Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

OVER the past few years, there have been significant efforts devoted to the research and development of cooperative unmannedsystems [1–3].The formationflyingofmultipleunmanned aerial vehicles (UAVs) has been studied for radar deception, reconnaissance, surveillance, and surface-to-air-missile jamming in military operations. An example of a cooperative operational scenario of multiple vehicles is that of a small UAV flying over an urban area, dispensingmultiplemicro aerial vehicles to examinepointsof interest fromclosedistances [4].Agroupofwell-organized low-costmultiple vehicles can be far superior to a single high-technology and high-cost UAV in effectiveness. Tactical missile systems as well as UAVs provide more capabilities when they are organized as a coordinated group than when they are operated independently. Modern antiship missiles need to be able to penetrate the formidable defensive systems of battleships such as antiair defense missile systems and close-in weapon system (CIWS). CIWS is a naval shipboard weapon system for detecting and destroying incoming antiship missiles and enemy aircraft at short range. These defensive weapons with powerful fire capability and various strategies seriously intimidate the survivability of the conventional antiship missiles. Hence, antiship missile developers have made great efforts to develop a high-performance missile system with ultimate sea-skimming flight and terminal evasive maneuvering capabilities despite a huge cost. On the other hand, cooperative attack strategies have been studied to enhance survivability of the conventional ones. Here, a cooperative attack means that multiple missiles attack a single target or multiple targets cooperatively or, in a specific case, simultaneously [5,6]. Clearly, it is difficult to defend a group of attackers bursting into sight at the same time, even though each member is the conventional one in performance. So the simultaneous attack ofmultiple missiles is a cost-effective and efficient cooperative attack strategy. A simultaneous attack of a group of missiles against a single common target can be achieved by two ways. The first approach is individual homing, inwhich a common impact time is commanded to all members in advance, and thereafter each missile tries to home on the target on time independently. The second is cooperative homing, inwhich themissiles communicate among themselves to synchronize the arrival times. In other words, the missiles with larger times-to-go try to take shortcuts, whereas others with shorter times-to-go take detours to delay the arrival times. The first concept requires determination of a suitable common impact time before homing, but the second needs online data links throughout the engagement. Despite a number of studies on guidance problems related to timeto-go [7–10], studies on guidance laws to control impact time for a simultaneous attack are rare, except a few recent works by the authors. An impact-time-control guidance law (ITCG) for antiship missiles was developed in [5] and, as an extension of this study, a guidance law to control both impact time and angle (ITACG) was presented in [11]. These individual homing methods are based on optimal control theory, providing analytical closed-loop guidance laws. Herein, the desired impact time is assumed to be prescribed before the homing phase starts. Alternatively, this Note is concerned with a new guidance law based on the second approach, cooperative homing, for a simultaneous attack of multiple missiles. Proportional navigation (PN) is a well-known homing guidance method in which the rate of turn of the interceptor is made proportional with a navigation ratio N to the rate of turn of the line of sight (LOS) between the interceptor and the target. The navigation constant N is a unitless gain chosen in the range from 3 to 5 [12]. Although PNwithN 3 is known to be energy-optimal, an arbitrary N > 3 is also optimal if a time-varying weighting function is included into the cost function of the linear quadratic energy-optimal problem [13,14]. In general, the navigation ratio is held fixed. In some cases, however, it can be considered as a control parameter to achieve a desired terminal heading angle [15].Although PN results in successful intercepts under a wide range of engagement conditions, its control-efficiency is not optimal, in general, especially for the case of maneuvering targets [16]. Augmented proportional navigation, a variant of PN, is useful in cases in which target maneuvers are significant [12]. Biased proportional navigation is also commonly used to compensate for target accelerations and sensor noises or to achieve a desired attitude angle at impact [17]. Even if PN and its variants are alreadywell known andwidely used, they are not directly applicable to many-to-one engagements. This Note proposes a homing guidance law called cooperative proportional navigation (CPN) for many-to-one engagements: CPN has the same structure as conventional PN except that it has a time-varying navigation gain that is adjusted based on the onboard time-to-go and the times-to-go of the other missiles. CPN uses the time-varying navigation gain as a control parameter for reducing the variance of times-on-target of multiple missiles. This Note begins with the formulation of the homing problem of multiple missiles against a single target, subject to constraints on the impact time. Next, preliminary concepts such as the relative time-togo error and the variance of times-to-go of multiple missiles are introduced and a new guidance law is proposed. Then the major property of the law is investigated and the characteristics of the law for the case of twomissiles are examined in detail. Finally, numerical simulation results illustrate the performances of the proposed law.

Homing Guidance Law for Cooperative Attack of Multiple Missiles

http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2008/data/papers/3557

State-Dependent Riccati Equation (SDRE) Control: A Survey

Vehicles are currently being developed and sold with increasing levels of connectivity and automation. As with all networked computing devices, increased connectivity often results in a heightened risk of a cyber security attack. Furthermore, increased automation exacerbates any risk by increasing the opportunities for the adversary to implement a successful attack. In this paper, a large volume of publicly accessible literature is reviewed and compartmentalized based on the vulnerabilities identified and mitigation techniques developed. This review highlighted that the majority of studies are reactive and vulnerabilities are often discovered by friendly adversaries (white-hat hackers). Many gaps in the knowledge base were identified. Priority should be given to address these knowledge gaps to minimize future cyber security risks in the connected and autonomous vehicle sector.

/pdf/cyber-threats-facing-autonomous-and-connected-vehicles-54s1r2hcjr.pdf

Cyber Threats Facing Autonomous and Connected Vehicles: Future Challenges

: Modeling, simulation, and integrated guidance-control of a kinetic warhead utilizing moving- mass actuators are discussed. Moving masses can be used in any speed range both in the atmosphere as well as outside it, as long as there is a force, either aerodynamic or propulsive, acting on the vehicle. Since they are contained entirely within the airframe geometric envelope, and because no mass expulsion is involved, moving-mass actuation technique offers significant advantages over conventional aerodynamic control surfaces and reaction control systems. The present research developed a high fidelity, nine degree-of-freedom simulation model of a kinetic warhead with three moving-mass actuators. This simulation model is used for actuator sizing and in the development of flight control systems. A software package for performing numerical feedback linearization technique is employed for the design of nonlinear flight control systems. Interception of non-maneuvering and weaving targets in both atmospheric and exo-atmospheric conditions are demonstrated.

/pdf/integrated-guidance-and-control-of-moving-mass-actuated-1fllqyav94.pdf

Integrated Guidance and Control of Moving-Mass Actuated Kinetic Warheads

A new suboptimal control method is proposed in this study to effectively design an integrated guidance and control system for missiles. Optimal formulations allow designers to bring together concerns about guidance law performance and autopilot responses under one unified framework. They lead to a natural integration of these different functions. By modifying the appropriate cost functions, different responses, control saturations (autopilot related), miss distance (guidance related), etc., which are of primary concern to a missile system designer, can be easily studied. A new suboptimal control method, called the thetas-D method, is employed to obtain an approximate closed-form solution to this nonlinear guidance problem based on approximations to the Hamilton-Jacobi-Bellman equation. Missile guidance law and autopilot design are formulated into a single unified state space framework. The cost function is chosen to reflect both guidance and control concerns. The ultimate control input is the missile fin deflections. A nonlinear six-degree-of-freedom (6-DOF) missile simulation is used to demonstrate the potential of this new integrated guidance and control approach

Integrated Guidance and Control of Missiles With $theta hbox - D$ Method

http://www.optisyn.com/research/publications/1999/MED99.pdf

Integrated Design of Agile Missile Guidance and Autopilot Systems

This paper proposes and evaluates a new guidance law termed generalized vector explicit guidance (GENEX). This guidance law can simultaneously achieve design specifications on miss distance and final missile-target relative orientation. The latter may be used to enhance the performance of warheads the effectiveness of which is influenced by the terminal encounter geometry. The GENEX guidance law is parameterized in terms of a design coefficient that determines the degree of curvature in the trajectory. Feasibility of GENEX guidance was demonstrated by its application to two weapon scenarios. The first was an air-to-air missile terminal homing scenario. Assuming ideal sensor information and a single-lag missile response model, the guidance was shown to perform well against an air target performing evasive maneuvers. A specified zero-aspect terminal encounter angle was achieved while simultaneously minimizing miss distance. The second application involved an air-to-surface munition released from an unmanned air vehicle. The GENEX guidance law was able to produce trajectories satisfying a terminal impact angle constraint. In addition, an engagement region of sufficient size was shown to be achievable using guidance gains scheduled with target location and weapon release altitude.

Generalized Vector Explicit Guidance

A x , B x = state-dependent system matrices of size n n and n m Q x , R x = state-dependent weighting matrices of sizes n n and m m r, _ r = range and range rate of the target with respect to the missile S = solution to the Riccati equation T = rocket motor thrust per unit mass acting along the longitudinal axis of the missile u = control vector of size m 1 upert = control perturbation vector of size m 1 x = state vector of size n 1 xpert = state perturbation vector of size n 1 X, Y, Z = relative position components of the target with respect to the missile y, z = position of the moving masses along the pitch and yaw axes with respect to the body yc, zc = moving-mass position commands , = pitch and yaw Euler angles of the missile y, z = line-of-sight angles

Ernest Ohlmeyer

Papers

Integrated Guidance and Control of Moving-Mass Actuated Kinetic Warheads

Integrated Guidance and Control of Missiles With $theta hbox - D$ Method

Integrated Design of Agile Missile Guidance and Autopilot Systems

Generalized Vector Explicit Guidance

Numerical State-Dependent Riccati Equation Approach for Missile Integrated Guidance Control