Attitude determination using earth horizon sensors

A method for spacecraft determining attitude, the method comprising:

• obtaining horizon sensor readings from a plurality of horizon sensors, each of the plurality of horizon sensors having a respective field-of-view (FOV), each of the plurality of horizon sensors having a sensitivity to the portion of the respective FOV obscured by Earth;
• determining an Earth disk radius in a spacecraft's body frame;
• converting the horizon sensor readings to nadir angles using an approximation selected in accordance with a sensitivity characteristic across the horizon sensor FOV;
• and
• estimating a nadir vector using the nadir angles and the Earth disk radius.

A method for spacecraft determining attitude, the method comprising:

• obtaining horizon sensor readings from a plurality of horizon sensors, each of the plurality of horizon sensors having a respective field-of-view (FOV), a sensitivity to the portion of the respective FOV obscured by Earth, and a boresight vector in a spacecraft body frame;
• determining an Earth disk radius in a spacecraft's body frame using a geocentric latitude of the spacecraft, an equatorial radius of the Earth, and a polar radius of the Earth;
• converting the horizon sensor readings to nadir angles;
• and
• estimating a nadir vector using the Earth disk radius and by finding the intersection of a plurality of cones, each cone defined by a boresight vector of a corresponding one of the plurality of horizon sensors and a corresponding one of the nadir angles.