Example Of Report On Determination Of A Spacecraft Location By The Spacecraft:
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ELEC 4504 Avionics Technical Report
The purpose of this report is to investigate how spacecrafts determine their location. The two main parameters required to obtain a spacecraft’s position are its orbit and its attitude, this report will focus more on orbit determination. An objects attitude is a measurement of the object’s position measured relative to a designated object or an inertial reference, attitude motion measures the objects rotational motion about its mass centre. The orbit of an object can be described as the curved path it follows around a point in space due to gravity, the point is usually the centre of a large object which has a gravitational field and they are usually elliptical. Determination of both these parameters is independent of the other; however they are related and may affect each other.
A combination of the attitude and orbit parameters is used to determine the position of the object in a reference frame. There are a few reference frames that are mainly used to calculate a spacecraft’s position, varying circumstances dictate which frames to use. It is important to understand the different reference frames and how they each apply to the determination of both parameters as they act as a base upon which all the data gathered can be used and understood. This report will focus mainly on orbits around the earth due to the lack of sufficient data for other planets and systems.
Astrodynamics is the term used when discussing the motion of an object orbiting the earth. It is the one of the most basic methods of calculating the object’s location, and although many models have been developed that calculate an object’s position more accurately the main features of its position can still be described quite well using basic Astrodynamics. There are also a variety of different methods used by scientists that will be discussed in greater depth and compared. Understanding the different methods as well as the most basic will allow better understanding of orbit and attitude determination as well as make rise to the basic design argument of which method to use for each unique spacecraft design.
The technology used to determine these parameters are needed to increase design optimization of each spacecraft. This report will also look into some of these technologies and how they can be used in cohesion to help increase the accuracy of their readings. An issue can arise from the different conditions around the spacecraft and hence a closer study of the environment around a spacecraft during its mission will be discussed along with the methods and technologies used to determining its position.
2.0 Orbital Locations and Errors
Spacecrafts are able to pinpoint their location in the orbit in order to be useful for GPS and similar applications. The errors that are involved in making the calculations for an accurate and precise location must be taken into account. For example, the error caused by a satellites nearness to the Perigee is especially large and cannot be ignored. The following discussion addresses common errors that need to be corrected when trying to calculate the real-time position in orbit, with emphasis on the perspective of the spacecraft. Satellites send information and data on weather, natural disasters and troop movements. Therefore, an accurate orbital position needs to be known so that the distance relationship from the satellite to earth can be calculated. In that way, the parameter being reported can be located with precision. The autonomous capabilities of satellites are carefully studied and refined because now-a-days it is expected that major tasks will be carried out automatically (Li, Wang, Zhang and Zhao 2009).
Li, Wang, Zhang and Zhao (2009:470) note that in order to meet the needs for satellites’ to carry out autonomous tasks, the “autonomous relative position and pose based on machine vision” is a global goal. The researchers developed a method based on motor algebra in order to implement autonomous relative navigational algorithms for very precise satellite based earth observations (30). The Global Positioning System (GPS) is one component of the Global Navigation Satellite System (GNSS). Navigation systems that are often used include the Inertial Navigation System (INS) and the Celestial Navigation System (CNS). The systems need communication with high speed links, whereas the system based on motor algebra and using algorithms is not dependent on good communication (470).
Orbits must be carefully planned for space missions due to the high budgets involved and the importance of the data that are sent to earth from satellites. Instrumentation carried by the satellites to provide date is expensive and hard to replace. The orbit choice of a satellite or space craft is highly dependent upon its intended purpose. In order to reach a preliminary estimate of an orbit, a calculation from identifying a specific altitude and specific control functions can be made.
The two parameters of orbit and altitude are clearly interdependent. The magnetic field strength and atmospheric density at a point in the atmosphere can be calculated from a satellite’s orbital location if the satellite is located in the lower altitudes of Earth’s orbit. The data for determining the orbit is available from references that are reporting positions external to the orbit. External references for real time or stored data include the Global Positioning System (GPS), radar, optics, and telemetric measurements. Each type of data producing system is appropriate for different measurements and can be used optimally dependent on the known variables.
The variables that indicate which system is the best are the desired orbit, the degree of accuracy necessary, and the spacecraft’s or satellite’s weight limitations. A satellite requires the consideration of more rigid limitations compared to a manned spacecraft because of the smaller size. The small size regulates constraints based on the mass and volume of a satellite. A satellite does not cost as much or require as much time for development as a larger spacecraft, on the other hand, risks are higher and the amount of reliability tolerance is increased.
2.2 Orbital Frameworks and Attitude
The satellite is considered a rigid spacecraft so its motion is determined by position, attitude, attitude motion and velocity. Orbit determinations are based on velocity and position measurements and the center of mass for the translation motion of the satellite is form of the output data. A variety of reference frames are used to calculate orbit, but generally the framework consists of the GPS vectors that are known, the Line of Sight (LOS) vectors, and the magnetic field.
The Body Framework is a practical reference frame that is based upon the satellite’s center mass. In that way, the body coordinate system does not vary, but remains fixed to the spacecraft and its control hardware, but not its altitude sensing hardware. The satellite’s attitude is described with reference to the orbit frame and the body frame when the satellite’s attitude is equal to 0° in all three directions of roll, pitch and yaw.
2.3 Astrodynamics models
Astrodynamics models are used to calculate and to predict the satellite’s position in orbit. The discussion below looks at what data is needed to learn a spacecraft’s position. The data applications and real-life examples clarify how the components work together.
The Satellite Orbit Analysis Program (SOAP) is one of the models that can be used to visualize and analyze space systems (Stodden and Galasso, 1995). SOAP is a three dimensional (3-D) interactive program so the entire system can be approximated and designed. The satellite in space is placed into the system in the context of other entities and their movements relative to the satellites. The main entity types with tracking devises are ships, airplanes and stations on the ground. The users can build coordinate axis for potential systems to hold the “wireframe spacecraft models” and “sensor shapes” (369). The model generates data reports and new coordinate XY plots. The orbit can also be determined by the satellite using two position vectors relative to the ground station in 3-D; the measurements of the distance and angles are simultaneous when the optimal conditions are present (Braden, Browning and Gelderloos, 223) A satellite’s orbital motion around the Earth requires measurements from six independent variables about the position and velocity of the satellite (Montenbruck and Gill 223).
A satellite’s Inertial Navigation System (INS) can cause a large error that must be corrected. so a satellite with and elliptical orbit stays on its orbital course. The error is caused by nearness to the Perigee of the satellite. Jia-lun, Nai-gang and Li-bin (2009) developed a way to correct the error and ensure precision navigation. INS is the navigational system generally used so the correction of the error is significantly important. The researchers developed two methods to calculate accurate information and the one that is simpler is to calculate the orbit. Both of the methods must take into account the error near the perigee, the errors cannot be omitted. The values comprised by the errors are attitude, position and velocity (4540).
Another type of program is used to design the capabilities needed for space vehicles and satellites to return to earth automatically (Braden, Browning and Gelderloos 1990). The Integrated Inertial Navigation System/Global Positioning System (INS/GPs) is an example of a programme that directs automatic return of small vehicles that can land with great precision “precision touch-down/landing” (409). The errors that are calculated from inputs into the program are of three main types (a) initialization parameters and errors, (b) sensor errors, and (c) GPS aiding device parameters and errors. The first category takes into account position, velocity, attitude errors. The errors for altitude directly impact accurate orbit calculations. Attitude errors considered in the model are azimuth and level.
Level errors are measurements with values that are outliers or noise. The first step of filtering out level errors is to calculate the satellite’s inertial state vector of the original data. The values used to derive the vector are the position and velocity measurements (Montenbruck and Gill 306). Programs are developed specifically to filter out level errors; an example is the RTOD program of a GPS (306). The filter performance is checked by using data of the known satellite position and its velocity in Earth’s orbit by using “a least squares orbit determination with an elaborate force model (306).
In a GPS the Standard Positioning Service (SPS) continually reports the position and timing information with global reference (204). The Precise Positioning Service (PPS) of the GPS records the velocity position and timing (204). The U.S. GPS system allows specific users access to these instantaneous measurement sets with the understanding that that “typical random and systematic errors” are included (204).
A model that first addressed azimuth errors is the Hopfield equation (1969 cited in Montenbruck and Gill, 223). The errors are calculated by taking into account the wet and the dry heights in the troposphere (223). The error is calculated for elevations above 5° and the results are errors ˂ 10 percent, whereas, the at elevations of 1° the errors can as large as 100 percent (223).
Technologies for design optimization are in demand and many researchers are developing optimization models. The Linearized Orbit Model requires range and angles and other measurement types as well as two or more tracking systems (Montenbruck and Gil, p. 297)
The reasons that accurate numerical values are necessary include the practical, immediate need to know the position of a satellite in its orbit. Other highly practical reasons are to stay on budget and to avoid collisions in space. The larger reasons based on the needs of society are parallel in their importance. The capability of a society to successfully keep satellites on orbit can rely on improved security and prestige as well as increased knowledge and as an ingredient for progressing social development.
Braden, K, Browning, C. and Gelderloos, H. Integrated inertial navigation system/global system (INS/GPS) for automatic space return vehicle. IEEE, 1990. Print.
Jia-lun, P, Nai-gang, CUI, and Li-bin, Z. Spacecraft inertial navigation errors nearby perigee and its elimination. Proceedings of the 2009 IEEE International Conference on Mechatronics and Automation, August 9-12, Changhun, China. 2009. Print.
Li, K, Wang, Q, .Zhang, Q, and Zhao, C. Vision autonomous relative navigation algorithm for distributed micro/nano satellite earth observation system based-on motor algebra. 2009 International Conference on Environmental Science and Information Application Technology, IEEE Computer Society. (2009) Print.
Montenbruck, O, and Gil, E. Satellite Orbits: Models, Methods, and Applications. 3rd ed. NYC:Springer. 2005.
Stodden, D, and Galasso, G. Space system visualization and analysis using the Satellite Orbit Analysis Program (SOAP). IEEE. 1995. Print.
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