The NASA Independent Verification and Validation (IV&V) Program's Independent Test Capability (IT... more The NASA Independent Verification and Validation (IV&V) Program's Independent Test Capability (ITC) team has developed a set of simulation technologies, called NASA Operational Simulator (NOS), which demonstrate a paradigm shift in the resources required for embedded software development. NOS technologies promote reusability of software simulation products across multiple missions, reducing mission cost and schedule risk. NOS technologies provide a means to simulate hardware in a software environment, enabling advanced verification and validation activities. NOS technologies have been utilized in the testing of several large spacecraft systems and subsystems to include the James Webb Space Telescope, Global Precipitation Measurement, Juno, and Deep Space Climate Observatory missions. On these missions, the technologies have demonstrated significant value to several user groups: software development, mission operations, verification and validation, test procedure development and check-out.
International Journal of Navigation and Observation, 2011
Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning Sys... more Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithm for attitude estimation, various methods of calculating the matrix square root were discussed and compared. Specifically, the diagonalization method, Schur method, Cholesky method, and five different iterative methods were compared. Additionally, a different method of handling the matrix square root requirement, the square-root UKF (SR-UKF), was evaluated. The different matrix square root calculations were compared based on computational requirements and the sensor fusion attitude estimation performance, which was evaluated using flight data from an Unmanned Aerial Vehicle (UAV). The roll and pitch angle estimates were compared with independently measured values from a high quality mechanical vertical gyroscope. This manuscript represents the first comprehensive analysis of the matrix square root calculations in the context of UKF. From this analysis, it was determined that the best overall matrix square root calculation for UKF applications in terms of performance and execution time is the Cholesky method.
AIAA Guidance, Navigation, and Control Conference, 2011
ABSTRACT This document presents a sensitivity analysis relative to different algorithm design par... more ABSTRACT This document presents a sensitivity analysis relative to different algorithm design parameters on the attitude performance of two different Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithms for estimating aircraft attitude angles, namely the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). The sensor fusion was performed using flight data acquired with three different WVU YF-22 research aircraft under a variety of flight conditions. The attitude estimates were compared with direct ‘truth’ measurements from an on-board mechanical vertical gyroscope. The sensitivity analysis was conducted on the following parameters: process and measurement noise covariance tuning, IMU and GPS sampling rates, GPS outages, time offset between GPS and IMU measurements, and acceleration due to gravity. Overall, the EKF and UKF performed very similarly in response to the different parameters for this study.
The extended Kalman filter (EKF) and unscented Kalman filter (UKF) for nonlinear state estimation... more The extended Kalman filter (EKF) and unscented Kalman filter (UKF) for nonlinear state estimation with both additive and nonadditive noise structures are presented and compared. Three different Global Positioning System (GPS)/inertial navigation system (INS) sensor fusion formulations for attitude estimation are used as case studies for the nonlinear state estimation problem. A diverse set of actual flight data collected from research unmanned aerial vehicles was used as empirical data for this study. Roll and pitch estimation results were compared with independent measurements from a mechanical vertical gyroscope to evaluate the performance. The performance of the EKF and UKF is compared in terms of noise assumptions, covariance matrix tuning, sampling rate, initialization error, GPS outages, robustness to inertial measurement unit bias and scale factors, and linearization. Similar sensitivity for this GPS/INS attitude estimation problem was found between the EKF and UKF for most cases. Small differences were seen between EKF and UKF for initialization error and GPS outages: the UKF was found to be more robust to inertial measurement unit calibration errors, and the EKF was determined to be more computationally efficient.
AIAA Guidance, Navigation, and Control Conference, 2012
Attitude estimation using Global Positioning System/Inertial Navigation System (GPS/INS) was used... more Attitude estimation using Global Positioning System/Inertial Navigation System (GPS/INS) was used as an example application to study three different methods of fusing redundant multi-sensor data used in the prediction stage of a nonlinear recursive filter. Experimental flight data were collected with an Unmanned Aerial Vehicle (UAV) containing GPS position and velocity calculations and four redundant Inertial Measurement Unit (IMU) sensors. Additionally, the aircraft roll and pitch angles were measured directly with a high-quality mechanical vertical gyroscope to be used as a 'truth' reference for evaluating attitude estimation performance. A simple formulation of GPS/INS sensor fusion using an Extended Kalman Filter (EKF) was used to calculate the results for this study. Each of the three presented fusion methods was shown to be effective in reducing the roll and pitch errors as compared to corresponding results using single IMU GPS/INS sensor fusion. Additionally, the fusion methods were shown to be effective in estimating roll and pitch angles without the aid of GPS (dead reckoning).
The NASA Independent Verification and Validation (IV&V) Program's Independent Test Capability (IT... more The NASA Independent Verification and Validation (IV&V) Program's Independent Test Capability (ITC) team has developed a set of simulation technologies, called NASA Operational Simulator (NOS), which demonstrate a paradigm shift in the resources required for embedded software development. NOS technologies promote reusability of software simulation products across multiple missions, reducing mission cost and schedule risk. NOS technologies provide a means to simulate hardware in a software environment, enabling advanced verification and validation activities. NOS technologies have been utilized in the testing of several large spacecraft systems and subsystems to include the James Webb Space Telescope, Global Precipitation Measurement, Juno, and Deep Space Climate Observatory missions. On these missions, the technologies have demonstrated significant value to several user groups: software development, mission operations, verification and validation, test procedure development and check-out.
International Journal of Navigation and Observation, 2011
Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning Sys... more Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithm for attitude estimation, various methods of calculating the matrix square root were discussed and compared. Specifically, the diagonalization method, Schur method, Cholesky method, and five different iterative methods were compared. Additionally, a different method of handling the matrix square root requirement, the square-root UKF (SR-UKF), was evaluated. The different matrix square root calculations were compared based on computational requirements and the sensor fusion attitude estimation performance, which was evaluated using flight data from an Unmanned Aerial Vehicle (UAV). The roll and pitch angle estimates were compared with independently measured values from a high quality mechanical vertical gyroscope. This manuscript represents the first comprehensive analysis of the matrix square root calculations in the context of UKF. From this analysis, it was determined that the best overall matrix square root calculation for UKF applications in terms of performance and execution time is the Cholesky method.
AIAA Guidance, Navigation, and Control Conference, 2011
ABSTRACT This document presents a sensitivity analysis relative to different algorithm design par... more ABSTRACT This document presents a sensitivity analysis relative to different algorithm design parameters on the attitude performance of two different Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithms for estimating aircraft attitude angles, namely the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). The sensor fusion was performed using flight data acquired with three different WVU YF-22 research aircraft under a variety of flight conditions. The attitude estimates were compared with direct ‘truth’ measurements from an on-board mechanical vertical gyroscope. The sensitivity analysis was conducted on the following parameters: process and measurement noise covariance tuning, IMU and GPS sampling rates, GPS outages, time offset between GPS and IMU measurements, and acceleration due to gravity. Overall, the EKF and UKF performed very similarly in response to the different parameters for this study.
The extended Kalman filter (EKF) and unscented Kalman filter (UKF) for nonlinear state estimation... more The extended Kalman filter (EKF) and unscented Kalman filter (UKF) for nonlinear state estimation with both additive and nonadditive noise structures are presented and compared. Three different Global Positioning System (GPS)/inertial navigation system (INS) sensor fusion formulations for attitude estimation are used as case studies for the nonlinear state estimation problem. A diverse set of actual flight data collected from research unmanned aerial vehicles was used as empirical data for this study. Roll and pitch estimation results were compared with independent measurements from a mechanical vertical gyroscope to evaluate the performance. The performance of the EKF and UKF is compared in terms of noise assumptions, covariance matrix tuning, sampling rate, initialization error, GPS outages, robustness to inertial measurement unit bias and scale factors, and linearization. Similar sensitivity for this GPS/INS attitude estimation problem was found between the EKF and UKF for most cases. Small differences were seen between EKF and UKF for initialization error and GPS outages: the UKF was found to be more robust to inertial measurement unit calibration errors, and the EKF was determined to be more computationally efficient.
AIAA Guidance, Navigation, and Control Conference, 2012
Attitude estimation using Global Positioning System/Inertial Navigation System (GPS/INS) was used... more Attitude estimation using Global Positioning System/Inertial Navigation System (GPS/INS) was used as an example application to study three different methods of fusing redundant multi-sensor data used in the prediction stage of a nonlinear recursive filter. Experimental flight data were collected with an Unmanned Aerial Vehicle (UAV) containing GPS position and velocity calculations and four redundant Inertial Measurement Unit (IMU) sensors. Additionally, the aircraft roll and pitch angles were measured directly with a high-quality mechanical vertical gyroscope to be used as a 'truth' reference for evaluating attitude estimation performance. A simple formulation of GPS/INS sensor fusion using an Extended Kalman Filter (EKF) was used to calculate the results for this study. Each of the three presented fusion methods was shown to be effective in reducing the roll and pitch errors as compared to corresponding results using single IMU GPS/INS sensor fusion. Additionally, the fusion methods were shown to be effective in estimating roll and pitch angles without the aid of GPS (dead reckoning).
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