Multiple Kalman filters model with shaping filter GPS real-time deformation analysis

In order to detect the deformation in real-time of the GPS time series and improve its reliability, the multiple Kalman filters model with shaping filter was proposed. Two problems were solved: firstly, because the GPS real-time deformation series with a high sampling rate contain coloured noise, the multiple Kalman filter model requires the white noise, and the multiple Kalman filters model is augmented by a shaping filter in order to reduce the colored noise; secondly, the multiple Kalman filters model with shaping filter can detect the deformation epoch in real-time and improve the quality of GPS measurements for the real-time deformation applications. Based on the comparisons of the applications in different GPS time series with different models, the advantages of the proposed model were illustrated. The proposed model can reduce the colored noise, detect the smaller changes, and improve the precision of the detected deformation epoch.

Cubature Kalman filters: Derivation and extension

This paper focuses on the cubature Kalman filters （CKFs） for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.

Strong tracking adaptive Kalman filters for underwater vehicle dead reckoning

To improve underwater vehicle dead reckoning, a developed strong tracking adaptive kalman filter is proposed. The filter is improved with an additional adaptive factor and an estimator of measurement noise covariance. Since the magnitude of fading factor is changed adaptively, the tracking ability of the filter is still enhanced in low velocity condition of underwater vehicles. The results of simulation tests prove the presented filter effective.

Generalized cubature quadrature Kalman filters:derivations and extensions

A new Gaussian approximation nonlinear filter called generalized cubature quadrature Kalman filter (GCQKF) is introduced for nonlinear dynamic systems. Based on standard GCQKF, two extensions are developed, namely square root generalized cubature quadrature Kalman filter (SR-GCQKF) and iterated generalized cubature quadrature Kalman filter (I-GCQKF). In SR-GCQKF, the QR decomposition is exploited to alter the Cholesky decomposition and both predicted and filtered error covariances have been propagated in square root format to make sure the numerical stability. In I-GCQKF, the measurement update step is executed iteratively to make full use of the latest measurement and a new terminal criterion is adopted to guarantee the increase of likelihood. Detailed numerical experiments demonstrate the superior performance on both tracking stability and estimation accuracy of I-GCQKF and SR-GCQKF compared with GCQKF.

Hybrid Kalman and unscented Kalman filters for INS/GPS integrated system considering constant lever arm effect

In inertial navigation system(INS) and global positioning system(GPS) integrated system, GPS antennas are usually not located at the same location as the inertial measurement unit(IMU) of the INS, so the lever arm effect exists, which makes the observation equation highly nonlinear. The INS/GPS integration with constant lever arm effect is studied. The position relation of IMU and GPS's antenna is represented in the earth centered earth fixed frame, while the velocity relation of these two systems is represented in local horizontal frame. Due to the small integration time interval of INS, i.e. 0.1 s in this work, the nonlinearity in the INS error equation is trivial, so the linear INS error model is constructed and addressed by Kalman filter's prediction step. On the other hand, the high nonlinearity in the observation equation due to lever arm effect is addressed by unscented Kalman filter's update step to attain higher accuracy and better applicability. Simulation is designed and the performance of the hybrid filter is validated.

Ensemble-based Kalman Filters in Strongly Nonlinear Dynamics

This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that occurs when the model jumps from one basin of attraction to the other. Four configurations of the ensemble-based Kalman filtering data assimilation techniques, including the ensemble Kalman filter, en- semble adjustment Kalman filter, ensemble square root filter and ensemble transform Kalman filter, are evaluated with their ability in predicting the regime transition （also called phase transition） and also are compared in terms of their sensitivity to both observational and sampling errors. The sensitivity of each ensemble-based filter to the size of the ensemble is also examined.

Adaptive nonlinear Kalman filters based on credibility theory with noise correlation

To solve the divergence problem and overcome the difficulty in guaranteeing filtering accuracy during estimation of the process noise covariance or the measurement noise covariance with traditional new information-based nonlinear filtering methods,we design a new method for estimating noise statistical characteristics of nonlinear systems based on the credibility Kalman Filter(KF)theory considering noise correlation.This method first extends credibility to the Unscented Kalman Filter(UKF)and Extended Kalman Filter(EKF)based on the credibility theory.Further,an optimization model for nonlinear credibility under noise related conditions is established considering noise correlation.A combination of filtering smoothing and credibility iteration formula is used to improve the real-time performance of the nonlinear adaptive credibility KF algorithm,further expanding its application scenarios,and the derivation process of the formula theory is provided.Finally,the performance of the nonlinear credibility filtering algorithm is simulated and analyzed from multiple perspectives,and a comparative analysis conducted on specific experimental data.The simulation and experimental results show that the proposed credibility EKF and credibility UKF algorithms can estimate the noise covariance more accurately and effectively with lower average estimation time than traditional methods,indicating that the proposed algorithm has stable estimation performance and good real-time performance.

Estimation of Equivalent Model of Photovoltaic Array Using Unscented Kalman Filters

This paper proposes the use of the unscented Kalman filter to estimate the equivalent model of a photovoltaic(PV)array,using external measurements of current and voltage at the inverter level.The estimated model is of interest to predict the power output of PV plants,in both planning and operation scenarios,and thus improves the efficient operation of power systems with high penetration of renewable energy.The proposed technique has been assessed in several simulated scenarios under different operating conditions.The results show that accurate estimates are provided for the model parameters,even in the presence of measurement noise and abrupt variations under the external conditions.

Parameter Estimation for Hot-spot Thermal Model of Power Transformers Using Unscented Kalman Filters

This paper presents a parameter estimation technique for the hot-spot thermal model of power transformers.The proposed technique is based on the unscented formulation of the Kalman filter,jointly considering the state variables and parameters of the dynamic thermal model.A two-stage estimation technique that takes advantage of different loading conditions is developed,in order to increase the number of parameters which can be identified.Simulation results are presented,which show that the observable parameters are estimated with an error of less than 3%.The parameter estimation procedure is mainly intended for factory testing,allowing the manufacturer to enhance the thermal model of power transformers and,therefore,its customers to increase the lifetime of these assets.The proposed technique could be additionally considered in field applications if the necessary temperature measurements are available.

A dual adaptive unscented Kalman filter algorithm for SINS-based integrated navigation system

In this study, the problem of measuring noise pollution distribution by the intertial-based integrated navigation system is effectively suppressed. Based on nonlinear inertial navigation error modeling, a nested dual Kalman filter framework structure is developed. It consists of unscented Kalman filter (UKF)master filter and Kalman filter slave filter. This method uses nonlinear UKF for integrated navigation state estimation. At the same time, the exact noise measurement covariance is estimated by the Kalman filter dependency filter. The algorithm based on dual adaptive UKF (Dual-AUKF) has high accuracy and robustness, especially in the case of measurement information interference. Finally, vehicle-mounted and ship-mounted integrated navigation tests are conducted. Compared with traditional UKF and the Sage-Husa adaptive UKF (SH-AUKF), this method has comparable filtering accuracy and better filtering stability. The effectiveness of the proposed algorithm is verified.

Traffic Control Based on Integrated Kalman Filtering and Adaptive Quantized Q-Learning Framework for Internet of Vehicles

Intelligent traffic control requires accurate estimation of the road states and incorporation of adaptive or dynamically adjusted intelligent algorithms for making the decision.In this article,these issues are handled by proposing a novel framework for traffic control using vehicular communications and Internet of Things data.The framework integrates Kalman filtering and Q-learning.Unlike smoothing Kalman filtering,our data fusion Kalman filter incorporates a process-aware model which makes it superior in terms of the prediction error.Unlike traditional Q-learning,our Q-learning algorithm enables adaptive state quantization by changing the threshold of separating low traffic from high traffic on the road according to the maximum number of vehicles in the junction roads.For evaluation,the model has been simulated on a single intersection consisting of four roads:east,west,north,and south.A comparison of the developed adaptive quantized Q-learning(AQQL)framework with state-of-the-art and greedy approaches shows the superiority of AQQL with an improvement percentage in terms of the released number of vehicles of AQQL is 5%over the greedy approach and 340%over the state-of-the-art approach.Hence,AQQL provides an effective traffic control that can be applied in today’s intelligent traffic system.

Unknown Environment Measurement Mapping by Unmanned Aerial Vehicle Using Kalman Filter-Based Low-Cost Estimated Parallel 8-Beam LIDAR

The measurement and mapping of objects in the outer environment have traditionally been conducted using ground-based monitoring systems,as well as satellites.More recently,unmanned aerial vehicles have also been employed for this purpose.The accurate detection and mapping of a target such as buildings,trees,and terrains are of utmost importance in various applications of unmanned aerial vehicles(UAVs),including search and rescue operations,object transportation,object detection,inspection tasks,and mapping activities.However,the rapid measurement and mapping of the object are not currently achievable due to factors such as the object’s size,the intricate nature of the sites,and the complexity of mapping algorithms.The present system introduces a costeffective solution for measurement and mapping by utilizing a small unmanned aerial vehicle(UAV)equipped with an 8-beam Light Detection and Ranging(LiDAR)system.This approach offers advantages over traditional methods that rely on expensive cameras and complex algorithm-based approaches.The reflective properties of laser beams have also been investigated.The system provides prompt results in comparison to traditional camerabased surveillance,with minimal latency and the need for complex algorithms.The Kalman estimation method demonstrates improved performance in the presence of noise.The measurement and mapping of external objects have been successfully conducted at varying distances,utilizing different resolutions.

Unscented Kalman filter for a low-cost GNSS/IMU-based mobile mapping application under demanding conditions

For the last two decades,low-cost Global Navigation Satellite System(GNSS)receivers have been used in various applications.These receivers are mini-size,less expensive than geodetic-grade receivers,and in high demand.Irrespective of these outstanding features,low-cost GNSS receivers are potentially poorer hardwares with internal signal processing,resulting in lower quality.They typically come with low-cost GNSS antenna that has lower performance than their counterparts,particularly for multipath mitigation.Therefore,this research evaluated the low-cost GNSS device performance using a high-rate kinematic survey.For this purpose,these receivers were assembled with an Inertial Measurement Unit(IMU)sensor,which actively transmited data on acceleration and orientation rate during the observation.The position and navigation parameter data were obtained from the IMU readings,even without GNSS signals via the U-blox F9R GNSS/IMU device mounted on a vehicle.This research was conducted in an area with demanding conditions,such as an open sky area,an urban environment,and a shopping mall basement,to examine the device’s performance.The data were processed by two approaches:the Single Point Positioning-IMU(SPP/IMU)and the Differential GNSS-IMU(DGNSS/IMU).The Unscented Kalman Filter(UKF)was selected as a filtering algorithm due to its excellent performance in handling nonlinear system models.The result showed that integrating GNSS/IMU in SPP processing mode could increase the accuracy in eastward and northward components up to 68.28%and 66.64%.Integration of DGNSS/IMU increased the accuracy in eastward and northward components to 93.02%and 93.03%compared to the positioning of standalone GNSS.In addition,the positioning accuracy can be improved by reducing the IMU noise using low-pass and high-pass filters.This application could still not gain the expected position accuracy under signal outage conditions.

WSN Mobile Target Tracking Based on Improved Snake-Extended Kalman Filtering Algorithm

A wireless sensor network mobile target tracking algorithm(ISO-EKF)based on improved snake optimization algorithm(ISO)is proposed to address the difficulty of estimating initial values when using extended Kalman filtering to solve the state of nonlinear mobile target tracking.First,the steps of extended Kalman filtering(EKF)are introduced.Second,the ISO is used to adjust the parameters of the EKF in real time to adapt to the current motion state of the mobile target.Finally,the effectiveness of the algorithm is demonstrated through filtering and tracking using the constant velocity circular motion model(CM).Under the specified conditions,the position and velocity mean square error curves are compared among the snake optimizer(SO)-EKF algorithm,EKF algorithm,and the proposed algorithm.The comparison shows that the proposed algorithm reduces the root mean square error of position by 52%and 41%compared to the SOEKF algorithm and EKF algorithm,respectively.

A Novel Method for Aging Prediction of Railway Catenary Based on Improved Kalman Filter

The aging prediction of railway catenary is of profound significance for ensuring the regular operation of electrified trains.However,in real-world scenarios,accurate predictions are challenging due to various interferences.This paper addresses this challenge by proposing a novel method for predicting the aging of railway catenary based on an improved Kalman filter(KF).The proposed method focuses on modifying the priori state estimate covariance and measurement error covariance of the KF to enhance accuracy in complex environments.By comparing the optimal displacement value with the theoretically calculated value based on the thermal expansion effect of metals,it becomes possible to ascertain the aging status of the catenary.To improve prediction accuracy,a railway catenary aging prediction model is constructed by integrating the Takagi-Sugeno(T-S)fuzzy neural network(FNN)and KF.In this model,an adaptive training method is introduced,allowing the FNN to use fewer fuzzy rules.The inputs of the model include time,temperature,and historical displacement,while the output is the predicted displacement.Furthermore,the KF is enhanced by modifying its prior state estimate covariance and measurement error covariance.These modifications contribute to more accurate predictions.Lastly,a low-power experimental platform based on FPGA is implemented to verify the effectiveness of the proposed method.The test results demonstrate that the proposed method outperforms the compared method,showcasing its superior performance.

Power Quality Disturbance Identification Basing on Adaptive Kalman Filter andMulti-Scale Channel Attention Fusion Convolutional Network

In light of the prevailing issue that the existing convolutional neural network(CNN)power quality disturbance identification method can only extract single-scale features,which leads to a lack of feature information and weak anti-noise performance,a new approach for identifying power quality disturbances based on an adaptive Kalman filter(KF)and multi-scale channel attention(MS-CAM)fused convolutional neural network is suggested.Single and composite-disruption signals are generated through simulation.The adaptive maximum likelihood Kalman filter is employed for noise reduction in the initial disturbance signal,and subsequent integration of multi-scale features into the conventional CNN architecture is conducted.The multi-scale features of the signal are captured by convolution kernels of different sizes so that the model can obtain diverse feature expressions.The attention mechanism(ATT)is introduced to adaptively allocate the extracted features,and the features are fused and selected to obtain the new main features.The Softmax classifier is employed for the classification of power quality disturbances.Finally,by comparing the recognition accuracy of the convolutional neural network(CNN),the model using the attention mechanism,the bidirectional long-term and short-term memory network(MS-Bi-LSTM),and the multi-scale convolutional neural network(MSCNN)with the attention mechanism with the proposed method.The simulation results demonstrate that the proposed method is higher than CNN,MS-Bi-LSTM,and MSCNN,and the overall recognition rate exceeds 99%,and the proposed method has significant classification accuracy and robust classification performance.This achievement provides a new perspective for further exploration in the field of power quality disturbance classification.

Application of Kalman Filter Method in the Forecast of Temperature in Nanchang

A temperature forecasting model was created firstly based on the Kalman filter method,and then used to predict the highest and lowest temperature in Nanchang station from October 27 to November 1,2017.Finally,according to the empirical forecasting method,guidance forecasts were established for the northern,central,and southern parts of Nanchang City.After inspection,it was found that the temperature prediction model established based on the Kalman filter method in Nanchang station had good prediction performance,and especially in the 24-hour forecast,it had advantages over the European Center.The accuracy of low temperature forecast was better than that of high temperature forecast.

Multi-scale Kalman filters algorithm for GPS common-view observation data based on correlation structure of discrete wavelet coefficients

Global positioning system(GPS)common-view observation data were processed by using the multi-scale Kalman algorithm based on a correlative structure of the discrete wavelet coefficients.Suppose that the GPS commonview observation data has the 1/f fractal characteristic,the algorithm of wavelet transform was used to estimate the Hurst parameter H of GPS clock difference data.When 0<H<1,the 1/f fractal characteristic of the GPS clock difference data is a Gaussian zero-mean and non-stationary stochastic process.Thus,the discrete wavelet coefficients can be discussed in the process of estimating multi-scale Kalman coefficients.Furthermore,the discrete clock difference can be estimated.The single-channel and multi-channel common-view observation data were processed respectively.Comparisons were made between the results obtained and the Circular T data.Simulation results show that the algorithm discussed in this paper is both feasible and effective.

A Novel Adaptive Kalman Filter Based on Credibility Measure

It is quite often that the theoretic model used in the Kalman filtering may not be sufficiently accurate for practical applications,due to the fact that the covariances of noises are not exactly known.Our previous work reveals that in such scenario the filter calculated mean square errors(FMSE)and the true mean square errors(TMSE)become inconsistent,while FMSE and TMSE are consistent in the Kalman filter with accurate models.This can lead to low credibility of state estimation regardless of using Kalman filters or adaptive Kalman filters.Obviously,it is important to study the inconsistency issue since it is vital to understand the quantitative influence induced by the inaccurate models.Aiming at this,the concept of credibility is adopted to discuss the inconsistency problem in this paper.In order to formulate the degree of the credibility,a trust factor is constructed based on the FMSE and the TMSE.However,the trust factor can not be directly computed since the TMSE cannot be found for practical applications.Based on the definition of trust factor,the estimation of the trust factor is successfully modified to online estimation of the TMSE.More importantly,a necessary and sufficient condition is found,which turns out to be the basis for better design of Kalman filters with high performance.Accordingly,beyond trust factor estimation with Sage-Husa technique(TFE-SHT),three novel trust factor estimation methods,which are directly numerical solving method(TFE-DNS),the particle swarm optimization method(PSO)and expectation maximization-particle swarm optimization method(EM-PSO)are proposed.The analysis and simulation results both show that the proposed TFE-DNS is better than the TFE-SHT for the case of single unknown noise covariance.Meanwhile,the proposed EMPSO performs completely better than the EM and PSO on the estimation of the credibility degree and state when both noise covariances should be estimated online.

Vehicle Detection and Tracking in UAV Imagery via YOLOv3 and Kalman Filter

Unmanned aerial vehicles(UAVs)can be used to monitor traffic in a variety of settings,including security,traffic surveillance,and traffic control.Numerous academics have been drawn to this topic because of the challenges and the large variety of applications.This paper proposes a new and efficient vehicle detection and tracking system that is based on road extraction and identifying objects on it.It is inspired by existing detection systems that comprise stationary data collectors such as induction loops and stationary cameras that have a limited field of view and are not mobile.The goal of this study is to develop a method that first extracts the region of interest(ROI),then finds and tracks the items of interest.The suggested system is divided into six stages.The photos from the obtained dataset are appropriately georeferenced to their actual locations in the first phase,after which they are all co-registered.The ROI,or road and its objects,are retrieved using the GrabCut method in the second phase.The third phase entails data preparation.The segmented images’noise is eliminated using Gaussian blur,after which the images are changed to grayscale and forwarded to the following stage for additional morphological procedures.The YOLOv3 algorithm is used in the fourth step to find any automobiles in the photos.Following that,the Kalman filter and centroid tracking are used to perform the tracking of the detected cars.The Lucas-Kanade method is then used to perform the trajectory analysis on the vehicles.The suggested model is put to the test and assessed using the Vehicle Aerial Imaging from Drone(VAID)dataset.For detection and tracking,the model was able to attain accuracy levels of 96.7%and 91.6%,respectively.