Kinematic Approximation of Position Accuracy Achieved Using Optical Observations of Distant Asteroids

NASA's Deep Space 1 mission demonstrated that a spacecraft can be navigated autonomously during deep-space cruise operations using only optical navigation measurements. A methodology is developed to evaluate the feasibility and accuracy of the Deep Space 1 orbit determination approach throughout the solar system as a function of a spacecraft's imaging capabilities. Feasibility can be addressed by comparing the apparent magnitudes of the known population of asteroids against the imaging system capabilities. An upper limit on the accuracy of the spacecraft position estimate at a given location can be formulated by assuming observations of at least two asteroids simultaneously. Example results are presented for three camera implementations that span the range of capabilities flown in deep space to date using orbit and absolute magnitude data for 50,129 of the brightest known asteroids. Broadly speaking, achievable accuracies range from approximately 200 to 12,000 km (1 - sigma) interior to the main asteroid belt and from 50 to 2000 km within the main belt, depending strongly on the chosen camera implementation. Between the main belt and Jupiter, only a current state-of-the-art imaging system is consistently capable of kinematic positioning using only asteroids. Beyond Jupiter, there are insufficient known asteroids to support this approach without including images of planets and moons. Although these levels of accuracy are far inferior to those achievable with radiometric navigation, they may yet be sufficient to satisfy cruise-phase requirements for many deep-space missions.