For the environment of target tracking with highly non-linear models and non-Gaussian noise, the tracking performance of the particle filter is better than extended Kalman filter; in addition, the design of particle filter is simpler, so it is quite suitable for the realistic environment. However, particle filter depends on the probability model of the noise. If the knowledge of the noise is incorrect, the tracking performance of the particle filter will degrade severely. To tackle the problem, cost function-based particle filters have been studied. Though suffering from minor degradation on the performance, the cost function-based particle filters do not need probability assumptions of the noises. The application of cost function-based particle filters will be more robust in any realistic environment. Cost function-based particle filters will enable maneuvering multiple target tracking to be suitable for any environment because it does not depend on the noise model. The difficulty lies in the link between the estimator and data association. The likelihood function are generally obtained from the algorithm of the data association; while cost functions are used in the cost function-based particle filter for moving the particles and update the corresponding weights without probability assumptions on the noises. The thesis is focused on the combination of data association and cost function-based particle filter, in order to make the algorithm of multiple target tracking more robust in noisy environments.

The use of visual sensors in providing the necessary information for the autonomous guidance and navigation of the unmanned-air vehicles (UAV) or micro-air vehicles (MAV) applications is inspired by biological systems and is motivated first of all by the reduction of the navigational sensor cost. Also, visual sensors can be more advantageous in military operations since they are difficult to detect. However, the design of a reliable guidance, navigation and control system for aerial vehicles based only on visual information has many unsolved problems, ranging from hardware/software development to pure control-theoretical issues, which are even more complicated when applied to the tracking of maneuvering unknown targets. This dissertation describes guidance law design and implementation algorithms for autonomous tracking of a flying target, when the information about the target's current position is obtained via a monocular camera mounted on the tracking UAV (follower). The visual information is related to the target's relative position in the follower's body frame via the target's apparent size, which is assumed to be constant, but otherwise unknown to the follower. The formulation of the relative dynamics in the inertial frame requires the knowledge of the follower's orientation angles, which are assumed to be known. No information is assumed to be available about the target's dynamics. The follower's objective is to maintain a desired relative position irrespective of the target's motion. Two types of guidance laws are designed and implemented in the dissertation. The first one is a smooth guidance law that guarantees asymptotic tracking of a target, the velocity of which is viewed as a time-varying disturbance, the change in magnitude of which has a bounded integral. The second one is a smooth approximation of a discontinuous guidance law that guarantees bounded tracking with adjustable bounds when the target's acceleration is viewed as a bounded but otherwise unknown time-varying disturbance. In both cases, in order to meet the objective, an intelligent excitation signal is added to the reference commands. These guidance laws are modified to accommodate measurement noise, which is inherently available when using visual sensors and image processing algorithms associated with them. They are implemented on a full scale non-linear aircraft model using conventional block backstepping technique augmented with a neural network for approximation of modeling uncertainties and atmospheric turbulence resulting from the closed-coupled flight of two aerial vehicles. / Ph. D.

Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection.

This thesis addresses several aerospace guidance and decision making problems using both no cooperative and cooperative game theoretical solution concepts in the differential games framework. In the first part of the thesis, state dependent Riccati equation (SDRE) method has been extended to a zero-sum nonlinear differential games setting. This framework is used to study problems of intercepting a manoeuvring target, with and without terminal impact angle constraints, in the zero-sum differential games theory perspective. The guidance laws derived according to the proposed method are in closed from and online implementable. In the second part of the thesis, cooperative game theoretic concepts are applied to make a group of unmanned aerial vehicles (UAV) achieve rendezvous, in a given finite time horizon. An algorithm has been proposed that enables the UAVs to realize Nash bargaining solution. In this context, criteria for time consistency of a cooperative solution of nonzero-sum linear quadratic differential games have been studied. The problems where the UAVs try to achieve rendezvous by implementing cooperative game theoretic strategies, based on local information structure only, is also addressed.

Multitarget tracking in the presence of false alarm is a difficult problem to consider. The objective of multitarget tracking is to estimate the number of targets and their states recursively from available observations. At any given time, targets can be born, die and spawn from already existing targets. Sensors can detect these targets with a defined threshold, where normally the observation is influenced by false alarm. Also if the targets are with low signal to noise ratio (SNR) then the targets may not be detected. The Random Finite Set (RFS) filters can be used to solve such multitarget problem efficiently. Specially, one of the best and most widely used RFS based filter is the Probability Hypothesis Density (PHD) filter. The PHD filter approximates the posterior probability density function (PDF) by the first order moment only, where the targets SNR assumed to be much higher. The PHD filter supports targets die, born, spawn and missed-detection by using the well known implementations including Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) and Gaussian Mixture Probability Hypothesis Density (GM-PHD) methods. The SMC-PHD filter suffers from the well known degeneracy problems while GM-PHD filter may not be suitable for nonlinear and non-Gaussian target tracking problems. It is desirable to have a filter that can provide continuous estimates for any distribution. This is the motivation for the use of B-Splines in this thesis. One of the main focus of the thesis is the B-Spline based PHD (SPHD) filters. The Spline is a well developed theory and been used in academia and industry for more than five decades. The B-Spline can represent any numerical, geometrical and statistical functions and models including the PDF and PHD. The SPHD filter can be applied to linear, nonlinear, Gaussian and non-Gaussian multitarget tracking applications. The SPHD continuity can be maintained by selecting splines with order of three or more, which avoids the degeneracy-related problem. Another important characteristic of the SPHD filter is that the SPHD can be locally controlled, which allow the manipulations of the SPHD and its natural tendency for handling the nonlinear problems. The SPHD filter can be further extended to support maneuvering multitarget tracking, where it can be an alternative to any available PHD filter implementations. The PHD filter does not work well for very low observable (VLO) target tracking problems, where the targets SNR is normally very low. For very low SNR scenarios the PDF must be approximated by higher order moments. Therefore the PHD implementations may not be suitable for the problem considered in this thesis. One of the best estimator to use in VLO target tracking problem is the Maximum-Likelihood Probability Data Association (ML-PDA) algorithm. The standard ML-PDA algorithm is widely used in single target initialization or geolocation problems with high false alarm. The B-Spline is also used in the ML-PDA (SML-PDA) implementations. The SML-PDA algorithm has the capability to determine the global maximum of ML-PDA log-likelihood ratio with high efficiency in terms of state estimates and low computational complexity. For fast passive track initialization, search and rescue operations the SML-PDA algorithm can be used more efficiently compared to the standard ML-PDA algorithm. Also the SML-PDA algorithm with the extension supports the multitarget tracking. / Thesis / Doctor of Philosophy (PhD)

Guidance is defined as the determination of a strategy for following a nominal path in the presence of o-nominal conditions, disturbances and uncertainties, and the strategy employed is called a guidance law. Variants of Proportional Navigation (PN), such as True Proportional Navigation (TPN) and Pure Proportional Navigation (PPN), have been studied extensively in the literature on tactical missile guidance. In the absence of target maneuvers, in a linear interceptor guidance problem, TPN was shown to be optimal. However, the standard PN class of guidance laws per se does not show good performance against maneuvering targets, and was found to be eective in intercepting a maneuvering target only from a restrictive set of initial geometries. Also, since these guidance laws were eectively designed for lower speed targets, they show a degraded performance when applied against higher speed targets. However, in the current defense scenario, two classes of agile targets, which are capable of continuous maneuver, and/or of much higher speed than the interceptor, are a reality. This thesis presents analysis of several variants of PN class of guidance laws against these two classes of agile targets. In the literature, an augmentation of the TPN guidance law, termed as Augmented Proportional Navigation (APN), was shown to be optimal in linearized engagement framework. The present work proposes an augmentation of the PPN guidance law, which is more realistic than TPN for an aerodynamically controlled interceptor, and an-alyzes its capturability in fully nonlinear framework, and develops sauciest conditions on speed ratio, navigation gain and augmentation parameter to ensure that all possible initial engagement geometries are included in the capture zone when applied against a target executing piecewise continuous maneuver. The thesis also obtains the capture zone in the relative velocity space for augmented PPN guidance law. In the literature, a novel guidance law was proposed for the interception of higher speed targets in planar engagement by using a negative navigation gain instead of the standard positive one, and was termed as Retro-PN. It was shown that even though the Retro-PN guided interceptor takes more time than PN guided one in achieving successful interception, Retro-PN performs significantly better than the classical PN law, in terms of capturability, lateral acceleration demand, and closing velocity, when used against higher speed targets. The thesis analyzes Retro-PN guidance law in 3-D engagement geometries to yield the complete capture zone of interceptors guided by Retro-PN guidance philosophy, and derives necessary and sucient conditions for the capture of higher speed non-maneuvering targets with and without a constraint on finiteness of lateral acceleration. Terminal impact angle control is crucial for enhancement of warhead eectiveness. In the literature, this problem has been addressed mostly in the context of targets with lower speeds than the interceptor. The thesis analyzes the performance of a composite PN guidance law, that uses standard PPN and the Retro-PN guidance laws based on initial engagement geometry and requirement of impact angle, against higher speed non-maneuvering targets. Then, to expand the set of achievable impact angles, it proposes a modified composite PN guidance scheme, and analyzes the same. For implementation of many modern guidance laws, a good estimate of time-to-go is essential. This requirement is especially severe in case of impact time constrained en-gagement scenarios. To this end, an ecient and fast time-to-go estimation algorithm for generic 3-D engagement is required. Two time-to-go estimation algorithms are presented and analyzed in this work for the engagement of a PPN or Retro-PN guided interceptor and a higher speed target. The first one is a closed form approximation of time-to-go in terms of range, nominal closing speed and an indicator of heading error, and the second one is a numerical recursive time-to-go estimation algorithm. To improve the odds of intercepting an intelligent target and destroying it, a salvo attack of two or more interceptors could be considered as a viable option. Moreover, this simultaneous salvo attack can also be further improved in eciency by incorporating the shoot-look-shoot approach in making a decision about launching interceptors. This can be considered as the first step towards a layered defense system, which has been described in the literature as a potentially eective strategy against short range or long range ballistic threat. To this end, the present work proposes two PPN and Retro-PN based guidance strategies for achieving simultaneous salvo attack on a higher speed non-maneuvering target. For the implementation of the same the numerical recursive time-to-go estimation technique proposed in this work is utilized