Efficient Simulation of Airborne SAR Raw Data in Case of Motion Errors

In the simulation of SAR raw data, it is well-known that the frequency-domain algorithm is more efficient than a time-domain algorithm, making it is more suitable for extended scene simulation. However, the frequency-domain algorithm is perhaps better suited for ideal linear motion and requires some degrees of approximations to take the nonlinear motion effects. This chapter presents an efficient simulation approach based on hybrid time and frequency-domain algorithms under certain assumptions. The algorithm has high efficiency and is suitable for the simulation of extended scenes, which demands highly computational resources. The computational complexity of the proposed algorithm is analyzed, followed by numerical results to demonstrate the effectiveness and efficiency of the proposed approach.

GNSS Signal Processing with EKF and UKF for Stationary User Position Estimation

Precise and accurate estimation of state vectors is an important process during position determination. In this study, Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) of stationary user, state vectors defined in Earth Centered Inertial (ECI) coordinate system, accompanied by GNSS measurement data. It is aimed to make estimations with methods. EKF and UKF methods were compared with each other. In this study, the effects of nonlinear motion analysis and linearization methods on state vector estimations were investigated. Thanks to this study, estimations of the positioning information required during the specific tasks of many moving platforms have been made.

A Numerical Simulation of Non-Linear Air-Gap for Deepwater Semi-Submersible Platform

Air gap is pivotal to the hydrodynamic performance for the semi-submersible platform as a key characteristic for the strength assessment and safety evaluation. Considering the metocean conditions of the Norse Sea, the hydrodynamic performance of a semi-submersible platform has been analyzed. Based on the three-dimensional potential flow theory, and combined with the full QTF matrix and the second-order difference frequency loads, the nonlinear motion characteristics and the prediction for air gap have been simulated. The wave frequency motion response, the second-order nonlinear air gap response and nonlinear motion response of the platform have been analyzed. By comparing the simulation results, the air gap response of the platform considering the nonlinear motion is more intense than the results simulated by the first-order motion without considering the second-order difference frequency loads. Under the heavy metocean conditions, for the heave and pitch motion of the platform, the non-linear simulation values for some air gap points and areas are negative which means the wave slam has been occurred, but the calculation results of linear motion response indicate that the air gap above has not appeared the wave slamming areas. The simulation results present that the influence of the second-order wave loads is a critical part in the air gap prediction for the semi-submersible platform.

Periodic Solutions of Nonlinear Relative Motion Satellites

The relative motion of an outline of the rendezvous problem has been studied by assuming that the chief satellite is in circular symmetric orbits. The legitimacy of perturbation techniques and nonlinear relative motion are investigated. The deputy satellite equations of motion with respect to the fixed references at the center of the chief satellite are nonlinear in the general case. We found the periodic solutions of the linear relative motion satellite and for the nonlinear relative motion satellite using the Lindstedt–Poincaré technique. Comparisons among the analytical solutions of linear and nonlinear motions and the obtained solution by the numerical integration of the explicit Euler method for both motions are investigated. We demonstrate that both analytical and numerical solutions of linear motion are symmetric periodic. However, the solutions of nonlinear motion obtained by the Lindstedt–Poincaré technique are periodic and the numerical solutions obtained by integration by using explicit Euler method are non-periodic. Thus, the Lindstedt–Poincaré technique is recommended for designing the periodic solutions. Furthermore, a comparison between linear and nonlinear analytical solutions of relative motion is investigated graphically.

The Meaning of Accelerated Motion

Unlike accelerated motion or curvalinear motion,a nonlinear motion state(non-inertial system) can be described by differential equations or the other algebric equations in axiom 2, the accelerated motion in axiom 3 can be considered to be described by using the equation of the linear and curvilinear process of the continuum extending to infinitely distance.Further, this linear and curvilinear process of the continuum is a quantitative continuum in essence as a unity of infinitely quantities and infinitely dimensions at infinite distance (infinity) relative to all orientations in which we exist. These indicates that an accelerated motion accumulates continuously started from a finite quantities, leaping to transit from finite to infinite quantities by an infinitely great accelerating force.