Atmospheric Polarization and Stellar Position as Alignment Aids and Updates to a Kalman Filter
Thomas Wheeler and Brian Michels, General Dynamics Mission Systems
Location: Ballroom A
Date/Time: Monday, Jun. 12, 2:50 p.m.
In recent years, the problem of navigating in a GPS-contested environment has spurred innovation in navigation techniques and sensor design. We propose a navigation suite which combines traditional sensors (accelerometers, gyroscopes, barometer, odometer) with skyward-facing optical aids which can provide position and yaw information. In particular, the SkyPASS® sensor from Polaris Sensor Technologies provides position and yaw information by sensing sky polarization and the sun direction during daytime and twilight hours. To cover night hours, we augment the system with a small optical camera and implement a stellar matching algorithm. We believe this to be two largely untapped areas of complimentary PNT research; while there are a few papers on rover-based navigation using a stellar sensor, the inclusion of atmospheric polarization in the solution seems to be novel. We demonstrate, in both covariance analysis and a real-time navigation algorithm, that the addition of these optical sensors can provide roughly order-of-magnitude improvement in navigation accuracy.
In the daytime solution, we use SkyPASS® only as a Kalman update, though it may be possible to initialize latitude, longitude, and yaw with SkyPASS® information. The sensor provides measurements from two channels: a polarimetric channel and a Sun channel. The polarimetric channel provides a heading measurement that is based on the polarization pattern of the atmosphere. This makes for a simple measurement update by merely subtracting the measurement from a filter state as a residual. The Sun channel provides a measure of azimuth and elevation of the Sun. To remove possible filter instabilities, we chose to convert these measurements into relative right ascensions and declinations. To create residuals, right ascension and declination values were calculated based on the low-precision formulas for the Sun as found in the Astronautical Almanac. All measurements required novel derivations of the observation mapping (H) matrix.
We collected sensor data from a car-based platform and sent the data through two versions of the navigation filter: one including the SkyPASS® and one without. We used a VectorNav VN300 IMU for inertial, barometric, and dual GPS data (for reference position and heading). Results show that the polarimetric heading provides a reasonable degree of accuracy. This paired with the Sun channel bound heading uncertainty in the order of a 0.1 degree. The Sun channel provides great position improvement as well. In a test of approximately an hour duration and roughly 60 miles driven without GPS measurements, horizontal errors are roughly 1,500 meters with SkyPASS® as opposed to 35,000 meters. We also believe that the SkyPASS® can provide enough information to also serve as an initial alignment aid, however that has not yet been implemented and tested.
The night-time stellar system was implemented with a Raspberry Pi HQ camera and a simple 12mm f/1.6 lens. We use a simple threshold when computing centroids, and then match centroid indices with star catalog indices using an algorithm similar to the Pyramid Technique from Mortari, et al. If enough centroids are identified with stars, we can compute the Direction Cosine Matrix (DCM) between the camera frame and the inertial frame using the Fast Optimal Attitude Matrix algorithm from Markley. As described by Enright, et al., we can use this DCM to compute other quantities, depending on which information is available. For example, if tilts (obtained with stationary accelerometer data) and time (obtained from a real-time clock) are available, we can solve for latitude, longitude, and yaw, which we use to initialize the navigation filter without the need for GPS. If position, attitude, and time are all available, we can use the stellar DCM to solve for the precise camera installation angles during calibration.
We were able to demonstrate that an inexpensive stellar system can provide user position and heading in real time without the need for GPS, magnetometers, or other aids. With only a real-time clock, barometer, IMU, and camera, we can determine initial position and attitude with reasonable accuracy. During navigation, this update could be quite helpful, though we have not yet implemented the navigation filter updates. Clearly, there are weather, time-of-day, and environmental limitations to such a system.
In summation, combining these two technologies in an inertial navigation filter allows for a continuous, GPS-free navigation solution at any time of day.