A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

Single network adaptive critic aided dynamic inversion for optimal regulation and command tracking with online adaptation for enhanced robustness

To combine the advantages of both stability and optimality-based designs, a single network adaptive critic (SNAC) aided nonlinear dynamic inversion approach is presented in this paper. Here, the gains of a dynamic inversion controller are selected in such a way that the resulting controller behaves very close to a pre-synthesized SNAC controller in the output regulation sense. Because SNAC is based on optimal control theory, it makes the dynamic inversion controller operate nearly optimal. More important, it retains the two major benefits of dynamic inversion, namely (i) a closed-form expression of the controller and (ii) easy scalability to command tracking applications without knowing the reference commands a priori. An extended architecture is also presented in this paper that adapts online to system modeling and inversion errors, as well as reduced control effectiveness, thereby leading to enhanced robustness. The strengths of this hybrid method of applying SNAC to optimize an nonlinear dynamic inversion controller is demonstrated by considering a benchmark problem in robotics, that is, a two-link robotic manipulator system. Copyright (C) 2013 John Wiley & Sons, Ltd.

An Algorithm for Tracking a Maneuvering Target in Clutter

We consider the problem of tracking a maneuvering target in clutter. In such an environment, missed detections and false alarms make it impossible to decide, with certainty, the origin of received echoes. Processing radar returns in cluttered environments consists of three functions: 1) target detection and plot formation, 2) plot-to-track association, and 3) track updating. Two inadequacies of the present approaches are 1) Optimization of detection characteristics have not been considered and 2) features that can be used in the plot-to-track correlation process are restricted to a specific class. This paper presents a new approach to overcome these limitations. This approach facilitates tracking of a maneuvering target in clutter and improves tracking performance for weak targets.

Studies on the Tracking and Erosion Resistance of RTV Silicone Rubber Nanocomposite

One of the problems associated with outdoor polymeric insulators is tracking and erosion of the weathershed which can directly influence the reliability of the power system. Flame retardants are added to the base material to enhance its tracking and erosion resistance. Hydroxide fillers are regarded as the best flame retardants. This paper deals with studies related to nano - sized magnesium dihydroxide (MDH) and micron-sized Alumina Trihydrate (ATH) fillers as flame retardants in RTV silicone rubber. Tracking and erosion resistance studies were carried out on MDH and ATH silicone rubber composites using an inclined plane tracking and erosion (IPT) resistance tester. The MDH filled (5% by wt) composites performed much better than ATH composites in terms of eroded mass, depth of erosion, width and length of erosion. The eroded mass of MDH composite is 49.8 % that of ATH composite which can be attributed to high surface area and higher thermal stability of MDH nanofillers.

On prequantization to reduce errors in double phase holograms

Prequantization has been forwarded as a means to improve the performance of double phase holograms (DPHs). We show here that any improvement (even under the best of conditions) is not large enough to help the DPH to compete favourably with other holograms.

New approach to improved detection and tracking performance in track-while-scan radars. Part 1: Introduction and review

The paper presents a new approach to improve the detection and tracking performance of a track-while-scan (TWS) radar. The contribution consists of three parts. In Part 1 the scope of various papers in this field is reviewed. In Part 2, a new approach for integrating the detection and tracking functions is presented. It shows how a priori information from the TWS computer can be used to improve detection. A new multitarget tracking algorithm has also been developed. It is specifically oriented towards solving the combinatorial problems in multitarget tracking. In Part 3, analytical derivations are presented for quantitatively assessing, a priori, the performance of a track-while-scan radar system (true track initiation, false track initiation, true track continuation and false track deletion characteristics). Simulation results are also shown.

New approach to improved detection and tracking performance in track-while-scan radars. Part 3: Performance prediction, optimisation and testing

The paper presents, in three parts, a new approach to improve the detection and tracking performance of a track-while-scan radar. Part 1 presents a review of the current status of the subject. Part 2 details the new approach. It shows how a priori information provided by the tracker can be used to improve detection. It also presents a new multitarget tracking algorithm. In the present Part, analytical derivations are presented for assessing, a priori, the performance of the TWS radar system. True track initiation, false track initiation, true track continuation and false track deletion characteristics have been studied. It indicates how the various thresholds can be chosen by the designer to optimise performance. Simulation results are also presented.

New approach to improved detection and tracking performance in track-while-scan radars. Part 2: Detection, track nitiation and association

he paper presents, in three parts, a new approach to improve the detection and tracking performance of a track-while-scan (TWS) radar. Part 1 presents a review of current status. In this part, Part 2, it is shown how the detection can be improved by utilising information from tracker. A new multitarget tracking algorithm, capable of tracking manoeuvring targets in clutter, is then presented. The algorithm is specifically tailored so that the solution to the combinatorial problem presented in a companion paper can be applied. The implementation aspects are discussed and a multiprocessor architecture identified to realise the full potential of the algorithm. Part 3 presents analytical derivations for quantitative assessment of the performance of the TWS radar system. It also shows how the performance can be optimised.

Incidence factors of the tracking systems used in parabolic-cylindrical concentrators

Several orientation and tracking systems employed in parabolic-cylindrical concentrators for focusing the direct solar radiation on the absorber tubes are analyzed from the technical and economic points of view. Case one, where the incidence factor was a function of declination and hour angle, showed that the maximum variations of incident factor from morning to noon was 0.5 at zero angle of declination. Case two, where the incidence factor was a function of declination, hour angle and latitude, showed the maximum variation of the incidence factor to be 0.128, which occurred during noon at the latitude of 30 degrees, corresponding to a change of declination from 0 to 23.5 degrees. In case three, the incidence factor, a function of declination only, showed that the maximum variation of the incidence factor corresponding to the change in declination from 0 to 23.5 degree was 0.0758. It is concluded that system three is the most efficient from the technical and economic point of view.

A feedback-based algorithm forMotion analysis with application to object tracking

We present a motion detection algorithm which detects direction of motion at sufficient number of points and thus segregates the edge image into clusters of coherently moving points. Unlike most algorithms for motion analysis, we do not estimate magnitude of velocity vectors or obtain dense motion maps. The motivation is that motion direction information at a number of points seems to be sufficient to evoke perception of motion and hence should be useful in many image processing tasks requiring motion analysis. The algorithm essentially updates the motion at previous time using the current image frame as input in a dynamic fashion. One of the novel features of the algorithm is the use of some feedback mechanism for evidence segregation. This kind of motion analysis can identify regions in the image that are moving together coherently, and such information could be sufficient for many applications that utilize motion such as segmentation, compression, and tracking. We present an algorithm for tracking objects using our motion information to demonstrate the potential of this motion detection algorithm.

Kernel-based spatial-color modeling for fast moving object tracking

Visual tracking has been a challenging problem in computer vision over the decades. The applications of Visual Tracking are far-reaching, ranging from surveillance and monitoring to smart rooms. Mean-shift (MS) tracker, which gained more attention recently, is known for tracking objects in a cluttered environment and its low computational complexity. The major problem encountered in histogram-based MS is its inability to track rapidly moving objects. In order to track fast moving objects, we propose a new robust mean-shift tracker that uses both spatial similarity measure and color histogram-based similarity measure. The inability of MS tracker to handle large displacements is circumvented by the spatial similarity-based tracking module, which lacks robustness to object's appearance change. The performance of the proposed tracker is better than the individual trackers for tracking fast-moving objects with better accuracy.

Tracking Random Walk of Individual Domain Walls in Cylindrical Nanomagnets with Resistance Noise

The stochasticity of domain-wall (DW) motion in magnetic nanowires has been probed by measuring slow fluctuations, or noise, in electrical resistance at small magnetic fields. By controlled injection of DWs into isolated cylindrical nanowires of nickel, we have been able to track the motion of the DWs between the electrical leads by discrete steps in the resistance. Closer inspection of the time dependence of noise reveals a diffusive random walk of the DWs with a universal kinetic exponent. Our experiments outline a method with which electrical resistance is able to detect the kinetic state of the DWs inside the nanowires, which can be useful in DW-based memory designs.

A Resonant Integrator Based PLL and AC Current Controller for Single Phase Grid Connected PWM-VSI

Grid connected PWM-VSIs are being increasingly used for applications such as Distributed Generation (DG), power quality, UPS etc. Appropriate control strategies for grid synchronisation and line current regulation are required to establish such a grid interconnection and power transfer. Control of three phase VSIs is widely reported in iterature. Conventionally, dq control in Synchronous Reference Frame(SRF) is employed for both PLL and line current control where PI-controllers are used to track the DC references. Single phase systems do not have defined direct (d) and quadrature (q) axis components that are required for SRF transformation. Thus, references are AC in nature and hence usage of PI controllers cannot yield zero steady state errors. Resonant controllers have the ability to track AC references accurately. In this work, a resonant controller based single phase PLL and current control technique are being employed for tracking grid frequency and the AC current reference respectively. A single phase full bridge converter is being operated as a STATCOM for performance evaluation of the control scheme.

Model Based Target Tracking in a Wireless Network of Passive Infrared Sensor Nodes

We consider the problem of tracking an intruder in a plane region by using a wireless sensor network comprising motes equipped with passive infrared (PIR) sensors deployed over the region. An input-output model for the PIR sensor and a method to estimate the angular speed of the target from the sensor output are proposed. With the measurement model so obtained, we study the centralized and decentralized tracking performance using the extended Kalman filter.