Search results for: orbit near fixed point

Authors: T. Martini, J. M. Martínez

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An algorithmic acceleration strategy based on quasi-Newton (or secant) methods is displayed for address the practical problem of accelerating the convergence of the Newton-Lagrange method in the case of convergence to critical multipliers. Since the Newton-Lagrange iteration converges locally at a linear rate, it is natural to conjecture that quasi-Newton methods based on the so called secant equation and some minimal variation principle, could converge superlinearly, thus restoring the convergence properties of Newton's method. This strategy can also be applied to accelerate the convergence of algorithms applied to fixed-points problems. Computational experience is reported illustrating the efficiency of this strategy to solve fixed-point problems with linear convergence rate.

Keywords: algorithmic acceleration, fixed-point problems, nonlinear programming, quasi-newton method

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Authors: Pradip Kumar Jha, Manoj Kumar

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We demonstrate in this work the effect of Rashba spin orbit interaction on multiphoton optical transitions of a quantum dot in the presence of THz laser field and external static magnetic field. This combination is solved by accurate non-perturbative Floquet theory. Investigations are made for the optical response of intraband transition between the various states of the conduction band with spin flipping. Enhancement and power broadening observed for excited states probabilities with increase of external fields are directly linked to the emission spectra of QD and will be useful for making future bioimaging devices.

Keywords: bioimaging, multiphoton processes, spin orbit interaction, quantum dot

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Authors: Muhammad Sufian Jusoh, Mesliza Mohamed

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In this paper, we investigate the existence of positive solutions for a Dirichlet second order boundary value problem by applying the Krasnosel'skii fixed point theorem on compression and expansion of cones.

Keywords: Krasnosel'skii fixed point theorem, positive solutions, Dirichlet boundary value problem, Dirichlet second order boundary problem

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Authors: Francis O. Nwawuru, Jeremiah N. Ezeora

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In this paper, a new algorithm for solving the system of split equilibrium and fixed point problems in real Hilbert spaces is considered. The equilibrium bifunction involves a nite family of pseudo-monotone mappings, which is an improvement over monotone operators. More so, it turns out that the solution of the finite family of nonexpansive mappings. The regularized parameters do not depend on Lipschitz constants. Also, the computations of the stepsize, which plays a crucial role in the convergence analysis of the proposed method, do require prior knowledge of the norm of the involved bounded linear map. Furthermore, to speed up the rate of convergence, an inertial term technique is introduced in the proposed method. Under standard assumptions on the operators and the control sequences, using a modified Halpern iteration method, we establish strong convergence, a desired result in applications. Finally, the proposed scheme is applied to solve some optimization problems. The result obtained improves numerous results announced earlier in this direction.

Keywords: equilibrium, Hilbert spaces, fixed point, nonexpansive mapping, extragradient method, regularized equilibrium

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Authors: Alemayehu Geremew Geremew

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We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.

Keywords: common fixed point, Mann iteration, multivalued mapping, weak convergence

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Authors: Hudson Akewe

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We prove that the convergence of explicit Mann, explicit Ishikawa, explicit Noor, explicit SP, explicit multistep and explicit multistep-SP fixed point iterative procedures are equivalent for the classes of multi-valued phi-contraction, phi-Zamfirescu and phi-quasi-contractive mappings in the framework of modular function spaces. Our results complement equivalence results on normed and metric spaces in the literature as they elegantly cut out the triangle inequality.

Keywords: multistep iterative procedures, multivalued mappings, equivalence results, fixed point

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Authors: Arun Kumar Yadav, Badam Singh Kushvah

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In the present work, we investigated displaced periodic orbits in the linear order in the circular restricted three-body Sun-Jupiter system, where the third mass-less body utilizes solar electric sail. The electric solar sail is a new space propulsion concept which uses the solar wind momentum for producing thrust, and it is somewhat like to the more well-known solar radiation pressure sail which is often called simply the solar sail. Moreover, we implement the feedback linearization control scheme to perform the stabilization and trajectory tracking for the nonlinear system. Further, we derived periodic orbits analytically in linear order by introducing a first order approximation. These approximate analytic solutions are utilized in a numerical search to determine displaced periodic orbit in the full nonlinear model. We found the displaced periodic orbit for the defined non-linear model and stabilized the model.

Keywords: solar electric sail, circular restricted three-body problem (CRTBP), displaced orbit, feedback linearization control

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Authors: Maged Assem Soliman Mossallam

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One of the main prospectives on the demand of space exploration is to reduce the costs and efforts for satellite design. Concerning this issue satellite down scaling attracts space scientists and engineers. Picosatellite is the smallest category of satellites. The overall mass is less than 1 kg and dimensions are 10x10x3 cm3. Thermal control target is to keep the Pico-satellite board temperature within the permissible limits of temperature. Thermal design is completely passive which relies mainly on the enhancement of the thermo-optical properties of aluminum using anodization. Transient analysis is given for two different orbits, ISS orbit and 600 km altitude orbit. Results show that board temperature lies within 3 oC to 22 oC using black anodization which is a permissible limit for the satellite internal electronic board.

Keywords: satellite thermal control, small satellites, thermooptical properties , transient orbit analysis

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Authors: Muhammad Akbar Hussain, Muhammad Mehdi Hussain, Waqar Haider

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There are tens of thousands of undetected and uncatalogued pieces of space debris in the Low Earth Orbit (LEO). They are not only difficult to be detected and tracked, their sheer number puts active satellites and humans in orbit around Earth into danger. With the entry of more governments and private companies into harnessing the Earth’s orbit for communication, research and military purposes, there is an ever-increasing need for not only the detection and cataloguing of these pieces of space debris, it is time to take measures to take them out and clean up the space around Earth. Current optical and radar-based Space Situational Awareness initiatives are useful mostly in detecting and cataloguing larger pieces of debris mainly for avoidance measures. Smaller than 10 cm pieces are in a relatively dark zone, yet these are deadly and capable of destroying satellites and human missions. A network of mobile observatories, connected to each other in real time and working in unison as a single instrument, may be able to detect small pieces of debris and achieve effective triangulation to help create a comprehensive database of their trajectories and parameters to the highest level of precision. This data may enable ground-based laser systems to help deorbit individual debris. Such a network of observatories can join current efforts in detection and removal of space debris in Earth’s orbit.

Keywords: space debris, low earth orbit, mobile observatories, triangulation, seamless operability

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Authors: Francis O. Nwawuru

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The convergence analysis of split monotone inclusion problems and fixed point problems of certain nonlinear mappings are investigated in the setting of real Hilbert spaces. Inertial extrapolation term in the spirit of Polyak is incorporated to speed up the rate of convergence. Under standard assumptions, a strong convergence of the proposed algorithm is established without computing the resolvent operator or involving Yosida approximation method. The stepsize involved in the algorithm does not depend on the spectral radius of the linear operator. Furthermore, applications of the proposed algorithm in solving some related optimization problems are also considered. Our result complements and extends numerous results in the literature.

Keywords: fixedpoint, hilbertspace, monotonemapping, resolventoperators

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Authors: Ibrahim Isa Ali (Pantami), Abdu Jaafaru Bambale, Abimbola Alale, Danjuma Ibrahim Ndihgihdah, Muhammad Alkali, Adamu Idris Umar, Samson Olufunmilayo Abodunrin, Muhammad Dokko Zubairu, Moshood Kareem

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This paper discusses the consideration and trade-offs used for the implementation of robust systems for orbit stability; Telemetry, Command and Ranging (TC& R) for Nigcomsat-1R and applicability for planned NigComSat-2 satellites. NigComSat-1R satellite was built by China Academy of Space Technology (CAST). The Satellite designed with quad-band payload (L, C, Ku, and Ka) was launched on the 20th of December 2011. The functionality of all satellite is driven by robust systems including Attitude & Orbit Control System (AOCS) and TC&R. The planned Nigcomsat-2 is a high throughput Satellite expected to function with better AOCS and TC&R.

Keywords: AOCS, CAST, Nigcomsat-1R, TC&R

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Authors: Hassan Al Salman, Ahmed Al Ghafli

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In this study we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed point theorem to prove existence of the approximations. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. Also, we prove an optimal error bound in time for d=1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the theoretical results.

Keywords: reaction diffusion system, finite element approximation, fixed point theorem, an optimal error bound

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Manop Aorpimai, Ponthep Navakitkanok

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In this paper, the development of the ephemeris generation module used for the Thaichote satellite operations is presented. It is a vital part of the flight dynamics system, which comprises, the orbit determination, orbit propagation, event prediction and station-keeping maneuver modules. In the generation of the spacecraft ephemeris data, the estimated orbital state vector from the orbit determination module is used as an initial condition. The equations of motion are then integrated forward in time to predict the satellite states. The higher geopotential harmonics, as well as other disturbing forces, are taken into account to resemble the environment in low-earth orbit. Using a highly accurate numerical integrator based on the Burlish-Stoer algorithm the ephemeris data can be generated for long-term predictions, by using a relatively small computation burden and short calculation time. Some events occurring during the prediction course that are related to the mission operations, such as the satellite’s rise/set viewed from the ground station, Earth and Moon eclipses, the drift in ground track as well as the drift in the local solar time of the orbital plane are all detected and reported. When combined with other modules to form a flight dynamics system, this application is aimed to be applied for the Thaichote satellite and successive Thailand’s Earth-observation missions.

Keywords: flight dynamics system, orbit propagation, satellite ephemeris, Thailand’s Earth Observation Satellite

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Authors: Safeer Hussain Khan

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In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

Keywords: contractive-like operator, iterative algorithm, fixed point, strong convergence

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Authors: Arif Armagan Gozutok, Alper Kule, Burak Tos, Selman Demirel

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Wireless communication chain requires effective ways to keep throughput efficiency high while it suffers location-dependent, time-varying burst errors. Several techniques are developed in order to assure that the receiver recovers the transmitted information without errors. The most fundamental approaches are error checking and correction besides re-transmission of the non-acknowledged packets. In this paper, stop & wait (SAW) and chase combined (CC) hybrid automated repeat request (HARQ) protocols are compared and analyzed in terms of throughput and average delay for the usage of low earth orbit (LEO) mega-constellations case. Several assumptions and technological implementations are considered as well as usage of low-density parity check (LDPC) codes together with several constellation orbit configurations.

Keywords: HARQ, LEO, satellite constellation, throughput

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Authors: A. E. Emam, M. Abd Elghany

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The change in orbit evolution between collocated satellites (X, Y) inside +/-0.09 ° E/W and +/- 0.07 ° N/S cluster, after one of these satellites is placed in an inclined orbit (satellite X) and the effect of this change in the collocation safety inside the cluster window has been studied and evaluated. Several collocation scenarios had been studied in order to adjust the location of both satellites inside their cluster to maximize the separation between them and safe the mission.

Keywords: satellite, GEO, collocation, risk assessment

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Authors: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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Authors: Yacine Arioua

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In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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Authors: S. Padmapriya, V. Lakshmi Prabha

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In this paper, an efficient reconfigurable fixed-point Least Mean Square Adaptive FIR filter is proposed. The proposed architecture has two methods of operation: one is area efficient design and the other is optimized power. Pipelining of the adder blocks and partial product generator are used to achieve low area and reversible logic is used to obtain low power design. Depending upon the input samples and filter coefficients, one of the techniques is chosen. Least-Mean-Square adaptation is performed to update the weights. The architecture is coded using Verilog and synthesized in cadence encounter 0.18μm technology. The synthesized results show that the area reduction ratio of the proposed when compared with conventional technique is about 1.2%.

Keywords: adaptive filter, carry select adder, least mean square algorithm, reversible logic

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Authors: Y. Heyrani Birak, R. Hizaji, J. Shahkarami

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Reinforced Concrete (RC) deep beams are special structural elements because of their geometry and behavior under loads. For example, assumption of strain- stress distribution is not linear in the cross section. These types of beams may have simple supports or fixed supports. A lot of research works have been conducted on simply supported deep beams, but little study has been done in the fixed-end RC deep beams behavior. Recently, using of fixed-ended deep beams has been widely increased in structures. In this study, the behavior of fixed-ended deep beams is investigated, and the important parameters in capacity of this type of beams are mentioned.

Keywords: deep beam, capacity, reinforced concrete, fixed-ended

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Authors: Anwesha Pathak

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Space law refers to all legal provisions that may regulate or apply to space travel, as well as to space-related activity. Although there is undoubtedly a core corpus of “space law,” rather than designating a conceptually distinct single kind of law, the phrase can be seen as a label applied to a bucket that includes a variety of different laws and regulations. Similar to ‘family law' or ‘environmental law' "space law" refers to a variety of laws that are identified by the subject matter they address rather than by the logical extension of a single legal concept. The word "space law" refers to the Law of Space, which can cover anything from the specifics of an insurance agreement for a specific space launch to the most general guidelines that direct state behaviour in space. Space debris, often referred to as space junk, space pollution, space waste, space trash, or space garbage, is a term used to describe abandoned human-made objects in space, primarily in Earth orbit. These include disused spacecraft, discarded launch vehicle stages, mission-related detritus, and fragmentation material from the destruction of disused rocket bodies and spacecraft, which is particularly prevalent in Earth orbit. Other types of space debris, besides abandoned human-made objects in orbit, include pieces left over from collisions, erosion, and disintegration, or even paint specks, solidified liquids ejected from spacecraft, and unburned components from solid rocket engines. The initial action of launching or using a spacecraft in near-Earth orbit imposes an external cost on others that is typically not taken into account or fully accounted for in the cost by the launcher or payload owner.

Keywords: space, outer space treaty, geostationary orbit, satellites, spacecrafts

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Authors: Akhilesh Kumar, Sathyanarayan G., Nirmala S.

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An unusual approach is developed to determine the orbit of satellites/space objects. The determination of orbits is considered a boundary value problem and has been solved using the finite difference method (FDM). Only positions of the satellites/space objects are known at two end times taken as boundary conditions. The technique of finite difference has been used to calculate the orbit between end times. In this approach, the governing equation is defined as the satellite's equation of motion with a perturbed acceleration. Using the finite difference method, the governing equations and boundary conditions are discretized. The resulting system of algebraic equations is solved using Tri Diagonal Matrix Algorithm (TDMA) until convergence is achieved. This methodology test and evaluation has been done using all GPS satellite orbits from National Geospatial-Intelligence Agency (NGA) precise product for Doy 125, 2023. Towards this, two hours of twelve sets have been taken into consideration. Only positions at the end times of each twelve sets are considered boundary conditions. This algorithm is applied to all GPS satellites. Results achieved using FDM compared with the results of NGA precise orbits. The maximum RSS error for the position is 0.48 [m] and the velocity is 0.43 [mm/sec]. Also, the present algorithm is applied on the IRNSS satellites for Doy 220, 2023. The maximum RSS error for the position is 0.49 [m], and for velocity is 0.28 [mm/sec]. Next, a simulation has been done for a Highly Elliptical orbit for DOY 63, 2023, for the duration of 6 hours. The RSS of difference in position is 0.92 [m] and velocity is 1.58 [mm/sec] for the orbital speed of more than 5km/sec. Whereas the RSS of difference in position is 0.13 [m] and velocity is 0.12 [mm/sec] for the orbital speed less than 5km/sec. Results show that the newly created method is reliable and accurate. Further applications of the developed methodology include missile and spacecraft targeting, orbit design (mission planning), space rendezvous and interception, space debris correlation, and navigation solutions.

Keywords: finite difference method, grid generation, NavIC system, orbit perturbation

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Authors: Nagi Mekhiel

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Many applications use vector operations by applying single instruction to multiple data that map to different locations in conventional memory. Transferring data from memory is limited by access latency and bandwidth affecting the performance gain of vector processing. We present a memory system that makes all of its content available to processors in time so that processors need not to access the memory, we force each location to be available to all processors at a specific time. The data move in different orbits to become available to other processors in higher orbits at different time. We use this memory to apply parallel vector operations to data streams at first orbit level. Data processed in the first level move to upper orbit one data element at a time, allowing a processor in that orbit to apply another vector operation to deal with serial code limitations inherited in all parallel applications and interleaved it with lower level vector operations.

Keywords: Memory Organization, Parallel Processors, Serial Code, Vector Processing

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Authors: Safeer Hussain Khan

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In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves and generalizes corresponding results in the literature in two ways: the iterative process is faster, operators are more general. In the end, we indicate that the results can also be proved with the iterative process with error terms.

Keywords: contractive-like operator, iterative process, fixed point, strong convergence

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Authors: Gilberto Goracci, Fabio Curti

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This work presents a robust, light, and inexpensive algorithm to perform autonomous orbit determination using onboard magnetometer data in real-time. Magnetometers are low-cost and reliable sensors typically available on a spacecraft for attitude determination purposes, thus representing an interesting choice to perform real-time orbit determination without the need to add additional sensors to the spacecraft itself. Magnetic field measurements can be exploited by Extended/Unscented Kalman Filters (EKF/UKF) for orbit determination purposes to make up for GPS outages, yielding errors of a few kilometers and tens of meters per second in the position and velocity of a spacecraft, respectively. While this level of accuracy shows that Kalman filtering represents a solid baseline for autonomous orbit determination, it is not enough to provide a reliable state estimation in the absence of GPS signals. This work combines the solidity and reliability of the EKF with the versatility of a Recurrent Neural Network (RNN) architecture to further increase the precision of the state estimation. Deep learning models, in fact, can grasp nonlinear relations between the inputs, in this case, the magnetometer data and the EKF state estimations, and the targets, namely the true position, and velocity of the spacecraft. The model has been pre-trained on Sun-Synchronous orbits (SSO) up to 2126 kilometers of altitude with different initial conditions and levels of noise to cover a wide range of possible real-case scenarios. The orbits have been propagated considering J2-level dynamics, and the geomagnetic field has been modeled using the International Geomagnetic Reference Field (IGRF) coefficients up to the 13th order. The training of the module can be completed offline using the expected orbit of the spacecraft to heavily reduce the onboard computational burden. Once the spacecraft is launched, the model can use the GPS signal, if available, to fine-tune the parameters on the actual orbit onboard in real-time and work autonomously during GPS outages. In this way, the provided module shows versatility, as it can be applied to any mission operating in SSO, but at the same time, the training is completed and eventually fine-tuned, on the specific orbit, increasing performances and reliability. The results provided by this study show an increase of one order of magnitude in the precision of state estimate with respect to the use of the EKF alone. Tests on simulated and real data will be shown.

Keywords: artificial intelligence, extended Kalman filter, orbit determination, magnetic field

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Authors: Maged Assem Soliman Mossallam

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Microsatellites' low available power limits the usage of active thermal control techniques in these categories of satellites. Passive thermal control techniques are preferred due to their high reliability and power saving which increase the satellite's survivability in orbit. Steady-state and transient simulations are applied to the microsatellite design in order to define severe conditions in orbit. Satellite thermal orbital three-dimensional simulation is performed using thermal orbit propagator coupled with Comsol Multiphysics finite element solver. Sensitivity study shows the dependence of the satellite temperatures on the internal heat dissipation and the thermooptical properties of anodization coatings. The critical case is defined as low power orbiting mode at the eclipse zone. Using black anodized aluminum drops the internal temperatures to severe values which exceed the permissible cold limits. Replacement with anodized titanium returns the internal subsystems' temperatures back to adequate temperature fluctuations limits.

Keywords: passive thermal control, thermooptical, anodized titanium, emissivity, absorbtiviy

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Authors: Kamel Al-Khaled

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A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving the Kuramoto-Sivashinsky equation is given. Both approaches depend on using Sinc basis functions. Firstly, a numerical scheme using Sinc-Galerkin method is developed to approximate the solution of Kuramoto-Sivashinsky equation. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The error in the solution is shown to converge to the exact solution at an exponential. The convergence proof of the solution for the discrete system is given using fixed-point iteration. Secondly, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. The methods are tested on two examples. The demonstrated results show that both of the presented methods more or less have the same accuracy.

Keywords: Sinc-Collocation, nonlinear PDEs, numerical methods, fixed-point

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Authors: Rajkumar N. Ingle

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In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

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Authors: Linjie Zhang, Baifen Ren, Xi Zhang, Genwang Liu

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Ship detection is of great significance for both military and civilian applications. Synthetic aperture radar (SAR) with all-day, all-weather, ultra-long-range characteristics, has been used widely. In view of the low time resolution of low orbit SAR and the needs for high time resolution SAR data, GEO (Geosynchronous orbit) SAR is getting more and more attention. Since GEO SAR has short revisiting period and large coverage area, it is expected to be well utilized in marine ship targets monitoring. However, the height of the orbit increases the time of integration by almost two orders of magnitude. For moving marine vessels, the utility and efficacy of GEO SAR are still not sure. This paper attempts to find the feasibility of GEO SAR by giving a GEO SAR simulator of moving ships. This presented GEO SAR simulator is a kind of geometrical-based radar imaging simulator, which focus on geometrical quality rather than high radiometric. Inputs of this simulator are 3D ship model (.obj format, produced by most 3D design software, such as 3D Max), ship's velocity, and the parameters of satellite orbit and SAR platform. Its outputs are simulated GEO SAR raw signal data and SAR image. This simulating process is accomplished by the following four steps. (1) Reading 3D model, including the ship rotations (pitch, yaw, and roll) and velocity (speed and direction) parameters, extract information of those little primitives (triangles) which is visible from the SAR platform. (2) Computing the radar scattering from the ship with physical optics (PO) method. In this step, the vessel is sliced into many little rectangles primitives along the azimuth. The radiometric calculation of each primitive is carried out separately. Since this simulator only focuses on the complex structure of ships, only single-bounce reflection and double-bounce reflection are considered. (3) Generating the raw data with GEO SAR signal modeling. Since the normal ‘stop and go’ model is not available for GEO SAR, the range model should be reconsidered. (4) At last, generating GEO SAR image with improved Range Doppler method. Numerical simulation of fishing boat and cargo ship will be given. GEO SAR images of different posture, velocity, satellite orbit, and SAR platform will be simulated. By analyzing these simulated results, the effectiveness of GEO SAR for the detection of marine moving vessels is evaluated.

Keywords: GEO SAR, radar, simulation, ship

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