An orbital gyrocompass heading reference for satellite vehicles.

Abstract

Achievement of a high-accuracy indication of the deviation of a satellite vehicle from the orbit plane about a vertical by gyrocompassin g techniques requires either extremely tight vehicle control or data handling in stabilized coordinates. Using the latter approach, this paper develops the mathematical model and error relationships. Two configurations, vertical and horizontal damping, are described, and it is shown that the former emphasizes low-fre- quency horizon sensor and gyro errors, whereas the latter emphasizes their high-frequency characteristics. It is shown that a systematic error due to earth's oblateness, if uncom- pensated, may be dominant and can produce over 0.1° of error at satellite altitudes of 250 naut miles. With appropriate compensation for this and horizon sensor biases, rms heading errors in the neighborhood of 1 arc-min may be achieved. O obtain an accurate indication of azimuth relative to the orbit plane by gyrocompassin g techniques requires the inertial data to be stabilized against vehicle motion. Using a stabilized platform technique, this paper develops a mathe- matical model for the orbital gyrocompass based on marine gyrocompass principles. A significant error source is shown to be a forced oscillation induced in the gyrocompass loop by the earth's oblateness. Because this error is systematic, it can be largely removed if the system has sufficient computa- tional capacity. An additional important source of error is the vertical reference sensor error, and the system is analyzed in terms of a mathematical model of horizon sensor noise. Determination of a vehicle's heading relative to the orbit plane by gyrocompassin g techniques may, in principle, be ac- complished by strapping down to the vehicle a rate gyro sensor whose input axis is in the nominal plane of the orbit. plane, the orbit rate sensor gyro must be stabilized. One method of achieving this objective, while still maintaining the desired property of dynamic exactness with respect to vehicle attitude motions, calls for making use of a stable platform with three orthogonal degrees of gyro freedom. Precession of the vertical in space at an average vector rate equivalent to orbital rate is required. With this constraint, the deviation of the vehicle orientation from the plane of the orbit may be deter- mined. Consider the coordinate system and angular transforma- tions described in Fig. 1. The unprimed coordinates are ref- erence coordinates and are defined by the orbit momentum vector and the vertical. The primed coordinates represent inertial platform coordinates. When the order of coordinate rotation is sequentially taken about Z, Y, X, the transforma- tion between angular rates in the unprimed and primed refer- ence axes are