicine, and security. A demanding emerging area is an Indoor Localization due to the increased fascination towards location-based services. Numerous inertial assessments unit-based indoor localization mechanisms have been suggested in this regard. However, these methods have many shortcomings pertaining to accuracy and consistency. In this study, we propose a novel position estimation system based on learning to the prediction model to address the above challenges. The designed system consists of two modules; learning to prediction module and position estimation using sensor fusion in an indoor environment. The prediction algorithm is attached to the learning module. Moreover, the learning module continuously controls, observes, and enhances the efficiency of the prediction algorithm by evaluating the output and taking into account the exogenous factors that may have an impact on its outcome. On top of that, we reckon a situation where the prediction algorithm can be applied to anticipate the accurate gyroscope and accelerometer reading from the noisy sensor readings. In the designed system, we consider a scenario where the learning module, based on Artificial Neural Network, and Kalman filter are used as a prediction algorithm to predict the actual accelerometer and gyroscope reading from the noisy sensor reading. Moreover, to acquire data, we use the next-generation inertial measurement unit, which contains a 3-axis accelerometer and gyroscope data. Finally, for the performance and accuracy of the proposed system, we carried out numbers of experiments, and we observed that the proposed Kalman filter with learning module performed better than the traditional Kalman filter algorithm in terms of root mean square error metric.

Fuzzy Adaptive Attitude Estimation for a Fixed-Wing UAV With a Virtual SSA Sensor During a GPS Outage

This paper proposes a novel robust attitude estimation algorithm for a small unmanned aerial vehicle (UAV) in the absence of GPS measurements. A synthetic sideslip angle (SSA) measurement formulated for use under the zeroangle assumption is newly proposed for a UAV without angle-of-attack (AOA)/SSA sensors to enhance the state estimation performance during a GPS outage. In addition, the nongravitational acceleration is estimated using the proposed Kalman filter and is then subtracted from the raw acceleration to yield a reliable gravity estimate. Then, a fuzzy-logic-aided adaptive measurement covariance matching algorithm is devised to adaptively reduce the weight given to disturbed acceleration and magnetic field measurements in the attitude estimation, yielding the fuzzy adaptive error-state Kalman filter (FAESKF) algorithm. Experimental flight results demonstrate that the proposed FAESKF algorithm achieves a remarkable improvement in attitude estimation compared to the conventional algorithm.

Generation of Regional Ionospheric TEC Maps With EIA Nowcasting/Forecasting Capability During Geomagnetic Storm Conditions

In this paper, ground based Global Positioning System (GPS) Total Electron Content (TEC) observations collected from the GPS Aided GEO Augmented Navigation (GAGAN) network over low latitude Indian subcontinent are assimilated into the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM). Gauss-Markov Kalman filter methodology is utilized and the background model error covariance (BMEC) matrix is framed using solar, geomagnetic, cross tail potential and hemispheric power indices using multivariate principal component analysis (MPCA) method. The model variations through different high latitude electric field models (Weimer and Heelis) are utilized in the data assimilation analysis. The proper attempt is modeled for providing TEC forecasts during geomagnetic storm conditions from 15th to 20th March 2015 days over Indian region. The more concentration is given in understanding the equatorial ionization anomaly (EIA) characteristics during the initial, main and recovery phase of St. Patrick’s Day March 2015 geomagnetic storm. The proposed model forecast outperforms the persistence forecast with maximum forecast score (1.6) and forecast skill (2.2) during recovery phase of storm. TEC forecasts are validated with current time step GPS observations and 93 % correlation is observed on quiet day (10th March 2015) and 82 % correlation is noticed on main phase of storm (17th March 2015). Also proposed TEC model analysis and forecast results are compared with International Global Navigation Satellite Service (IGS) TEC stations datasets. A clear negative storm effect (EIA inhibition) has been forecasted well with the proposed Kalman filter and MPCA methodology aspects.

An Iterative Extended Kalman Filter for Coherent Measurements of Incoherent Network Nodes in Positioning Systems

Many positioning and tracking applications use spatially distributed sensor stations, each equipped with coherent measurement channels. The coherent data set of each node is incoherently measured to the data sets of all other nodes, avoiding expensive synchronization procedures between the stations. Usually, the measurements are evaluated by mapping the incoherently measured complex valued data on real valued data like angle of arrival or received signal strength. After this preprocessing step, recursive filters fuse the real valued data to estimate a system state. Unfortunately, even though the original measurements are performed in additive white Gaussian noise environments, the preprocessing step can result in correlated, noise shaped errors, whose variance is system state dependent. Hence, the additive white Gaussian noise assumption, which is commonly drawn in Kalman filters, is violated. Therefore, this paper proposes an iterative extended Kalman filter, which estimates the state of a nonlinear real valued system via a complex valued measurement model that consists of incoherent sensor stations, each with several coherent measurement channels. Since the proposed iterative extended Kalman filter is well suited for distributed positioning systems with several stations, a transmitter is localized in a simulation via two sensor stations, each measuring the received signal's amplitude and phase at four channels. To illustrate the advantages of the proposed algorithm, the direct measurement evaluation using the proposed algorithm is compared to a Kalman filter that evaluates the received signal strengths and angle of arrivals at each sensor station. Finally, a reflecting wall is incorporated into the simulation scenario to demonstrate the flexibility of the proposed Kalman filter.

Kalman filtering to real-time trace water level measurements using ultrasonic sensor

Water level monitoring systems are needed in various related fields. However, to accurately determine water levels typically difficult due to the effect like sloshing in dynamic environments. In this paper, we proposed Kalman filter based approach to reduce uncertainty in the water level measurements. Experiments have been performed by filling the tank with water and installing an ultrasonic sensor module at the top center of the tank. The water tank is vibrated with an artificial vibrator, then measuring the water level is done by the ultrasonic sensor. To reduce measurement errors we introduced the Kalman filtering. This technique is developed for improving the precision of water level measurements in the presence of various noise sources. The Kalman filter performance is demonstrated to be adaptive to real-time noise. Experiment results indicate reducing the errors of measurement significantly up to about 60% for a dynamic water condition by adjusting appropriately the Kalman filter tuning parameters.

Bias-Compensated Diffusion Pseudolinear Kalman Filter Algorithm for Censored Bearings-Only Target Tracking

This letter proposes a novel bias-compensated diffusion pseudolinear Kalman filter algorithm for censored bearings-only target tracking. The proposed algorithm considers two biases caused by the censored bearing angle measurements and the correlation between the measurement vector and the pseudolinear noise. First, the inverse Mills ratio is used to rebuild the uncensored measurements, which can efficiently compensate the bias arising from the censored measurements. Then, we present a bias analysis for the censored diffusion pseudolinear Kalman filter to develop a bias compensation method, leading to the BC-DPLKF-C algorithm. Simulation results show the improved performance of the proposed Kalman filter compared with existing algorithms.

Kalman Filter for Noise Reducer on Sensor Readings

Most systems nowadays require high-sensitivity sensors to increase its system performances. However, high-sensitivity sensors, i.e. accelerometer and gyro, are very vulnerable to noise when reading data from environment. Noise on data-readings can be fatal since the real measured-data contribute to the performance of a controller, or the augmented system in general. The paper will discuss about designing the required equation and the parameter of modified Standard Kalman Filter for filtering or reducing the noise, disturbance and extremely varying of sensor data. The Kalman Filter equation will be theoretically analyzed and designed based on its component of equation. Also, some values of measurement and variance constants will be simulated in MATLAB and then the filtered result will be analyzed to obtain the best suitable parameter value. Then, the design will be implemented in real-time on Arduino to reduce the noise of IMU (Inertial Measurements Unit) sensor reading. Based on the simulation and real-time implementation result, the proposed Kalman filter equation is able to filter signal with noises especially if there is any extreme variation of data without any information available of noise frequency that may happen to sensor- reading. The recommended ratio of constants in Kalman Filter is 100 with measurement constant should be greater than process variance constant.

A Kalman filter application for rainfall estimation using radar reflectivity measurements

The rainfall amount observed at a given location mostly depend on the cloud density, which can be quantified with the reflectivity values observed by meteorology weather radars. In this study, we aim to estimate the rainfall amount using a Kalman filter with radar reflectivity measurements. We first assume that the amount of rainfall observed at automatic weather observation stations (AWOSs) are elements of an unknown state vector and consider the Kalman filter process model as the true rainfall amounts observed at these AWOSs over time. For the measurement model of the Kalman filter, we use the radar reflectivity values observed at each AWOS location. For the execution of the Kalman filter, a number of rainfall amount and radar reflectivity value pairs are first required to learn the process and measurement models of the Kalman filter. The estimation performance of the proposed Kalman filter is then compared with empirical reflectivity (Z) - rainfall (R) relationships. Numerical results show that when the Kalman filter is executed with radar reflectivity measurements observed around a large number of AWOS locations, the mean squared errors of the Kalman filter rainfall estimates are smaller than the ones obtained with empirical ZR relationships.