Modeling of roll/pitch determination with horizon sensors - Oblate Earth

Abstract

Fairly complete analytical models are developed, relating horizon sensor locations, measurements and their mounting geometry with rolUpitch attitude of a spacecraft orbiting an oblate earth. Two arrangements of a pair of horizon sensors are considered: left and right of the velocity vector (that is, along the pitch axis), and aft and forward (along the roll axis). RolYpitch oblateness corrections are formulated involving a) noncircularity of earth disc and b) slight changes in azimuth angles of horizon crossing points and in scanwheel angles spanning the earth. A simple algorithm is developed to determine these small changes numerically, arriving at results in agreement with those in the literature. The analysis retains only the first order terms of the flattening factor in a standard oblateness model. The rolYpitch corrections thus computed are compared with the alternate closed-form rolYpitch components of the angle between geodetic and geocentric normals along the spacecraft orbit. This alternate approach is also developed in the paper. The two approaches yield nearly the same result if a spacecraft is equipped with a pair of sensors, suggesting, in that circumstance, the use onboard of the simple closed-form expressions for oblateness corrections, independent of sensor geometry and location. However, if due to cost weight, or configuration constraints, only one earth sensor is used, the corrections will then depend on the sensor geometry and location and may be determined for a given orbit before flight, and stored numerically, to minimize processing load on the flight computer.