Dual Cone-Scanning Horizon Sensor Orbit and Attitude Corrections for Earth Oblateness

Abstract

I NFRARED-SCANNING horizon sensors are typically used as attitude sensors for spinning and three-axis stabilized satellites. The nadir vector or the nadir angle is determined by detecting the infrared radiation at the horizon with infrared detectors and pencil beams. By integrating the scanning horizon sensors with other sensors, both orbit and attitude can be determined. Examples of such systems include the Microcosm Autonomous Navigation System (MANS) [1,2], which uses dual cone scanners and two slit sun/moon sensors, and the Multimission Attitude Determination and Autonomous Navigation System [3], which employs one scanning horizon sensor and three star sensors. The accuracy of a scanning horizon sensor is limited by random instrumental errors and systematic errors arising from the seasonal variation in Earth’s radiance, the oblate shape of the Earth and satellite altitude variations, the ambient temperature of the sensors, changes in the spin/scan period, and misalignment and biases [4,5]. The random errors can be reduced by increasing the number of measurements that are used in the estimator [6]. However, the systematic errors cannot be reduced in a simple manner. Alex and Shrivastava [4] summarized the error budget for scanning Earth sensors and derived simple relations by using least-squares curve fitting for the on-board correction of systematic errors. With the corrections, the amplitude of the total error is reduced to nearly oneeighth of the original amplitude. Alex and Seshamani [7] established a generalized analytical model of the radiation that can be used to correct the attitude errors induced by the variation of the location and the seasons in Earth’s infrared horizon. Van der Ha [6,8,9], Palimaka et al. [10], Sullivan et al. [11], and Fraiture [12], etc., have studied the effects of bias errors in the sensor measurements and have provided useful methods to reduce the errors. Of these systematic errors, the Earth’s oblateness contributes one of the more significant effects on determination of the nadir vector or the nadir angle [13]. The impact of the oblateness of the Earth on attitude estimation accuracy has been studied in Wertz [14] and the references therein. Roll and pitch errors correction algorithms for the Earth’s oblateness were proposed in Tekawy et al. [13] and Li [15], and also in Hablani [5] with altitude correction, but they all require the satellite’s position information. The impact of the Earth’s oblateness on the nadir vector determination, which can be used for orbit and attitude determination, has not yet been studied. In this note, the systematic error caused by oblateness for a dual cone sensor (DCS) is considered, and the orbit and attitude corrections for the Earth’s oblateness are presented. Compared with themethods described in Hablani [5], Tekawy et al. [13], and Li [15], the problem is transferred from the roll and pitch angle errors’ correction to nadir vector determination around the oblate Earth. According to the principle of measurement, an algorithm determining the nadir vector that accounts for the Earth’s oblateness is derived with the Gauss-Newton method. The nadir vector information, combined with the measurements of other sensors, can be used for orbit determination as well as attitude determination. The nadir vector determination algorithm is verified, and the orbit and attitude corrections for the Earth’s oblateness is illustrated by an integrated algorithm of least-squares orbit determination and twovector attitude determination based on the orientation information of the sun, Earth and moon.