In this thesis, development of a control system is aimed for a 1 DOF haptic device, namely Haptic Box. Besides, it is also constructed. Haptic devices are the manipulators that reflect the interaction forces with virtual or remote environments to its users. In order to reflect stiffness, damping and inertial forces on a haptic device position, velocity and acceleration measurements are required. The only motion sensor in the system is an incremental optical encoder attached to the back of the DC motor. The encoder is a good position sensor but velocity and acceleration estimations from discrete position and time data is a challenging work. To estimate velocity and acceleration some methods in the literature are employed on the Haptic Box and it is concluded that Kalman filtering gives the best results. After the velocity and acceleration estimations are acquired haptic control algorithms are tried experimentally. Finally, a virtual environment application is presented.

In this thesis, a new guidance method for fighter aircrafts and a new guidance method for missiles are developed. Also, guidance and control systems of the aircraft and the missile used are designed to simulate the generic engagement scenarios between the missile and the aircraft. Suggested methods have been tested under excessive simulation studies. The aircraft guidance method developed here is a rule based missile evasion method. The main idea to develop this method stems from the maximization of the miss distance for an engagement scenario between a missile and an aircraft. To do this, an optimal control problem with state and input dependent inequality constraints is solved and the solution method is applied on different problems that represent generic scenarios. Then, the solutions of the optimal control problems are used to extract rules. Finally, a method that uses the interpolation of the extracted rules is given to guide the aircraft. The new guidance method developed for missiles is formulated by modifying the classical proportional navigation guidance method using the position estimates. The position estimation is obtained by utilization of a Kalman based filtering method, called interacting multiple models.

For an autonomous mobile robot, localization and map building are vital capabilities. The localization ability provides the robot location information, so the robot can navigate in the environment. On the other hand, the robot can interact with its environment using a model of the environment (map information) which is provided by map building mechanism. These two capabilities depends on each other and simultaneous operation of them is called SLAM (Simultaneous Localization and Map Building). While various sensors are used for this algorithm, vision-based approaches are relatively new and have attracted more interest in recent years. In this thesis work, a versatile Visual SLAM system is constructed and presented. In the core of this work is a vision-based simultaneous localization and map building algorithm which uses point features in the environment as visual landmarks and Extended Kalman Filter for state estimation. A detailed analysis of this algorithm is made including state estimation, feature extraction and data association steps. The algorithm is extended to be used for both stereo and single camera systems. The core of both algorithms is same and we mention the differences of both algorithms originated from the measurement dissimilarity. The algorithm is run also in different motion modes, namely predefined, manual and autonomous. Secondly, a map management strategy is developed especially for extended environments. When the robot runs the SLAM algorithm in large environments, the constructed map contains a great number of landmarks obviously. The efficiency algorithm takes part, when the total number of features exceeds a critical value for the system. In this case, the current map is rarefied without losing the geometrical distribution of the landmarks. Furthermore, a well-organized graphical user interface is implemented which enables the operator to select operational modes, change various parameters of the main SLAM algorithm and see the results of the SLAM operation both textually and graphically. Finally, a basic mission concept is defined in our system, in order to illustrate what robot can do using the outputs of the SLAM algorithm. All of these ideas mentioned are implemented in this thesis, experiments are conducted using a real robot and the analysis results are discussed by comparing the algorithm outputs with ground-truth measurements.

Heart is a vital organ that pumps blood to whole body. Synchronous contraction of the heart muscles assures that the required blood flow is supplied to organs. But sometimes the synchrony between those muscles is distorted, which results in reduced cardiac output that might lead to severe diseases, and even death. The most common of heart diseases are myocardial infarction and arrhythmias. The contraction of heart muscles is controlled by the electrical activity of the heart, therefore determination of that electrical activity could give us the information regarding the severeness and type of the disease. In order to diagnose heart diseases, classical 12 lead electrocardiogram (ECG) is the standard clinical tool. Although many cardiac diseases could be diagnosed with the 12 lead ECG, measurements from sparse electrode locations limit the interpretations. The main objective of this thesis is to determine the cardiac electrical activity from dense body surface measurements. This problem is called the inverse problem of electrocardiography. The high resolution maps of epicardial potentials could supply the physician the information that could not be obtained with any other method. But the calculation of those epicardial potentials are not easy / the problem is severely ill-posed due to the discretization and attenuation within the thorax. To overcome this ill-posedness, the solution should be constrained using prior information on the epicardial potential distributions. In this thesis, spatial and spatio-temporal Bayesian maximum a posteriori estimation (MAP), Tikhonov regularization and Kalman filter and Kalman smoother approaches are used to overcome the ill-posedness that is associated with the inverse problem of ECG. As part of the Kalman filter approach, the state transition matrix (STM) that determines the evolution of epicardial potentials over time is also estimated, both from the true epicardial potentials and previous estimates of the epicardial potentials. An activation time based approach was developed to overcome the computational complexity of the STM estimation problem. Another objective of this thesis is to study the effects of geometric errors to the solutions, and modify the inverse solution algorithms to minimize these effects. Geometric errors are simulated by changing the size and the location of the heart in the mathematical torso model. These errors are modeled as additive Gaussian noise in the inverse problem formulation. Residual-based and expectation maximization methods are implemented to estimate the measurement and process noise variances, as well as the geometric noise.

In this thesis, the passive localization problem is studied. Robust and recursive solutions are presented by the use of Time Difference of Arrival (TDOA). The TDOA measurements are assumed to be gathered by moving sensors which makes the number of the sensors increase synthetically. First of all, a location estimator should be capable of processing the new measurements without omitting the past data. This task can be accomplished by updating the estimate recursively whenever new measurements are available. Convenient forms of the recursive filters, such as the Kalman filter, the Extended Kalman filter etc., can be applied. Recursive filter can be divided to two major groups: (a) The first type of recursive estimators process the TDOA measurements directly, and (b) the second type of the recursive estimators is the post processing estimators which process the TDOA indirectly, instead they fuse or smooth available location estimates. In this sense, recursive passive localization methods are presented for both types. In practice, issues like being spatially distant from each other and/or a radar with a rotating narrow beam may prevent the sensors to receive the same pulse. In such a case, the sensors can not construct common TDOA measurements which means that they can not accomplish the location estimation procedure. Additionally, there may be more than one sensor group making TDOA measurements. An estimator should be capable of fusing the measurements from different sensor groups. A sensor group consists of sensors which are able to receive the same pulse. In this work, solutions of these tasks are also given. Performances of the presented methods are compared by simulation studies. The method having the best performance, which is based on the Kalman Filter, is also capable of estimating the track of a moving emitter by directly processing the TDOA measurements.

The focus of the present thesis is on the joint use of cameras and inertial sensors, a recent area of active research. Within our scope, the performance of body state estimation is investigated with isolated inertial sensors, isolated cameras and finally with a fusion of two types of sensors within a Kalman Filtering framework. The study consists of both simulation and real hardware experiments. The body state estimation problem is restricted to a single axis rotation where we estimate turn angle and turn rate. This experimental setup provides a simple but effective means of assessing the benefits of the fusion process. Additionally, a sensitivity analysis is carried out in our simulation experiments to explore the sensitivity of the estimation performance to varying levels of calibration errors. It is shown by experiments that state estimation is more robust to calibration errors when the sensors are used jointly. For the fusion of sensors, the Indirect Kalman Filter is considered as well as the Direct Form Kalman Filter. This comparative study allows us to assess the contribution of an accurate system dynamical model to the final state estimates. Our simulation and real hardware experiments effectively show that the fusion of the sensors eliminate the unbounded error growth characteristic of inertial sensors while final state estimation outperforms the use of cameras alone. Overall we can v demonstrate that the Kalman based fusion result in bounded error, high performance estimation of body state. The results are promising and suggest that these benefits can be extended to body state estimation for multiple degrees of freedom.

The basic problem with angle-only or bearings-only tracking is to estimate the trajectory of a target (i.e., position and velocity) by using noise corrupted sensor angle data. In this thesis, the tracking platform is an Aerial Vehicle and the target is simulated as another Aerial Vehicle. Therefore, the problem can be defined as a single-sensor bearings only tracking. The state consists of relative position and velocity between the target and the platform. In the case where both the target and the platform travel at constant velocity, the angle measurements do not provide any information about the range between the target and the platform. The platform has to maneuver to be able to estimate the range of the target. Two problems are investigated and tested on simulated data. The first problem is tracking non-maneuvering targets. Extended Kalman Filter (EKF), Range Parameterized Kalman Filter and particle filter are implemented in order to track non-maneuvering targets. As the second problem, tracking maneuvering targets are investigated. An interacting multiple model (IMM) filter and different particle filter solutions are designed for this purpose. Kalman filter covariance matrix initialization and regularization step of the regularized particle filter are discussed in detail.

The trajectories of ballistic targets are determined significantly by the characteristics that are specific to them. In this thesis, these characteristics are presented and a set of algorithms in order to track short-range ballistic targets are given. Firstly, motion and measurement models for the ballistic targets are formed and then four different filtering techniques are built on these models which are the extended Kalman filter, the unscented Kalman filter, the particle filter and the marginalized particle filter. The performances of these filters are evaluated by making Monte Carlo simulation. The simulations are run using target scenarios obtained according to six degrees-of-freedom trajectory for ballistic targets. Apart from the tracking errors of the filters, drag parameter estimations and the effect of drift calculation on the filter performances are investigated. The estimation results obtained by each filter are discussed in detail by making various simulations.

Orthogonal Frequency Division Multiplexing (OFDM) techniques have been used in many wireless communication systems to improve the system capacity and achieve high data-rate. It possesses good spectral efficiency and robustness against interferences. The OFDM system has been adopted in many communication standards, such as the 802.11a/g standards for the high-speed WLAN, HIPERLAN2, and IEEE 802.16 standard, and meanwhile, it is also employed in the European DAB and DVB systems. To avoid the inter-block interference (IBI), usually, in the transmitter of OFDM systems the redundancy with sufficient length is introduced, it allows us to overcome the IBI problem, due to highly dispersive channel. Many redundancy insertion methods have been proposed in the literatures, there are cyclic prefix (CP), zero padding (ZP) and the pseudorandom postfix (PRP). Under such system we have still to know the correct channel state information for equalizing the noisy block signal. Especially, in time-varying channel, the incorrect channel state information may introduce serious inter-symbol interference (ISI), if the channel estimation could not perform correctly. In this thesis, the PRP-OFDM system is considered. According to the PRP-OFDM scheme, the redundancy with pseudorandom postfix (PRP) approach is employed to make semi-blind channel estimation with order-one statistics of the received signal. But these statistic characteristics may not be available under time-varying channel. Hence, in this thesis, we propose a modified PRP-OFDM system with assistant training sequences, which is equipped with minimum mean-square-error equalizer and utilize Kalman filter algorithm to implement time-varying channel estimation. To do so, we first model time-varying channel estimation problem with a dynamic system, and adopt the Kalman filter algorithm to estimate the true channel coefficients. Unfortunately, since most parameters in dynamic system are random and could not to be known in advance. We need to apply effective estimation schemes to estimate the statistics of true parameters for implementing the Kalman filter algorithm. When the channel state information is known, MMSE equalizer follows to suppress the inter-symbol interference (ISI). Moreover, after making decision the binary data can be used to re-modulate PRP-OFDM symbol and to be re-used in Kalman filter to obtain more accurate CSI to improve the effectiveness of the equalizer. Via computer simulations, we verify that desired performance in terms of bit error rate (BER), can be achieved compared with the CP-OFDM systems.

Orbit of a spacecraft in three dimensional Inertial Reference Frame is in general represented by a standard set of six parameters like Keplerian Orbital Elements namely semimajor axis, eccentricity, inclination, argument of perigee, right ascension of ascending node, and true anomaly. An orbit can also be represented by an equivalent set of six parameters namely the position and velocity vectors, hereafter referred as orbit-vectors. The process of determining the six orbital parameters from redundant set of observations (more than the required minimum observations) is known as Orbit Determination (OD) process. This is, in general, solved using Least Squares principle. Availability of accurate, almost continuous, space borne observations provide tremendous scope for simplifications and new directions in Autonomous OD (AOD). The objective of this thesis is to develop a suitable scheme for onboard autonomy in OD, specifically for low-earth-orbit-missions that are in high demand in the immediate future. The focus is on adopting a simple orbit model by a thorough study and analysis by considering the individual contributions from the different force models or component accelerations acting on the spacecraft. Second step in this work is to address the application of an onboard estimation scheme like Kalman Filter for onboard processing. The impact of the approximation made in the orbit model for filter implementation manifests as propagation error or estimation residuals in the estimation. The normal procedure of tuning the filter is by getting an appropriate state and measurement noise covariance matrices by some means, sometimes through trial and error basis. Since this tuning is laborious and the performance may vary with different contexts, it is attempted to propose a scheme on a more general footing, with dynamically compensating for the model simplification. There are three parts of this problem namely (i) Analysis of different Orbit Dynamics Models and selection of a simplified Onboard Model (ii) Design of an Estimator Filter based on Kalman Filter approach for Onboard Applications and (iii) Development of a suitable Filter Compensation procedure to ensure best estimates of orbit vectors even with the simplified orbit model. Development of a Numerical Integration scheme (and a software tool) and extensive simulation exercises to justify the conclusion on the simple model to be used in the estimation procedure forms the first part of the thesis. Tables quantify the effect of individual accelerations and demonstrate the effects of various model components on orbit propagation. In general, it is well known that the atmospheric drag is a non-conservative force and reduces energy; it is also known that the effect of first zonal harmonic term is predominant than any other gravity parameters; such anticipated trends in the accuracies are obtained. This particular exercise is carried out for orbits of different altitudes and different inclinations. The analysis facilitates conclusions on a limited model orbit dynamics suitable for onboard OD. Procedures and results of this model selection analysis is published in Journal of Spacecraft Technology, Vol. 16, No.1,pp 8-30, Jan 2006, titled “Orbit Model Studies for Onboard Orbit Estimation” [69]. Design of Estimator based on Kalman Filter There are two steps involved in dealing with the next part of the defined work: • Design and implementation of Extended Kalman Filter Estimation (EKF) scheme • Steps to compensate for approximation made in the reduced orbit dynamics The GPS receivers on board some of the IRS satellites (for example, the Resource-Sat-1), output the GPS Navigation Solutions (GPSNS) namely the position and velocity vectors of the IRS satellite along with the Pseudo-range measurements. These are recorded onboard for about two orbits duration, and are down loaded. An Extended Kalman Filter Algorithm for the estimation of the orbit vectors using these GPSNS observations is developed. Estimation is carried out assuming a Gaussian white noise models for the state and observation noises. The results show a strong dependence on the initial covariance of the noise involved; reconstruction of the observations results only if the assumption of realistic noise characteristics (which are unknown) is strictly adhered. Hence this simple non-adaptive EKF is found inadequate for onboard OD scheme. Development of the Dynamics Filter Compensation (DFC) Scheme In next part of the thesis, the problem of dealing with the un-modeled accelerations has been addressed. A suitable model-compensation scheme that was first developed by D.S Ingram el at [60] and successfully applied to Lunar missions, has been modified suitably to treat the problem posed by the reduced orbit dynamics. Here, the un-modeled accelerations are approximated by the OU stochastic process described as the solution of the Langavin stochastic differential equation. A filter scheme is designed where the coefficients of the un- modeled acceleration components are also estimated along with the system state yielding a better solution. Further augmentation to the filter include a standard Adaptive Measurement Noise covariance update; results are substantiated with actual data of IRS-P6 (Resource–Sat 1, see chapter 4). Classified as the Structured Adaptive Filtering Scheme, this results in a Dynamic Filter Compensation(DFC) Scheme which provides distinctly improved results in the position of the state. First, the estimation is carried out using actual GPS Navigation Solutions as observations. What is to be estimated itself is observed; the State-Observation relation is simple. The results are seen to improve the orbit position five times; bringing down the position error from 40 meters to about 8 meters. However, this scheme superimposes an extra factor of noise in the velocity vector of the GPSNS solutions. It is noted that this scheme deals only with the process noise covariance. To tackle the noise introduced in the velocity components, modifications of the original scheme by introducing an adaptive measurement noise covariance update is done. This improves the position estimate further by about 2 meters and also removes the noise introduced in the velocity components and reconstructs the orbit velocity vector output of the GPSNS. The results are confirmed using one more set of actual data corresponding to a different date. This scheme is shown to be useful for obtaining continuous output –without data gaps- of the GPSNS output. Next, the estimation is carried out taking the actual GPS observations which are the Pseudo Range, Range rate measurements from the visible GPS satellites (visible to the GPS receiver onboard ). Switching over to the required formulation for this situation in the state-measurement relation profile, estimation is carried out. The results are confirmed in this case also. Clear graphs of comparisons with definitive orbital states (considered as actual) versus estimated states show that the model reduction attempted at the first part has been successfully tackled in this method. In this era of space-borne GPS observations, where frequent sampling of the orbiting body is suggestive of reduced orbit models, an attempt for replacement of the conventional treatment of expensive and elaborate OD procedure is proved feasible in this thesis work.