{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/49102"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/49102","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Kalman Filter Implementation to Determine Orbit and Attitude of a Satellite in a Molniya Orbit","abstract":"This thesis details the development and implementation of an attitude and orbit determining Kalman filter algorithm for a satellite in a Molniya orbit. To apply the Kalman Filter for orbit determination, the equations of motion of the two body problem were propagated using Cowell's formulation. Four types of perturbing forces were added to the propagated model in order to increase the accuracy of the orbit prediction. These four perturbing forces are Earth oblateness, atmospheric drag, lunar gravitational forces and solar radiation pressure. Two cases were studied, the first being the implementation of site track measurements when the satellite was over the ground station. It is shown that large errors, upwards of ninety meters, grow as time from last measurement input increases. The next case studied was continuous measurement inputs from a GPS receiver on board the satellite throughout the orbit. This algorithm greatly decreased the errors seen in the orbit determining algorithm due to the accuracy of the sensor as well as the continuous measurement inputs throughout the orbit. It is shown that the accuracy of the orbit determining Kalman filter also depends on the length of time between each measurement update. The errors decrease as the time between measurement updates decreases. Next the Kalman filter is applied to determine the satellite attitude. The rotational equations of motion are propagated using Cowell's Formulation and numerical integration. To increase the fidelity of the model four disturbing torques are included in the rotational equations of motion model: gravity gradient torque, solar pressure torque, magnetic torque, and aerodynamic torque. Four cases were tested corresponding to four different on board attitude determining sensors: magnetometer, Earth sensor, sun sensor, and star tracker. A controlled altitude path was chosen to test the accuracy of each of these cases and it was shown that the algorithm using star tracker measurements was three hundred times more accurate than that of the magnetometer algorithm.","abstract_html":"This thesis details the development and implementation of an attitude and orbit determining Kalman filter algorithm for a satellite in a Molniya orbit. To apply the Kalman Filter for orbit determination, the equations of motion of the two body problem were propagated using Cowell's formulation. Four types of perturbing forces were added to the propagated model in order to increase the accuracy of the orbit prediction. These four perturbing forces are Earth oblateness, atmospheric drag, lunar gravitational forces and solar radiation pressure. Two cases were studied, the first being the implementation of site track measurements when the satellite was over the ground station. It is shown that large errors, upwards of ninety meters, grow as time from last measurement input increases. The next case studied was continuous measurement inputs from a GPS receiver on board the satellite throughout the orbit. This algorithm greatly decreased the errors seen in the orbit determining algorithm due to the accuracy of the sensor as well as the continuous measurement inputs throughout the orbit. It is shown that the accuracy of the orbit determining Kalman filter also depends on the length of time between each measurement update. The errors decrease as the time between measurement updates decreases. Next the Kalman filter is applied to determine the satellite attitude. The rotational equations of motion are propagated using Cowell's Formulation and numerical integration. To increase the fidelity of the model four disturbing torques are included in the rotational equations of motion model: gravity gradient torque, solar pressure torque, magnetic torque, and aerodynamic torque. Four cases were tested corresponding to four different on board attitude determining sensors: magnetometer, Earth sensor, sun sensor, and star tracker. A controlled altitude path was chosen to test the accuracy of each of these cases and it was shown that the algorithm using star tracker measurements was three hundred times more accurate than that of the magnetometer algorithm.","abstract_has_math":false,"creators":["Keil, Elizabeth Marie"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Aerospace Engineering","degree_department":"Aerospace and Ocean Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["McGwier, Robert W."],"committee_members":["Woolsey, Craig A.","Sultan, Cornel"],"year":2014,"date_issued":"2014-06-23","date_published":"2014-06-23","updated_at":"2026-07-22T22:19:00Z","subjects":["Attitude","Orbit","Determination","Kalman Filter"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:3092"],"render_values":[{"text":"vt_gsexam:3092","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/49102","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["McGwier, Robert W."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Woolsey, Craig A.","Sultan, Cornel"]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace and Ocean Engineering"]},{"key":"dc:creator","label":"Author","values":["Keil, Elizabeth Marie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-06-24T08:00:37Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-06-24T08:00:37Z"]},{"key":"dc:date.issued","label":"Date","values":["2014-06-23"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Attitude","Orbit","Determination","Kalman Filter"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:3092"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/49102"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis details the development and implementation of an attitude and orbit determining Kalman filter algorithm for a satellite in a Molniya orbit. To apply the Kalman Filter for orbit determination, the equations of motion of the two body problem were propagated using Cowell's formulation. Four types of perturbing forces were added to the propagated model in order to increase the accuracy of the orbit prediction. These four perturbing forces are Earth oblateness, atmospheric drag, lunar gravitational forces and solar radiation pressure. Two cases were studied, the first being the implementation of site track measurements when the satellite was over the ground station. It is shown that large errors, upwards of ninety meters, grow as time from last measurement input increases. The next case studied was continuous measurement inputs from a GPS receiver on board the satellite throughout the orbit. This algorithm greatly decreased the errors seen in the orbit determining algorithm due to the accuracy of the sensor as well as the continuous measurement inputs throughout the orbit. It is shown that the accuracy of the orbit determining Kalman filter also depends on the length of time between each measurement update. The errors decrease as the time between measurement updates decreases. Next the Kalman filter is applied to determine the satellite attitude. The rotational equations of motion are propagated using Cowell's Formulation and numerical integration. To increase the fidelity of the model four disturbing torques are included in the rotational equations of motion model: gravity gradient torque, solar pressure torque, magnetic torque, and aerodynamic torque. Four cases were tested corresponding to four different on board attitude determining sensors: magnetometer, Earth sensor, sun sensor, and star tracker. A controlled altitude path was chosen to test the accuracy of each of these cases and it was shown that the algorithm using star tracker measurements was three hundred times more accurate than that of the magnetometer algorithm."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Kalman Filter Implementation to Determine Orbit and Attitude of a Satellite in a Molniya Orbit"]}]}],"canonical_facts":{"dc:contributor.committeechair":["McGwier, Robert W."],"dc:contributor.committeemember":["Woolsey, Craig A.","Sultan, Cornel"],"dc:contributor.department":["Aerospace and Ocean Engineering"],"dc:creator":["Keil, Elizabeth Marie"],"dc:date.accessioned":["2014-06-24T08:00:37Z"],"dc:date.available":["2014-06-24T08:00:37Z"],"dc:date.issued":["2014-06-23"],"dc:description.abstract":["This thesis details the development and implementation of an attitude and orbit determining Kalman filter algorithm for a satellite in a Molniya orbit. To apply the Kalman Filter for orbit determination, the equations of motion of the two body problem were propagated using Cowell's formulation. Four types of perturbing forces were added to the propagated model in order to increase the accuracy of the orbit prediction. These four perturbing forces are Earth oblateness, atmospheric drag, lunar gravitational forces and solar radiation pressure. Two cases were studied, the first being the implementation of site track measurements when the satellite was over the ground station. It is shown that large errors, upwards of ninety meters, grow as time from last measurement input increases. The next case studied was continuous measurement inputs from a GPS receiver on board the satellite throughout the orbit. This algorithm greatly decreased the errors seen in the orbit determining algorithm due to the accuracy of the sensor as well as the continuous measurement inputs throughout the orbit. It is shown that the accuracy of the orbit determining Kalman filter also depends on the length of time between each measurement update. The errors decrease as the time between measurement updates decreases. Next the Kalman filter is applied to determine the satellite attitude. The rotational equations of motion are propagated using Cowell's Formulation and numerical integration. To increase the fidelity of the model four disturbing torques are included in the rotational equations of motion model: gravity gradient torque, solar pressure torque, magnetic torque, and aerodynamic torque. Four cases were tested corresponding to four different on board attitude determining sensors: magnetometer, Earth sensor, sun sensor, and star tracker. A controlled altitude path was chosen to test the accuracy of each of these cases and it was shown that the algorithm using star tracker measurements was three hundred times more accurate than that of the magnetometer algorithm."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:3092"],"dc:identifier.uri":["http://hdl.handle.net/10919/49102"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Attitude","Orbit","Determination","Kalman Filter"],"dc:title":["Kalman Filter Implementation to Determine Orbit and Attitude of a Satellite in a Molniya Orbit"],"dc:type":["Thesis"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:00Z"}