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NASA NTRS2019

Optical Geolocation for Small Unmanned Aerial Systems

This paper presents an airborne optical geolocation system using four optical targets to provide position and attitude estimation for a sUAS supporting the NASA Acoustic Research Mission (ARM), where the goal is to reduce nuisance airframe noise during approach and landing. A large precision positioned microphone array captures the airframe noise for multiple passes of a Gulfstream III aircraft. For health monitoring of the microphone array, the Acoustic Calibration Vehicle (ACV) sUAS completes daily flights with an onboard speaker emitting tones at frequencies optimized for determining microphone functionality. An accurate position estimate of the ACV relative to the array is needed for microphone health monitoring. To this end, an optical geolocation system using a downward facing camera mounted to the ACV was developed. The 3D positioning of the ACV is computed using the pinhole camera model. A novel optical geolocation algorithm first detects the targets, then a recursive algorithm tightens the localization of the targets. Finally, the position of the sUAS is computed using the image coordinates of the targets, the 3D world coordinates of the targets, and the camera matrix. A Real-Time Kinematic GPS system is used to compare the optical geolocation system.

Dolph, Chester V.↗

NASA NTRS2023

Backup Optical Navigation Attitude for Artemis-1 Backup Attitude Ground Tool

The Backup Optical Navigation Attitude (BONA) software was developed as a response to the Artemis1 Power Distribution Unit (PDU) hardware problems found early in 2021. The hardware problem, a capacitor installed incorrectly, removes the intended redundant path for which the PDU can relay its power and data to attached devices. Specific to the BONA context, the concern is that a failure of the single remaining path in this PDU would lead to an inability to communicate with one of the two-star trackers (STs) on Orion. By flight rule, being reduced to a single star tracker means an immediate turn around end-of-mission. The BONA software is not intended to extend the mission, but instead act as a single star tracker attitude confirmation tool. Insurance, if you will, for the Orion project that a ground tool is available to compare the single remaining ST results with optical navigation images retrieved during the mission. Engineers operating BONA in the Mission Control Center (MCC) Mission Evaluation Room (MER) will analyze the downlinked star field images and based on the stars identified and known time of image, derive vehicle attitude estimates, which can be compared with the ST results. Potentially, in extreme situations, and with expert recommendation, the derivations could lead to navigation state updates being commanded to Orion.

GNC↗

NASA NTRSDate not supplied

Visual and Inertial Datasets for an eVTOL Aircraft Approach and Landing Scenario

A National Aeronautics and Space Administration (NASA) project developing computer vision algorithms for autonomous flight is producing real-world datasets with cameras mounted on aircraft. In related domains, such as autonomous driving, open datasets are key to innovation and advancement in computer vision and autonomous perception for future Advanced Air Mobility (AAM) operations. Few vision datasets, however, are publicly available in the aviation context. This paper introduces preliminary datasets containing several examples of approach and landing scenarios. The platform aircraft include a multirotor small unmanned aerial system (sUAS) and a crewed helicopter as surrogates for future electric vertical take-off and landing (eVTOL) aircraft. The dataset provides video imagery with associated inertial navigation system-global positioning system (INS-GPS) position and attitude estimates and other sensors. Surveyed locations of the visual features of the landing area are included. This dataset is the first to be released in an ongoing effort to collect and share large, diverse datasets relevant to autonomous aviation; community critique that can inform and improve future flight campaigns is welcome.

Nelson Brown↗

NASA NTRSDate not supplied

Optical Deep-Space Instrument for Navigation (ODIN)

The Optical Deep-Space Instrument for Navigation (ODIN) is a proposed multiple camera, multiple field of view, optical navigation (OPNAV) instrument currently under development. ODIN aims to create a self-sufficient system which can perform imaging target acquisition, star field based attitude estimation, and position estimation using horizon-based OPNAV of known celestial bodies. ODIN will complete these tasks autonomously, thereby contributing to the advancement of OPNAV as an option for truly autonomous mission operations.

Optical Navigation↗

NASA NTRSDate not supplied

Optical Deep-Space Instrument for Navigation (ODIN)

Optical Navigation↗

NASA NTRS2007

Using Visual Odometry to Estimate Position and Attitude

A computer program in the guidance system of a mobile robot generates estimates of the position and attitude of the robot, using features of the terrain on which the robot is moving, by processing digitized images acquired by a stereoscopic pair of electronic cameras mounted rigidly on the robot. Developed for use in localizing the Mars Exploration Rover (MER) vehicles on Martian terrain, the program can also be used for similar purposes on terrestrial robots moving in sufficiently visually textured environments: examples include low-flying robotic aircraft and wheeled robots moving on rocky terrain or inside buildings. In simplified terms, the program automatically detects visual features and tracks them across stereoscopic pairs of images acquired by the cameras. The 3D locations of the tracked features are then robustly processed into an estimate of overall vehicle motion. Testing has shown that by use of this software, the error in the estimate of the position of the robot can be limited to no more than 2 percent of the distance traveled, provided that the terrain is sufficiently rich in features. This software has proven extremely useful on the MER vehicles during driving on sandy and highly sloped terrains on Mars.

Maimone, Mark↗

NASA NTRS1997

Attitude and Trajectory Determination using Magnetometers and Estimated Rates

A simultaneous attitude and orbit determination algorithm which uses magnetometer measurements and estimated attitude rates is presented. This is an extension of an algorithm which uses magnetometer and rate gyro measurements. The new algorithm is intended for gyroless spacecraft, or in the case of gyro failures/saturation. Torque control input data is used in forming the rate estimates. Simulation tests of the algorithm are presented. First, tests were performed using the 'true' rate values at each time step. This simulated using accurate gyro measurements. Then, tests were performed estimating the rates. Using estimated rates rather than 'gyro measurements' did not significantly degrade the algorithm's performance if accurate estimates of the initial rates were available. An initial Root-Sum-Square (RSS) position error of 1,400 km was reduced to an average error of approximately 100 km within the first two minutes. The RSS attitude error converged to less than 1.5 degrees within three orbits.

Schierman, J. D.↗

NASA NTRS1988

Attitude determination and parameter estimation using vector observations

Procedures for attitude determination based on Wahba's loss function are generalized to include the estimation of parameters other than the attitude, such as sensor biases. Optimization with respect to the attitude requires either the singular value decomposition of a 3x3 matrix or finding the maximum eigenvalue and corresponding eigenvector of a 4x4 symmetric matrix, but does not require an a priori estimate of the attitude. Optimization with respect to the other parameters employs an iterative approach, which does require an a priori estimate of these parameters. Conventional state estimation methods require a priori estimates of both the parameters and the attitude, while the algorithms presented in this paper always compute the exact optimal attitude for given values of the parameters. The proposed method is shown to give the correct solution of an example problem. An expression for the covariance of the attitude and parameter estimates is derived.

Markley, F. Landis↗

NASA NTRS2000

A LEO Satellite Navigation Algorithm Based on GPS and Magnetometer Data

The Global Position System (GPS) has become a standard method for low cost onboard satellite orbit determination. The use of GPS as an attitude and rate sensor has also been developed in the recent past. Additionally, focus has been given to attitude and orbit estimation using the magnetometer, a low cost, reliable sensor. Combining measurements from both GPS and a magnetometer can provide a robust navigation system which takes advantage of the estimation qualities of both measurements. Ultimately a low cost, accurate navigation system can result, potentially eliminating the need for more costly sensors, including gyroscopes. This work presents the development and preliminary testing of a unified navigation algorithm which produces estimates of attitude, angular rate, position, and velocity for a low earth orbit (LEO) spacecraft. The system relies on GPS phase, range, and range rate data as well as magnetometer data. The algorithm used is an extended Kalman filter (EKF) developed to provide LEO attitude, orbit, and rate estimates using magnetometer and sun sensor data. Incorporating sun sensor data into the EKF improved the attitude and rate estimates. For many LEO spacecraft the sun data is available during only a portion of the orbit. However, GPS data is available continuously throughout the orbit. GPS can produce accurate orbit estimates and combining GPS and magnetometer data improves the attitude and rate estimates. The magnetometer based EKF can converge from large initial errors in position, velocity, and 3 attitude . Combining the magnetometer and GPS data into a single EKF will provide a more robust and accurate system. The EKF is based on an existing EKF. The GPS measurement models for phase, range, and range rate are incorporated into the existing structure of the filter. The original EKF produced the orbit estimates in terms of Keplerian elements. Due to the nature of the GPS measurements and ease of computation, the orbit estimates are converted to the Cartesian position and velocity. The measurement model for the magnetometer is adjusted for this change in the state and the measurements. Preliminary test results based on simulated GPS and magnetometer data are included.

Deutschmann, Julie↗

NASA NTRS1989

Attitude determination and parameter estimation using vector observations - Theory

Procedures for attitude determination based on Wahba's loss function are generalized to include the estimation of parameters other than the attitude, such as sensor biases. Optimization with respect to the attitude is carried out using the q-method, which does not require an a priori estimate of the attitude. Optimization with respect to the other parameters employs an iterative approach, which does require an a priori estimate of these parameters. Conventional state estimation methods require a priori estimates of both the parameters and the attitude, while the algorithm presented in this paper always computes the exact optimal attitude for given values of the parameters. Expressions for the covariance of the attitude and parameter estimates are derived.

Markley, F. Landis↗

NASA NTRS1994

Comparison of Kalman filter and optimal smoother estimates of spacecraft attitude

Given a valid system model and adequate observability, a Kalman filter will converge toward the true system state with error statistics given by the estimated error covariance matrix. The errors generally do not continue to decrease. Rather, a balance is reached between the gain of information from new measurements and the loss of information during propagation. The errors can be further reduced, however, by a second pass through the data with an optimal smoother. This algorithm obtains the optimally weighted average of forward and backward propagating Kalman filters. It roughly halves the error covariance by including future as well as past measurements in each estimate. This paper investigates whether such benefits actually accrue in the application of an optimal smoother to spacecraft attitude determination. Tests are performed both with actual spacecraft data from the Extreme Ultraviolet Explorer (EUVE) and with simulated data for which the true state vector and noise statistics are exactly known.

Sedlak, J.↗

NASA NTRS1986

Optimal estimation for the satellite attitude using star tracker measurements

An optimal estimation scheme is presented, which determines the satellite attitude using the gyro readings and the star tracker measurements of a commonly used satellite attitude measuring unit. The scheme is mainly based on the exponential Fourier densities that have the desirable closure property under conditioning. By updating a finite and fixed number of parameters, the conditional probability density, which is an exponential Fourier density, is recursively determined. Simulation results indicate that the scheme is more accurate and robust than extended Kalman filtering. It is believed that this approach is applicable to many other attitude measuring units. As no linearization and approximation are necessary in the approach, it is ideal for systems involving high levels of randomness and/or low levels of observability and systems for which accuracy is of overriding importance.

Lo, J. T.-H.↗

NASA NTRS2003

Pseudo Linear Gyro Calibration

Previous high fidelity onboard attitude algorithms estimated only the spacecraft attitude and gyro bias. The desire to promote spacecraft and ground autonomy and improvements in onboard computing power has spurred development of more sophisticated calibration algorithms. Namely, there is a desire to provide for sensor calibration through calibration parameter estimation onboard the spacecraft as well as autonomous estimation on the ground. Gyro calibration is a particularly challenging area of research. There are a variety of gyro devices available for any prospective mission ranging from inexpensive low fidelity gyros with potentially unstable scale factors to much more expensive extremely stable high fidelity units. Much research has been devoted to designing dedicated estimators such as particular Extended Kalman Filter (EKF) algorithms or Square Root Information Filters. This paper builds upon previous attitude, rate, and specialized gyro parameter estimation work performed with Pseudo Linear Kalman Filter (PSELIKA). The PSELIKA advantage is the use of the standard linear Kalman Filter algorithm. A PSELIKA algorithm for an orthogonal gyro set which includes estimates of attitude, rate, gyro misalignments, gyro scale factors, and gyro bias is developed and tested using simulated and flight data. The measurements PSELIKA uses include gyro and quaternion tracker data.

Harman, Richard↗

NASA NTRS1980

Wallops waveform analysis of SEASAT-1 radar altimeter data

Fitting a six parameter model waveform to over ocean experimental data from the waveform samplers in the SEASAT-1 radar altimeter is described. The fitted parameters include a waveform risetime, skewness, and track point; from these can be obtained estimates of the ocean surface significant waveheight, the surface skewness, and a correction to the altimeter's on board altitude measurement, respectively. Among the difficulties encountered are waveform sampler gains differing from calibration mode data, and incorporating the actual SEASAT-1 sampled point target response in the fitted wave form. There are problems in using the spacecraft derived attitude angle estimates, and a different attitude estimator is developed. Points raised in this report have consequences for the SEASAT-1 radar altimeter's ocean surface measurements are for the design and calibration of radar altimeters in future oceanographic satellites.

Hayne, G. S.↗

NASA NTRS2004

Pseudo Linear Attitude Determination of Spinning Spacecraft

This paper presents the overall mathematical model and results from pseudo linear recursive estimators of attitude and rate for a spinning spacecraft. The measurements considered are vector measurements obtained by sun-sensors, fixed head star trackers, horizon sensors, and three axis magnetometers. Two filters are proposed for estimating the attitude as well as the angular rate vector. One filter, called the q-Filter, yields the attitude estimate as a quaternion estimate, and the other filter, called the D-Filter, yields the estimated direction cosine matrix. Because the spacecraft is gyro-less, Euler's equation of angular motion of rigid bodies is used to enable the estimation of the angular velocity. A simpler Markov model is suggested as a replacement for Euler's equation in the case where the vector measurements are obtained at high rates relative to the spacecraft angular rate.

Harman, Richard R.↗

NASA NTRS2004

Pseudo-Linear Attitude Determination of Spinning Spacecraft

This paper presents the overall mathematical model and results from pseudo linear recursive estimators of attitude and rate for a spinning spacecraft. The measurements considered are vector measurements obtained by sun-sensors, fixed head star trackers, horizon sensors, and three axis magnetometers. Two filters are proposed for estimating the attitude as well as the angular rate vector. One filter, called the q-Filter, yields the attitude estimate as a quaternion estimate, and the other filter, called the D-Filter, yields the estimated direction cosine matrix. Because the spacecraft is gyro-less, Euler s equation of angular motion of rigid bodies is used to enable the estimation of the angular velocity. A simpler Markov model is suggested as a replacement for Euler's equation in the case where the vector measurements are obtained at high rates relative to the spacecraft angular rate. The performance of the two filters is examined using simulated data.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS1998

Efficient and Optimal Attitude Determination Using Recursive Global Positioning System Signal Operations

In this paper, a new and efficient algorithm is developed for attitude determination from Global Positioning System signals. The new algorithm is derived from a generalized nonlinear predictive filter for nonlinear systems. This uses a one time-step ahead approach to propagate a simple kinematics model for attitude determination. The advantages of the new algorithm over previously developed methods include: it provides optimal attitudes even for coplanar baseline configurations; it guarantees convergence even for poor initial conditions; it is a non-iterative algorithm; and it is computationally efficient. These advantages clearly make the new algorithm well suited to on-board applications. The performance of the new algorithm is tested on a dynamic hardware simulator. Results indicate that the new algorithm accurately estimates the attitude of a moving vehicle, and provides robust attitude estimates even when other methods, such as a linearized least-squares approach, fail due to poor initial starting conditions.

Crassidis, John L.↗

NASA NTRS2004

Kalman Filter Estimation of Spinning Spacecraft Attitude using Markley Variables

There are several different ways to represent spacecraft attitude and its time rate of change. For spinning or momentum-biased spacecraft, one particular representation has been put forward as a superior parameterization for numerical integration. Markley has demonstrated that these new variables have fewer rapidly varying elements for spinning spacecraft than other commonly used representations and provide advantages when integrating the equations of motion. The current work demonstrates how a Kalman filter can be devised to estimate the attitude using these new variables. The seven Markley variables are subject to one constraint condition, making the error covariance matrix singular. The filter design presented here explicitly accounts for this constraint by using a six-component error state in the filter update step. The reduced dimension error state is unconstrained and its covariance matrix is nonsingular.

Sedlak, Joseph E.↗