Non-holonomic **leader**-**follower** **robot** must be capable to find its own position in order to be able to navigate autonomously in the environment this problem is known as **localization**. A common way to estimate the **robot** pose by **using** odometer. However, odometry measurement may cause inaccurate result due to the wheel slippage or other small noise sources. In this research, the **Extended** **Kalman** **Filter** (EKF) is proposed to minimize the error or the inaccuracy caused by the odometry measurement. The EKF algorithm works by fusing odometry and landmark information to produce a better estimation. A better estimation acknowledged whenever the estimated position lies close to the actual path, which represents a system without noise. Another experiment is conducted to observe the influence of numbers of landmark to the estimated position. The results show that the EKF technique is effective to estimate the **leader** pose and orientation pose with small error and the **follower** has the ability traverse close to **leader** based-on the actual path.

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Abstract. The non-invasive and radiation-free imaging of the electrical activity of the heart with Electrocardiogra- phy (ECG) or Magnetocardiography (MCG) can be help- ful for physicians for instance in the **localization** of the ori- gin of cardiac arrhythmia. In this paper we compare two **Kalman** **Filter** algorithms for the solution of a nonlinear state-space model and for the subsequent imaging of the activation/depolarization times of the heart muscle: the Ex- tended **Kalman** **Filter** (EKF) and the Unscented **Kalman** Fil- ter (UKF). The algorithms are compared for simulations of a (6 × 6) magnetometer array, a torso model with piecewise homogeneous conductivities, 946 current dipoles located in a small part of the heart (apex), and several noise levels. It is found that for all tested noise levels the convergence of the activation times is faster for the UKF.

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Extensions to visual odometry are SLAM (Simultaneous **localization** and mapping) and PTAM (Parallel tracking and mapping) [JTD14]. SLAM and PTAM use visual odometry techniques to calculate the relative motion but at the same time also maps the environment simultaneously (or parallel). The additional information the map provides can then be used to help with the drift. The map also helps the system to be able to recover fast when it loses track of its pose, for example when movement between two frames is large enough that little to no features of the previous frame are visible in the new frame. If the new frame does contain features which are already mapped before, it should be able to recover relatively fast. It should be noted that during the map generation drift is still present.

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Mobile **robot** navigation is one of the fascinating research which supports a truly autonomous mobile **robot** behavior. It is one of the aspects that really means in nowadays applications especially when a **robot** needs to perform a task to replace human operation. **Robot** has been known to functionally works in explorations, underwater navigation, mining and military by performing different kind of tasks. Depends on the applications, the mobile **robot** may require several conditions to be satisfied about its design and specifications. In navigation, one of its challenges is known as Simultaneous **Localization** and Mapping problem where mobile **robot** has to identify its location with reference to any of landmarks being observed and at the same time building a map based on its observations. This problem addressed several issues to be solved such as operating in dynamic environment, computational cost, uncertainties and data association [1]-[2].

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[21] used EKF SLAM and Fast SLAM to introduce a probabilistic approach to a SLAM problem under Gaussian and non Gaussian conditions. They presented the navigation of an autonomous **robot** **using** Simultaneous **Localization** and Mapping (SLAM) in outdoor environments. Fast SLAM is an algorithm that used Rao- Blackwellised method for particle filtering, estimated the path of **robot** while the landmarks positions which were mutually independent and with no correlation, can be estimated by EKF. Hence, a real outdoor autonomous **robot** was presented and several experiments had been performed based on both methods. The disadvantages were no correlation between any pairs of landmarks in the map, while landmarks in this network were mutually independent. Figs. 2.9 and 2.10 show vehicle coordinate system and estimation of the trajectory **using** EKF with Gaussian implication.

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Abstract. **Localization** via Radio Frequency Identification (RFID) is frequently used in different applications nowadays. It has the advantage that next to its ostensible purpose of identifying objects via their unique IDs it can simultaneously be used for the **localization** of these objects. In this work it is shown how Received Signal Strength Indicator (RSSI) mea- surements at different antennae of a passive UHF RFID label can be combined for **localization**. The **localization** is only done based on the RSSI measurements and a **Kalman** **Filter** (KF). Because of non-linearities in the measurement func- tion it is necessary to incorporate an **Extended** **Kalman** **Filter** (EKF) or an Unscented **Kalman** **Filter** (UKF) where simula- tions have shown that the UKF performs better than the EKF. Additionally to the selection of the **filter** there are different possibilities to increase the **localization** accuracy of the UKF: The advantages of **using** Reference Tags (RT) or more than one tag per trolley (relative positioning) in combination with an Unscented **Kalman** **Filter** are discussed and simulations results show that the **localization** error can be decreased sig- nificantly via these methods. Another possibility to increase the **localization** accuracy and in addition to achieve a more realistic simulation is the consideration of the angle between reader antenna and tag. Simulation results with the incor- poration of different numbers of fixed antennae lead to the conclusion that this is a useful surplus in the **localization**.

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In the three-node triangulation system, three angles are often measured between the **robot** heading and the direc- tions to the nodes. These angles are coupled with the **robot** plane coordinates and heading by nonlinear equations. The equations can be solved for unknown **robot** coordinates and heading. However, accuracy is commonly insufficient in noisy environments and optimal estimators are re- quired. The estimation theory offers several useful meth- ods to solve the triangulation problem. One of the most common approaches is the **extended** **Kalman** **filter** (EKF) proposed by Cox [14] and others. It suggests expanding the nonlinear functions to the first-order Taylor series and then **using** linear **Kalman** filtering. The EKF was used in tracking and robotics extensively [1–3,15,16] and has become a tool for moving vehicular navigation, tracking, **localization**, and self-**localization** [17,18]. The benefit of the EKF resides in the following facts:

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The proposed idea shows that automatically obtained person density estimates can be used to improve person **localization** and tracking performance in crowded scenes. It has formulated the person detection task as a minimization of a joint energy function incorporating scores of individual detections, pair-wise non-overlap constraints, and constraints imposed by the estimated person density over the scene, and also have demonstrated significant gains in detection and tracking performance on challenging videos of frames with varying density. Currently, video frames are processed individually and obtained detections are tracked in post-processing. There are hundreds of cameras deployed in public places (eg. Streets, shopping malls, airports). However, only a small fraction of the cameras outputs (<5%) is regularly observed by humans. Most of the video information is stored or destroyed without being watched or processed. This means that current surveillance systems are not able to detect abnormal events in real time. A large effort has been recently done to develop algorithms to track objects ( persons, vehicles) in video sequences and to recognize activities and unusual behaviours. In the future work the gradient based algorithm is used for activity based tracking which is more efficient than the other methods. In addition to this work a accuracy of the tracking can be calculated by **using** precision and recall factor.

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This paper presents a study for the effect of several **filter** approaches in the behavior of **robot** localizer **using** radio beacons that provide the ability to measure range only. Different filters namely **Extended** **Kalman** **Filter** (EKF), Particle **Filter** (PF) and a proposed Enhanced Particle/**Kalman** **Filter** (EPKF) are implemented in Matlab environment and their behavior are evaluated. The Enhanced Particle/ **Kalman** **Filter** (EPKF) provide the required initial location while there is no significant change in the computational cost compared with **Extended** **Kalman** **Filter** (EKF). Moreover in some data sets, the performance of the proposed **filter** approach is superior in terms of **localization** errors.

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Mrinal Kanti Bhowmik et. al. [16] performed a comparative study on fusion of visual and thermal images **using** different wavelet transformations like Haar and Daubechies (db2). They found wavelet a useful transformation for face recognition. Boqing Gong et. al. [17] proposed a method based on extracting facial features for 3-D faces. They emphasized on two components one for corresponding basic face structure and another corresponding expression change in the face based on the change in shape of 3D face. N. Sudha et al. [18] proposed an efficient self-configurable systolic architecture for very large scale integration implementation of a face recognition system. The proposed system applied principal component neural network (PCNN) with generalized Hebbian learning for extracting eigenfaces from the face database . Further Wonjun Hwang et al. [19] proposed a method which has two stages. First, in the preprocessing stage, a face image was transformed into an illumination-(insensitive image, called an “integral normalized gradient image,” by normalizing and integrating the smoothed gradients of a facial image. The hybrid Fourier features were extracted from different Fourier domains in different frequency bandwidths and then each feature was individually classified by linear discriminant analysis. Further Arindam Biswas et. al. [20] proposed a novel algorithm for extracting the region of interest of a face like eye pair, nostrils, and mouth area. Bart Karoon et. al. [21] addressed the influence of eye **localization** accuracy on face matching performance in

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The rms errors of the analysis from the optimal interpo- lation, the reduced-rank **extended** **Kalman** **filter** and the en- semble **Kalman** **filter** for the high viscosity case are shown in Fig. 13. All filtering techniques are able to significantly reduce the analysis error relative to the run without data as- similation. The forecast error from the unconstrained model run exhibits a striking quasi-periodic behavior with a period of approximately 9 years. The analysis error from the opti- mal interpolation exhibits similar behavior but with a smaller amplitude. The quasi-periodic behavior severely diminishes after the reduced-rank **extended** **Kalman** filtering is applied and it is nearly invisible in the rms errors of the analysis from the ensemble **Kalman** **filter**. The errors of the analysis from the optimal interpolation, the reduced-rank **extended** **Kalman** **filter** and the ensemble **Kalman** **filter** decrease dramatically during the first two years. After two years, the analysis error of the optimal interpolation is on average 30% of the fore- cast error when no data are assimilated; the analysis error of the reduced-rank **extended** **Kalman** **filter** is on average 10% of the forecast error without data assimilation; and the anal- ysis error of the ensemble **Kalman** **filter** is on average 6% of the forecast error without data assimilation. For the high vis-

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In this paper, the simulation model is a ten degree-of-freedom of a full-vehicle model that includes vertical suspension dynamics, roll, yaw and pitch motion. **Using** the vehicle speed, yaw rate, longitudinal and lateral accelerations of the vehicle at c.g. As the measurement vectors, the steering angle, and the braking as input control, the vehicle state histories and tire forces variables were estimated. The vehicle parameters for the Carsim and simulation are given in Table 1. **Using** equation (16), the observability matrixwas invertible at the current state and input as its Jacobian matrix has a full rank, hence the system was observable. Then, the estimated results were compared with the obtained responses from the Carsim. Figures 3 - 7 show the comparison of the results obtained from the Carsim and the estimated values **using** an EKF algorithm.

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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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In above equations, 𝛥𝑡 represents the length of the sampling interval. Obviously, the smaller 𝛥𝑡 is better the Euler approximation is; otherwise this requires a fast microprocessor system for the on-line implementation of the **filter**. The employment of a stochastic approach overcomes in part these difficulties, because it intrinsically takes into account the model mismatching and therefore a not very small length 𝛥𝑡 can be chosen.

Accurate indoor **localization** often depends on infrastructure support for distance estimation in rangebased techniques. One can also trade off accuracy to reduce infrastructure investment by **using** relative positions of other nodes, as in rangefree **localization**. Even for rangebased meth ods where accurate UltraWideBand (UWB) signals are used, non lineofsight (NLOS) conditions pose significant difficulty in accurate indoor **localization**. Existing solutions rely on additional measurements from sensors and typically correct the noise **using** a **Kalman** **filter** (KF). Solutions can also be customized to specific environments through extensive profiling. In this work, a range based indoor **localization** algorithm called PSO **Kalman** **Filter** Fusion (PKFF) is proposed that minimizes the effects of NLOS on **localization** error without **using** additional sensors or profiling. Location estimates from a windowed Particle Swarm Optimization (PSO) and a dynamically ad justed KF are fused based on a weighted variance factor. PKFF achieved a 40 % lower 90percentile rootmeansquare **localization** error (RMSE) over the standard least squares trilateration algorithm at 61 cm compared to 102 cm.

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In the presence of non-linear functions the predicted states are approximated as the function of prior mean. The covariance are determined by linearizing the dynamic equations , and then the posterior covariance matrices are determined analytically for the linear system in EKF approach. In case of the EKF, a GRV is determined approximating the state distribution and then this GRV is propagated analytically through the ``first-order'' linearization of the nonlinear system. In this case the EKF can be credited with providing ``first-order'' approximations to the optimal terms such as optimal prediction, optimal gain. But these approximations, are not helpful always. Where the non- linearity value is more it can even introduce large errors in the true posterior mean as well as in the covariance of the transformed (Gaussian) random variable. This is not being an healthy approach to linearization might lead to sub-optimal performance and sometimes divergence (instability) of the **filter**. It is these ``flaws'' which will be amended in the next section **using** the UKF. [24]

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[9] F. Benchabane, A. Titaouine, O. Bennis, K. Yahia and D. Taibi, “Systematic Fuzzy Sliding Mode Approach with **Extended** **Kalman** **Filter** for Permanent-Magnet Synchr nous Motor,” Proceedin f the IEEE international co ference on Systems Ma d Cybernetics (SMC), 2010

In this study, the estimation power of **Extended** **Kalman** **Filter** is tested within a simple Keynesian macroeconomic model. After the model is written in a non-linear state space form, **Extended** **Kalman** **Filter** emerges as the appropriate methodology to estimate both state variables and the parameters. The simulation results suggest that such a methodology can also be employed in explaining more complex macroeconomic dynamics.

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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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