In the procedure of designing an underwater vehicle or robot, its maneuverability and controllability must be simulated and tested, before the product is finalized for manufacturing. Since the hydrodynamic forces and moments highly affect the dynamic and maneuverability of the system, they must be estimated with a reasonable accuracy. In this study, hydrodynamic coefficients of an autonomous underwater vehicle (AUV) are identified using velocity and displacement measurements, and implementing an **Extended** **Kalman** **Filter** (EKF) estimator. The hydrodynamic coefficients are included in the augmented state vector of a six DOF nonlinear model. The accuracy and the speed of the convergence of the algorithm are improved by selecting a proper covariance matrix using the ARMA process model. This algorithm is used to estimate the hydrodynamic coefficients of two different sample AUVs: NPS AUV II and ISIMI. The comparison of the outputs of the identified models and the outputs of the real simulated models confirms the accuracy of the identification algorithm. This identification method can be used as an efficient tool for evaluating the hydrodynamic coefficients of underwater vehicles (robots), using the experimental data obtained from the test runs.

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In this article, the conventional observer combined with the **Extended** **Kalman** **Filter** is presented. The accu- rate estimation of states is very essential to achieve better control and performance of the PMSM drives. Here the EKF is utilized for the precise estimation of the rotor speed and stator q-axis current. Since the drive speed and drive current are measured directly from the machine terminals contain noise, they are not precise for speed control. In the proposed approach, the speed and q-axis current are estimated accurately by introducing EKF al- gorithm theory. The estimated current acts as an input to the state observer while the estimated speed is compared with the reference speed. The proposed method yields a smooth and quick speed tracking, reduction in the dis- turbance applied to the system, and better control of the control signal variation. The overall system performance is greatly enhanced with the proposed method.

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acceptance, after a long period of time. The development of better estimator algorithms for nonlinear Systems has therefore attracted a great deal of interest in the scientific community, because the improvements will undoubtedly have great impact in a wide range of engineering fields. This paper deals with how to estimate a nonlinear model with **Extended** **Kalman** **filter** (EKF). The approach in this paper is to analyze **Extended** **Kalman** **filter** where EKF provides better probability of state estimation for a satellite determination in the space, based upon the value of readings of Magnetometer and Sun Sensor.

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in Section II. Then, the structure of the second-order fault-tolerant **extended** **Kalman** **filter** (second-order FTEKF) is derived in Section III. After that, Section IV presents special cases, which are the second-order fault-tolerant **extended** **Kalman** **filter** without estimator-gain uncertainties, and the second-order **extended** **Kalman** **filter**. Application to a benchmark problem involving reconstructing the trajectory of a target using the recorded range measurements is discussed in Section V. In this section, comparisons of the first-, second-order **extended** **Kalman** **filter** (EKF), and the second-order fault tolerant **extended** **Kalman** **filter** (FTEKF) nonlinear estimation are illustrated through computer simulation studies. Finally, conclusion is reached in Section VI.

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Well understanding the internal mechanisms connected with fault symptoms during battery fault process helps to establish a complete and accurate diagnosis system. In this paper, we focus on two fault modes which commonly occur during battery applications, especially during electric vehicle (EV) operation: (1) Dissolution of copper current collector due to over-discharge and (2) lithium plating at low temperature. First, we analyze the fault mechanisms for these faults to see what indeed happen inside the battery; then a serial of abusive experiments are carried out to extract external feature of related fault modes. Finally a fault diagnosis based on **extended** **Kalman** **filter** (EKF) and incremental capacity analysis (ICA) is achieved for fault diagnosis and isolation.

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The **Kalman** **Filter** is also known as Linear Quadratic Estimation (LQE). It is an algorithm which uses measurements data taken over time, containing noise i.e. random variations and other inaccuracies. It produces estimates of unknown variables that are more precise than the single measurement alone. It operates recursively on streams of noisy input data to produce a statistically optimal estimate of the underlying system state .The **Extended** **Kalman** **Filter** (EKF) is known as the nonlinear version of the **Kalman** **filter** which linearizes about an estimate of the current mean and covariance.

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In recent years there has been a growing concern by researchers in developing algorithm for face recognition. The proposed work addresses the problem of face recognition in still images using **Extended** **Kalman** **Filter** for machine learning. The algorithm comprises of designing a feature vector which has discrete wavelet coefficients of the face and, a coefficient representing parameters of the face. Global features of the face are captured by wavelet coefficients and the local feature of the face is captured by facial parameter. The coefficients of the feature vector are used as inputs to the recurrent neural network using EKF algorithm for training.. The proposed algorithm has been tested on various real images and its performance is found to be quite satisfactory when compared with the performance of conventional methods of face recognition such as the Eigen- face method.

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Wind speed is measured behind the rotor by an anemometer that provides inaccurate measurements of the wind impacting the rotor, making the estimation of wind speed necessary in modern wind turbine controllers. Wind speed estimation with **extended** **Kalman** **filter** (EKF) has been presented in [7] and with Luenberger nonlinear observer in [8]. These results are improved by using the EKF to estimate the wind field impacting on each blade individually. The model used in the EKF is a 3-D wind model which incorporates induced wind turbine unbalanced loads at the turbine rotational frequency, also called 1P. The incorporation of 1P loads allows the detection of various wind anomalies as well as turbine The Science of Making Torque from Wind (TORQUE 2016) IOP Publishing Journal of Physics: Conference Series 753 (2016) 052010 doi:10.1088/1742-6596/753/5/052010

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In this letter, we attempt a classification for the different types of drift, which we believe is a prerequisite for any further analysis. In the case of state dependent reversible drift we argue that the **Extended** **Kalman** **Filter** (EKF) constitutes a simple and efficient baseline approach for drift estimation in weakly stationary sensors. We discuss three possible implementations of EKF-based drift estimators in the case of weakly nonlinear sensors and compare their performance in simulation. Finally our approach is validated by estimating the drift in real accelerometer output data.

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To use KF with non linear system models it is necessary to first linearize the model about a nominal or auxiliary state trajectory to produce a linear perturbation model. The basic KF is used to estimate the perturbation states and then these are combined with the auxiliary states to produce the state estimates of the non linear model. When the auxiliary state is made equal to the most recent KF estimate the procedure is known as the **Extended** **Kalman** **Filter** (EKF). The EKF can be applied as a state estimator for non linear systems. It can carry out combined state and parameter estimation treating selected parameters as extra states and forming an augmented state vector. The result is that whether the original state space model was linear or not the augmented model will be non linear because of multiplication of states.

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In this paper, the self-sensing capability of SMA wire actuator has been harnessed using an **Extended** **Kalman** **Filter** based Artificial Neural Network. The effectiveness of the developed model (ANN-I) is demonstrated by comparing its response with that of another Artificial Neural Network model (ANN-II), trained based on experimental data. ANN- I concedes EKF estimated response; whereas ANN-II intakes experimentally measured inputs. Both ANN comprises same number of neurons and are trained using the same method. For the same training data, EKF based ANN model yields satisfactory performance in comparison to ANN based on experimental response, particularly at higher frequencies.

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The Discrete Time [9] **Extended** **Kalman** **Filter** (EKF) considers discrete-time dynamics and discrete-time measurements. This situation is often considered in practice. Even if the underlying system dynamics are continuous time, the EKF usually needs to be implemented in a digital computer. This means there might not be enough computational power to integrate the system dynamics as required in a continuous-time [9] EKF or a hybrid [9] EKF. So the dynamics are often discretized [9] and then discrete-time EKF can be used.

In mobile positioning, it is very important to estimate correctly the delay between the transmitter and the receiver. When the re- ceiver is in line-of-sight (LOS) condition with the transmitter, the computation of the mobile position in two dimensions becomes straightforward. In this paper, the problem of LOS detection in WCDMA for mobile positioning is considered, together with joint estimation of the delays and channel coeﬃcients. These are very challenging topics in multipath fading channels because LOS component is not always present, and when it is present, it might be severely aﬀected by interfering paths spaced at less than one chip distance (closely spaced paths). The **extended** **Kalman** **filter** (EKF) is used to estimate jointly the delays and complex channel coeﬃcients. The decision whether the LOS component is present or not is based on statistical tests to determine the distribution of the channel coeﬃcient corresponding to the first path. The statistical test-based techniques are practical, simple, and of low computation complexity, which is suitable for WCDMA receivers. These techniques can provide an accurate decision whether LOS component is present or not.

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In EKF, the actual value of Tdo in p.u is 0.13. observe ring from the estimated value is 0.44.The dynamic state of power system at the steady state value after applying the non-linear state estimator to get the steady state value is 0.43. It‟s to be get the system be stabilized. The figure is drawn between the D actual to the estimated value. The states are observed by the scope to be jointed to the **extended** **kalman** **filter**. The subsystem which consists of the SMIB to the **kalman** **filter**. The errors of D, J, Tq0, and Tdo can be observ

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Caius et. al [22] executed a project called Mobile Robot Position Estimation using **Kalman** **Filter**. This project presented the position estimation with the help of the **Kalman** **Filter** (KF) and the **Extended** **Kalman** **Filter** (EKF) for an autonomous mobile robot based on Ackermann steering. It focused on 2D model which was easier to implement while measurement by using overhead camera. The advantage of the proposed approach is two different method of **filter** that can be compared of the localisation accuracy between these two methods. The disadvantage of the approach is the position of robot is in unknown location that is difficult to know accurately the position of the robot. Figs. 2.11 and 2.12 show the trajectory estimation with the **Kalman** **Filter** and trajectory estimation with the **Extended** **Kalman** **Filter**.

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The following modified version of the EKF algorithm, termed the Discontinuous Extended Kalman Filter, DEKF , is now formulated for such systems: Let us assume that at a given time instan[r]

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Since decades, a great number of research works have been devoted to the problem of estimating the attitude of a spacecraft based on a sequence of noisy vector observations such as [2][3][4][5].Different algorithms have been designed and implemented in satellite attitude estimation problem. Early applications relied mostly on the **Kalman** **filter** for attitude estimation. **Kalman** **filter** was the first applied algorithm for attitude estimation for the Apollo space program in 1960s. Due to limitation of **Kalman** **filter** which work optimal for linear system only, several famous new approaches have been implemented to deal with the nonlinearity in satellite attitude system including **Extended** **Kalman** **Filter** (EKF) [6][7][4], Unscented **Kalman** **Filter** (UKF) [8][9][10], Particle **Filter** (PF)[11][12][13], and predictive filtering [14][15]. EKF is an **extended** version of **Kalman** **filter** for nonlinear system whereby the nonlinear equation is approximated by linearized equation through Taylor series expansion. UKF, an alternative to the EKF uses a deterministic sampling technique known as the unscented transform to pick a minimal set of sample points called sigma points to propagate the non-linear functions. EKF and UKF approaches is restricted assume the noise in the system is Gaussian white noise process. While, PF is a nonlinear estimation algorithm that approximates the nonlinear function using a set of random samples without restricted to a specific noise distribution as EKF and UKF. However, EKF was found as most widely used algorithm both in theory and in real practice by spacecraft community due to simplicity for implementation and theoretically attractive in the sense that it minimizes the variance of the estimation error.

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In this paper, a new filtering algorithm is proposed for system control of the sensorless BLDC motor based on the Ensemble **Kalman** **filter** (EnKF). The proposed EnKF algorithm is used to estimate the speed and rotor position of the BLDC motor only using the measurements of terminal voltages and three-phase currents. The speed estimation performance of developed EnKF was compared with the **Extended** **Kalman** **Filter** (EKF) under the same conditions. Results indicate that the proposed EnKF as an observer shows better performance than that of the EKF.

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Fuzzy Logic is based on the idea that in fuzzy sets each element in the set can assume a value from 0 to 1, not only 0 or 1, as in crisp set theory. The degree of membership function is defined as the gradation in the extent to which an element is belonging to the relevant sets. Optimizing the membership functions of a fuzzy system can be viewed as a system identification problem for nonlinear dynamic system. In this paper two input and one output fuzzy controller is designed for the dynamic process of aircraft. The addition of an EKF in the feedback loop improved the system response by blocking possible effects of measurement error based on Predictor- Corrector algorithm. An **Extended** **Kalman** **Filter** approach to optimize the membership functions of the inputs and outputs of the fuzzy controller. The performance of the fuzzy system before and after the optimization are compared, as well as the membership functions.

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