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.

Multiple model PHD filter for tracking sharply maneuvering targets using recursive RANSAC based adaptive birth estimation

An algorithm to track multiple sharply maneuvering targets without prior knowledge about new target birth is proposed. These targets are capable of achieving sharp maneuvers within a short period of time, such as drones and agile missiles.The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems. However, the standard PHD filter operates on the single dynamic model and requires prior information about target birth distribution, which leads to many limitations in terms of practical applications. In this paper,we introduce a nonzero mean, white noise turn rate dynamic model and generalize jump Markov systems to multitarget case to accommodate sharply maneuvering dynamics. Moreover, to adaptively estimate newborn targets’information, a measurement-driven method based on the recursive random sampling consensus (RANSAC) algorithm is proposed. Simulation results demonstrate that the proposed method achieves significant improvement in tracking multiple sharply maneuvering targets with adaptive birth estimation.

Notes on Convergence and Modeling for the Extended Kalman Filter

The goal of this work is to provide an understanding of estimation technology for both linear and nonlinear dynamical systems.A critical analysis of both the Kalman filter(KF)and the extended Kalman filter(EKF)will be provided,along with examples to illustrate some important issues related to filtering convergence due to system modeling.A conceptual explanation of the topic with illustrative examples provided in the paper can help the readers capture the essential principles and avoid making mistakes while implementing the algorithms.Adding fictitious process noise to the system model assumed by the filter designers for convergence assurance is being investigated.A comparison of estimation accuracy with linear and nonlinear measurements is made.Parameter identification by the state estimation method through the augmentation of the state vector is also discussed.The intended readers of this article may include researchers,working engineers,or engineering students.This article can serve as a better understanding of the topic as well as a further connection to probability,stochastic process,and system theory.The lesson learned enables the readers to interpret the theory and algorithms appropriately and precisely implement the computer codes that nicely match the estimation algorithms related to the mathematical equations.This is especially helpful for those readers with less experience or background in optimal estimation theory,as it provides a solid foundation for further study on the theory and applications of the topic.

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.

Cubature Kalman Filter Based Millimeter Wave Beam Tracking for OTFS Systems

In this paper,a Millimeter wave(mmWave)beam tracking problem is studied in orthogonal time frequency space(OTFS)systems.Considering the nonlinearity of beamforming and the constraints of existing Kalman-filtering based beam tracking schemes,we propose a novel Cubature Kalman Filter(CKF)framework tracking the channel state information(CSI)to manage the challenge of highspeed channel variation in single-user moving scene for OTFS systems.Aiming for low complexity for mobile settings,this paper trains only one beam pair to track a path to maintain the reliable communication link in the analog beamforming architecture.Simulation results show that our proposed method has better tracking performance to improve the accuracy of the estimated beam angle compared with prior work.

Assimilation of temporal-spatial leaf area index into the CERES-Wheat model with ensemble Kalman filter and uncertainty assessment for improving winter wheat yield estimation

To accurately estimate winter wheat yields and analyze the uncertainty in crop model data assimilations, winter wheat yield estimates were obtained by assimilating measured or remotely sensed leaf area index （LAI） values. The performances of the calibrated crop environment resource synthesis for wheat （CERES-Wheat） model for two different assimilation scenarios were compared by employing ensemble Kalman filter （EnKF）-based strategies. The uncertainty factors of the crop model data assimilation was analyzed by considering the observation errors, assimilation stages and temporal-spatial scales. Overalll the results indicated a better yield estimate performance when the EnKF-based strategy was used to comprehen- sively consider several factors in the initial conditions and observations. When using this strategy, an adjusted coefficients of determination （R2） of 0.84, a root mean square error （RMSE） of 323 kg ha-1, and a relative errors （RE） of 4.15% were obtained at the field plot scale and an R2 of 0.81, an RMSE of 362 kg ha-1, and an RE of 4.52% were obtained at the pixel scale of 30 mx30 m. With increasing observation errors, the accuracy of the yield estimates obviously decreased, but an acceptable estimate was observed when the observation errors were within 20%. Winter wheat yield estimates could be improved significantly by assimilating observations from the middle to the end of the crop growing seasons. With decreasing assimilation frequency and pixel resolution, the accuracy of the crop yield estimates decreased; however, the computation time decreased. It is important to consider reasonable temporal-spatial scales and assimilation stages to obtain tradeoffs between accuracy and computation time, especially in operational systems used for regional crop yield estimates.

A “Dressed” Ensemble Kalman Filter Using the Hybrid Coordinate Ocean Model in the Pacific

The computational cost required by the Ensemble Kalman Filter （EnKF） is much larger than that of some simpler assimilation schemes, such as Optimal Interpolation （OI） or three-dimension variational as- similation （3DVAR）. Ensemble optimal interpolation （EnOI）, a crudely simplified implementation of EnKF, is sometimes used as a substitute in some oceanic applications and requires much less computational time than EnKF. In this paper, to compromise between computational cost and dynamic covariance, we use the idea of ＂dressing＂ a small size dynamical ensemble with a larger number of static ensembles in order to form an approximate dynamic covariance. The term ＂dressing＂ means that a dynamical ensemble seed from model runs is perturbed by adding the anomalies of some static ensembles. This dressing EnKF （DrEnKF for short） scheme is tested in assimilation of real altimetry data in the Pacific using the HYbrid Coordinate Ocean Model （HYCOM） over a four-year period. Ten dynamical ensemble seeds are each dressed by 10 static ensemble members selected from a 100-member static ensemble. Results are compared to two EnKF assimilation runs that use 10 and 100 dynamical ensemble members. Both temperature and salinity fields from the DrEnKF and the EnKF are compared to observations from Argo floats and an OI SST dataset. The results show that the DrEnKF and the 100-member EnKF yield similar root mean square errors （RMSE） at every model level. Error covariance matrices from the DrEnKF and the 100-member EnKF are also compared and show good agreement.

Investigation of the different weight models in Kalman filter:A case study of GNSS monitoring results

During geodetic monitoring with GNSS technology one of important steps is the correct processing and analysis of the measured displacements. We used the processing method of Kalman filter smoothing algorithm, which allows to evaluate not only displacements, but also the speed, acceleration, and other characteristics of the deformation model. One of the important issues is the calculation of the obser- vations weight matrix in the Kalman filter. Recurrence algorithm of Kalman filtering can calculate and specify the weights during processing. However, the weights obtained in such way do not always exactly correspond to the actual observation accuracy. We established the observations weights based on the accuracy of baseline measurements. In the presented study, we offered and investigated different models of establishing the accuracy of the baselines. The offered models and the processing of the measured displacements were tested on an experimentally geodetic GNSS network. The research results show that despite of different weight models, changing weights up to 2 times do not change Kalman filtering ac- curacy extremely. The significant improvements for Kalman filtering accuracy for baselines shorter than 10 km were not got. Therefore, for typical GNSS monitoring networks with baseline range 10-15 km, we recommend to use any kind of models. The compulsory condition for getting correct and reliable results is checking results on blunders. For baselines, which are longer than 15 km we propose to use weight model which include baseline standard deviation from network adjustment and corrections for baseline length and its accuracy.

Efficient hemodynamic states stimulation using fNIRS data with the extended Kalman filter and bifurcation analysis of balloon model

This paper introduces a stochastic hemodynamic system to describe the brain neural activity based on the balloon model. A continuous-discrete extended Kalman filter is used to estimate the nonlinear model states. The stability, controllability and observability of the proposed model are described based on the simulation and measurement data analysis. The observability and controllability characteristics are in- troduced as significant factors to validate the preference of different hemodynamic factors to be considered for diagnosis and monitoring in clinical applications. This model also can be efficiently applied in any monitoring and control platform include brain and for study of hemodynamics in brain imaging modalities such as pulse oximetry and functional near infrared spectroscopy. The work is on progress to extend the proposed model to cover more hemodynamic and neural brain signals for real-time in-vivo application.

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.

Impact of Perturbation Schemes on the Ensemble Prediction in a Coupled Lorenz Model

Based on a simple coupled Lorenz model,we investigate how to assess a suitable initial perturbation scheme for ensemble forecasting in a multiscale system involving slow dynamics and fast dynamics.Four initial perturbation approaches are used in the ensemble forecasting experiments:the random perturbation(RP),the bred vector(BV),the ensemble transform Kalman filter(ETKF),and the nonlinear local Lyapunov vector(NLLV)methods.Results show that,regardless of the method used,the ensemble averages behave indistinguishably from the control forecasts during the first few time steps.Due to different error growth in different time-scale systems,the ensemble averages perform better than the control forecast after very short lead times in a fast subsystem but after a relatively long period of time in a slow subsystem.Due to the coupled dynamic processes,the addition of perturbations to fast variables or to slow variables can contribute to an improvement in the forecasting skill for fast variables and slow variables.Regarding the initial perturbation approaches,the NLLVs show higher forecasting skill than the BVs or RPs overall.The NLLVs and ETKFs had nearly equivalent prediction skill,but NLLVs performed best by a narrow margin.In particular,when adding perturbations to slow variables,the independent perturbations(NLLVs and ETKFs)perform much better in ensemble prediction.These results are simply implied in a real coupled air–sea model.For the prediction of oceanic variables,using independent perturbations(NLLVs)and adding perturbations to oceanic variables are expected to result in better performance in the ensemble prediction.

Modified unscented Kalman filter using modified filter gain and variance scale factor for highly maneuvering target tracking

To improve the low tracking precision caused by lagged filter gain or imprecise state noise when the target highly maneuvers, a modified unscented Kalman filter algorithm based on the improved filter gain and adaptive scale factor of state noise is presented. In every filter process, the estimated scale factor is used to update the state noise covariance Qk, and the improved filter gain is obtained in the filter process of unscented Kalman filter （UKF） via predicted variance Pk｜k-1, which is similar to the standard Kalman filter. Simulation results show that the proposed algorithm provides better accuracy and ability to adapt to the highly maneuvering target compared with the standard UKF.

Impact of Coastal Radar Observability on the Forecast of the Track and Rainfall of Typhoon Morakot(2009)Using WRF-based Ensemble Kalman Filter Data Assimilation

This study explored the impact of coastal radar observability on the forecast of the track and rainfall of Typhoon Morakot （2009） using a WRF-based ensemble Kalman filter （EnKF） data assimilation （DA） system. The results showed that the performance of radar EnKF DA was quite sensitive to the number of radars being assimilated and the DA timing relative to the landfall of the tropical cyclone （TC）. It was found that assimilating radial velocity （Vr） data from all the four operational radars during the 6 h immediately before TC landfall was quite important for the track and rainfall forecasts after the TC made landfall. The TC track forecast error could be decreased by about 43% and the 24-h rainfall forecast skill could be almost tripled. Assimilating Vr data from a single radar outperformed the experiment without DA, though with less improvement compared to the multiple-radar DA experiment. Different forecast performances were obtained by assimilating different radars, which was closely related to the first-time wind analysis increment, the location of moisture transport, the quasi-stationary rainband, and the local convergence line. However, only assimilating Vr data when the TC was farther away from making landfall might worsen TC track and rainfall forecasts. Besides, this work also demonstrated that Vr data from multiple radars, instead of a single radar, should be used for verification to obtain a more reliable assessment of the EnKF performance.

Low-cost adaptive square-root cubature Kalman filter forsystems with process model uncertainty

A novel low-cost adaptive square-root cubature Kalmanfilter （LCASCKF） is proposed to enhance the robustness of processmodels while only increasing the computational load slightly.It is well-known that the Kalman filter cannot handle uncertainties ina process model, such as initial state estimation errors, parametermismatch and abrupt state changes. These uncertainties severelyaffect filter performance and may even provoke divergence. Astrong tracking filter （STF）, which utilizes a suboptimal fading factor,is an adaptive approach that is commonly adopted to solvethis problem. However, if the strong tracking SCKF （STSCKF）uses the same method as the extended Kalman filter （EKF） tointroduce the suboptimal fading factor, it greatly increases thecomputational load. To avoid this problem, a low-cost introductorymethod is proposed and a hypothesis testing theory is applied todetect uncertainties. The computational load analysis is performedby counting the total number of floating-point operations and it isfound that the computational load of LCASCKF is close to that ofSCKF. Experimental results prove that the LCASCKF performs aswell as STSCKF, while the increase in computational load is muchlower than STSCKF.

A new real-time eye tracking based on nonlinear unscented Kalman filter for monitoring driver fatigue

A new scheme for driver fatigue detection is presented, which is based on the nonlinear unscented Kalman filter and eye tracking. Assuming a probability distribution than to approximate an arbitrary nonlinear function or transformation, eye nonlinear tracking can be achieved using an unscented transformation (UT), which adopts a set of deterministic sigma points to match the posterior probability density function of the eye movement. Driver fatigue can be detected using the percentage of eye closure (PERCLOS) framework in a realistic driving condition after the eye nonlinear tracking. This system was tested adequately in realistic driving environments with subjects of different genders, with/without glasses, in day/night driving, being commercial/noncommercial drivers, in continuous driving time, and under different road conditions. The last experimental results show that the proposed method not only improves the robustness for nonlinear eye tracking, but also can provide more accurate estimation than the traditional Kalman filter.

Airship aerodynamic model estimation using unscented Kalman filter

An airship model is made-up of aerostatic,aerodynamic,dynamic,and propulsive forces and torques.Besides others,the computation of aerodynamic forces and torques is difficult.Usually,wind tunnel experimentation and potential flow theory are used for their calculations.However,the limitations of these methods pose difficulties in their accurate calculation.In this work,an online estimation scheme based on unscented Kalman filter(UKF)is proposed for their calculation.The proposed method introduces six auxiliary states for the complete aerodynamic model.UKF uses an extended model and provides an estimate of a complete state vector along with auxiliary states.The proposed method uses the minimum auxiliary state variables for the approximation of the complete aerodynamic model that makes it computationally less intensive.UKF estimation performance is evaluated by developing a nonlinear simulation environment for University of Engineering and Technology,Taxila(UETT)airship.Estimator performance is validated by performing the error analysis based on estimation error and 2-σ uncertainty bound.For the same problem,the extended Kalman filter(EKF)is also implemented and its results are compared with UKF.The simulation results show that UKF successfully estimates the forces and torques due to the aerodynamic model with small estimation error and the comparative analysis with EKF shows that UKF improves the estimation results and also it is more suitable for the under-consideration problem.

Assimilation of Remote Sensing and Crop Model for LAI Estimation Based on Ensemble Kalman Filter

Data assimilation in agricultural remote sensing research is of great significance to integrate with remote sensing observations and model simulations for parameters estimation. The present investigation not only designed and realized the Ensemble Kalman Filtering algorithm （EnKF） assimilation by combing the crop growth model （CERES-Wheat） with remote sensing data, but also optimized and updated the key parameters （LAI） of winter wheat by using remote sensing data. Results showed that the assimilation LAI and the observation ones agreed with each other, and the R2 reached 0.8315. So assimilation remote sensing and crop model could provide reference data for the agricultural production.

基于自适应强跟踪Kalman滤波的GNSS跟踪环路设计

为提高GNSS接收机跟踪环路在复杂环境下的跟踪性能,提出一种基于自适应强跟踪Kalman滤波(ASTKF)的跟踪环路,在传统跟踪环路的基础上,以鉴相器输出为观测量进行自适应强跟踪Kalman滤波,滤波结果用于计算导航滤波器的观测量,同时将伪码频率和载波多普勒频率反馈到码NCO和载波NCO,在ASTKF中使用基于卡方分布的渐消因子计算方法,提升跟踪环路鲁棒性。半物理仿真实验表明,相比于基于Kalman滤波的跟踪环路和基于强跟踪Kalman滤波(STKF)的跟踪环路,所提出方法在水平方向上的位置误差和速度误差减小20%以上,有效提高了卫星导航接收机的定位性能。