A Practical Robust Long Term Yield Curve Model

High dynamic aircraft is a very attractive new generation vehicles, in which provides near space aviation with large flight envelope both speed and altitude, for example the hypersonic vehicles. The complex flight environments for high dynamic vehicles require high accuracy and stability navigation scheme. Since the conventional Strapdown Inertial Navigation System (SINS) and Global Position System (GPS) federal integrated scheme based on EKF (Extended Kalman Filter) is invalidation in GPS single blackout situation because of high speed flight, a new high precision and stability integrated navigation approach is presented in this paper, in which the SINS, GPS and Celestial Navigation System (CNS) is combined as a federal information fusion configuration based on nonlinear Unscented Kalman Filter (UKF) algorithm. Firstly, the new integrated system state error is modeled. According to this error model, the SINS system is used as the navigation solution mathematic platform. The SINS combine with GPS constitute one error estimation filter subsystem based on UKF to obtain local optimal estimation, and the SINS combine with CNS constitute another error estimation subsystem. A non-reset federated configuration filter based on partial information is proposed to fuse two local optimal estimations to get global optimal error estimation, and the global optimal estimation is used to correct the SINS navigation solution. The χ 2 fault detection method is used to detect the subsystem fault, and the fault subsystem is isolation through fault interval to protect system away from the divergence. The integrated system takes advantages of SINS, GPS and CNS to an immense improvement for high accuracy and reliably high dynamic navigation application. Simulation result shows that federated fusion of using GPS and CNS to revise SINS solution is reasonable and availably with good estimation performance, which are satisfied with the demands of high dynamic flight navigation. The UKF is superior than EKF based integrated scheme, in which has smaller estimation error and quickly convergence rate.

State of Charge (SOC) estimation plays a crucial role in managing the performance and longevity of electric vehicle (EV) batteries. Various estimation techniques, including various Kalman Filters (KF), have been employed for this purpose. The mathematical process and limits of different KF family algorithms are analysed. In this study, an impact of nonlinear KF parameters on SOC estimation accuracy for EV batteries is analyzed. Specifically, the performance of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF) is examined. EKF is most preferred for SOC estimation whereas introducing sigma points in UKF is the basic difference between EKF and UKF. In comparison to EKF and UKF, PF is more flexible since it applies to nonlinear systems with non-Gaussian distributions. Utilising a sequence of noisy measurements, KF is a recursive method that approximates the state of a dynamic system. It requires accurate parameters such as process noise covariance (Q) and measurement noise covariance (R) to work effectively. In this work, the effect of these parameters on state of charge estimation using nonlinear KFs has been analysed under different settings of noise covariance matrices. Tuning these parameters is essential for optimizing the performance of the KF and ensuring accurate and reliable state estimation in real-world applications. To find parameter values that provide the best balance between accuracy, robustness, and computational efficiency, the tuning process involves experimentation, simulation, and validation using real-world data. According to the results observed, the filter parameters such as three diagonal elements of Q are selected as 2e-8, 0.005, 0.003 and R as 2e-6. By evaluating the state estimation accuracy under different driving scenarios, robustness and sensitivity of filtering technique in estimating SOC for EV batteries has been studied. This analysis contributes to the optimization of SOC estimation algorithms, enhancing the reliability and efficiency of EV battery management systems.

Many technologies need to be established to realize autonomous ships. In particular, accurate state estimation in real time is one of the most important technologies. In the ship and ocean engineering fields, there have been many studies on state estimation using nonlinear Kalman filters. Several methods have been proposed for nonlinear Kalman filters. However, there is insufficient verification on the selection of which filter should be applied among them. Therefore, this study aims to validate the filter selection to provide a guideline for filter selection. The effects of modeling error, observation noise, and type of maneuvers on the estimation accuracy of the unscented Kalman filter (UKF) and ensemble Kalman filter (EnKF) used in this study were investigated. In addition, it was verified whether filtering could be performed in real time. The results show that modeling error significantly impacts the estimation accuracy of the UKF and EnKF. However, the observation noise and types of maneuvers did not have an impact like the modeling error. Thus, we obtained the guideline that UKF and EnKF should be used differently depending on the required computation time. We also obtained that keeping the modeling error sufficiently small is essential to improving the estimation accuracy.

The problem of tracking epidemic spreading on networks is relevant to the control of morbidity. The transmission dynamics of an epidemic can be described by a simple compartmental model. Specifically, the estimation of epidemic spreading on networks can be achieved by a nonlinear Kalman filter, which is a tool for state estimation of nonlinear systems. In this article, epidemic spreading on networks is described by compartmental models, such as susceptible-infected-susceptible, susceptible-infected-recovered, and susceptible-infected-recovered-susceptible models. The dynamics of epidemic spreading on homogeneous networks, including Erdös-Renyi network, Watts-Strogatz network, and Newman-Watts network, are estimated by several nonlinear Kalman filters, including extended Kalman filter, unscented Kalman filter, and third-degree and fifth-degree cubature Kalman filters. The performance comparison in terms of accuracy and stability forms a guideline of utilizing nonlinear Kalman filters for tracking epidemic spreading. The theoretical analysis has been validated through numerical experiments.

Attitude control system plays the important role for to maintain the satellite to desired orientation. To control the satellite it is necessary to do the attitude stabilization. Attitude stabilization achieved by Star sensor, sun sensor, Earth sensors. Attitude control is mainly use for antenna pointing accuracy, camera focus to earth surface and solar panel pointing toward sun. Due to tumbling effects, satellite will rotate all the direction in the space. To maintain the orientation of the satellite it is necessary to design the attitude determination and control. Satellite consider as the rigid body. Inertia matrix describes the rigid body dynamics. The orientation of the satellite determine by Euler angle and Quaternion. The Low earth orbiting satellite will have enormous amount of aerodynamic drag stinking the satellite body and gravitational attraction another problem. Because of that satellite dwell, time is reduced. It means satellite more time spending particular part of the earth. The attitude estimation is measures by the orientation of vectors. Attitude estimation means to find the position and orientation of flying object with respect to the fixed reference of reference. Vector remains considered in the frame of reference to compute for find the orientation of the body of the satellite in the inertial reference system. The Earth is an inertial reference frame, and Satellite is a body frame. Attitude sensor used to measure the satellite orientation in the reference frame. This will help in accurately predicting the orbit deviation and a control system to correct if any by providing the satellite momentum means ‘mass in motion’ changes in a body rapidly in Low earth orbit due to centripetal force acting on a satellite. Attitude control system (ACS) need the numerical simulation to find the required torque demand by the help of difference between reference input (Attitude) signal and feedback signal measure by attitude sensor to trim the control surface maintain the actuator required orientation . The results will consist of two parts the first part consisting of the attitude estimation using Euler angle and Quaternion method, second part consist of estimate the control torque from magnetic torquer and error estimation using non-linear filter (Unscented Kalman Filter) with MATLAB simulation. Â

This paper presents the efficient Unscented Kalman filter (UKF) based estimation and control of a 3-DOF Omni bundle robot. The angular trajectory tracking becomes more difficult under highly non-linear measurement noise and process noise. A rapidly converging Unscented Kalman Filter (UKF) is presented in the paper. The extended Kalman filter (EKF) provides less accurate results in the highly non-linear system and sometime may become unstable because of convergence related issues, whereas in UKF the results in the non-linear system are better than EKF. UKF is more accurate in state and noise estimation. The computed torque technique is taken as a model to apply UKF. After, estimation the noise is removed. The experiment is conducted on Omni bundle with process and measurement noise. The results prove the superiority of presented UKF over conventional UKF and EKF.

Traffic state estimation problems must deal with imperfect information. Imperfect information may occur as a result of misalignments between reality and the assumptions or simplifications made when developing the models as well as incomplete or corrupted data. One of the well-known methods of handling imperfect information is the Kalman filter algorithm and its variations, such as the extended Kalman filter and the unscented Kalman filter. While the standard Kalman filter and the extended Kalman filter have been widely applied to the state estimation of linear systems, the unscented Kalman filter has been reported the better choice in the multiclass traffic state estimation. In many applications of Kalman filters to traffic estimation problems, the model and measurement noise covariance matrices are normally estimated. When there is a mismatch between the true and the assumed noise distribution, however, the filter often suffers from performance degradation and even divergence in certain situations. To this end, this paper presents a more efficient and accurate algorithm embedded in the unscented Kalman filter to simultaneously estimate the traffic state and the model noise distribution statistics. The proposed method is facilitated through a simultaneous update of the model noise covariance matrix in the predicted covariance equations of the unscented Kalman filter algorithm. It is found through simulation that the proposed algorithm may improve the model performance over the standard algorithm.

Fast non-intrusive estimation of liquid-phase interface and boundary heat flux in participating media by the Kalman filtering methods

The stellar refraction navigation is a type of autonomous celestial navigation method for satellites that uses high-accuracy star sensors to obtain the stellar refraction. The apparent height and the stellar refraction angle are two kinds of measurements for the satellite stellar refraction navigation system. A better navigation performance can be achieved by the stellar refraction angle rather than the refraction apparent height. However, the measurement model of the stellar refraction angle is an implicit function, which needs an implicit filter method. A new implicit unscented Kalman filter (UKF) method is proposed and applied to the satellite stellar refraction navigation system in this paper. The main difference between the classical UKF and the implicit UKF lies in the measurement update. First, since the implicit measurement model can be rearranged into an equation whose one side is zero, the vector of zeros is regarded as the equivalent measurement, and the difference between the predicted measurement and its true value is utilized for updating the predicted state and its covariance matrix. Second, the measurement noise and its covariance matrix are transformed based on the unscented transformation principle. In addition, the implicit UKF is compared with the implicit extended Kalman filter (IEKF), the iterative IEKF, and the UKF. Simulations show that the proposed implicit UKF method can obtain about 19.0% and 17.5% improvements in three-dimensional root mean square position estimation compared to the IEKF and the iterative IEKF, respectively. Although the navigation performance of the UKF is close to the implicit UKFs, the computational time of the implicit UKF is much shorter than the UKFs. In addition, the sensitivities of the four different Kalman filters to the star sensor's faults and the atmosphere perturbation are compared, respectively.

Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems that produce these data, appropriate analysis tools are needed. The Kalman filter is a frequently used technique to infer, assuming a model of the system, the parameters of the model from uncertain observations. A well-known implementation of the Kalman filter, the unscented Kalman filter (UKF), was recently shown to be able to infer the connectivity of a set of coupled chaotic oscillators. In this work, we test whether the UKF can also reconstruct the connectivity of small groups of coupled neurons when their links are either electrical or chemical synapses. In particular, we consider Izhikevich neurons and aim to infer which neurons influence each other, considering simulated spike trains as the experimental observations used by the UKF. First, we verify that the UKF can recover the parameters of a single neuron, even when the parameters vary in time. Second, we analyze small neural ensembles and demonstrate that the UKF allows inferring the connectivity between the neurons, even for heterogeneous, directed, and temporally evolving networks. Our results show that time-dependent parameter and coupling estimation is possible in this nonlinearly coupled system.

Unscented Kalman Filter (UKF) has been proved to be a superior alternative to the extended Kalman filter (EKF) when solving the nonlinear system in recent years. In order to improve the real-time of the UKF, A new kind of UKF called Sequence UKF is proposed in this paper. Like Rao-Blackwellised Unscented Kalman Filter (RBUKF) [4], it also deals with nonlinear stochastic discrete-time system with linear measurement equation, however it can decrease the computational complexity with the same filtering accuracy. This algorithm reduces the measurement vector to scalars in measurement-update of UKF by sequence method, so it can avoid inversing the covariance of measurement and reduce a great mount of computation bound. Special algorithm is deduced in this paper. The high performance of sequence UKF is verified by using Monte Carlo simulations.

The prediction of the human motion plays an important role in the predictive motion controller of human-assisting mobile robot, and precise prediction requires a precise motion model. In this paper, a novel human motion prediction method is proposed. This prediction method is based on a hybrid motion model which combines the inverted pendulum model and constant velocity model. Derivations of the kinematics, especially the inverted pendulum model, are presented in this paper. Estimation of the prediction by inverted pendulum and constant velocity models based on the Unscented kalman filter(UKF) and Kalman filter(KF) respectively, are also given. The hybrid model precisely describes the walking cycle. Experiments verifying the effectiveness of the proposed model are also presented.

Requirements of highly precise pointing performance have been imposed on recently developed spacecrafts for a variety of missions. The stringent requirements have called on on-orbit estimation of spacecraft dynamics parameters and calibration of on-board sensors as indispensible practices. Consequently, on-orbit estimation of the mass moment of inertia of spacecraft has been a major issue mostly due to the changes by solar panel deployment and a large portion of fuel consumption (Creamer et al., 1996; Ahmed et al., 1998; Bordany et al., 2000; VanDyke et al., 2004; Myung et al., 2007; Myung & Bang, 2008; Sekhavat et al., 2009). As for measurement sensors, on-board calibration of alignment and bias errors of attitude and rate sensors is one of the main concerns of attitude sensor calibration researches (Pittelkau, 2001 & 2002, Lai et al., 2003). Pittelkau (2002) proposed an attitude estimator based on the Kalman filter (Kalman, 1960), in which spacecraft attitude quaternion, rate sensor misalignment and bias, and star tracker misalignments are taken into consideration as states, whereas the body rate is dealt as a synthesized signal by the estimates. Lai at al. (2003) derived a method for alignment estimation of attitude and rate sensors based on the unscented Kalman filter (UKF) (Julier and Uhlmann, 1997). Ma and Jiang (2005) presented spacecraft attitude estimation and calibration based only magnetometer measurements using an UKF. An interesting point is that we need predesigned 3-axis excitation manoeuvres of spacecraft for both dynamics parameter estimation and sensor calibration. Therefore, this study is motivated to merge above estimation and calibration processes into a single filtering problem. It is noteworthy that poor information of moments of inertia is to be treated as a system uncertainty while the rate sensor model errors are to be incorporated into the measurement process. As a filtering algorithm, this study employs a UKF. Extended Kalman filters (EKFs) have been successfully applied to the nonlinear attitude estimation problem (Crassidis et al., 2007). Hybrid estimation using the EKF has been reported by Myung at al. (2007). However, the EKF estimates using the first order linearization, which may lead to instability of the filter (ValDyke et al., 2004). The UKF approximates the nonlinear model to the second order by spreading points 1 sigma apart from the a priori mean. Performing nonlinear

The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

An iterative augmented unscented Kalman filter for simultaneous state-parameter-input estimation for systems with/without direct feedthrough