The required number of detected stars, which we denote as Nmin, varies depending on the operating mode of the star tracker and the performance of the matching algorithm. If no previous attitude information is known, at least three stars are required to solve the lost-in-space (LIS) problem using star tracker measurements. This limit of three stars stems not from the solution for attitude using vector observations, which only requires two stars [7,8], but from the identification of stars within an image [9]. If only two stars are detected in an image, typically not enough information is known to identify one star from another. Therefore, at least one additional star is required.This lower bound of Nmin = 3 represents the most optimistic case, which implies the matching algorithm can correctly identify each star based on the respective three-star pattern.
Due to pattern ambiguity in the star catalog, this lower bound is commonly increased to Nmin = 4, which is a more conservative representation of matching performance. Once the attitude of the spacecraft is known, the star tracker can switch into a tracking mode. In this mode, only two stars are generally required in each image to determine the incremental change in attitude between sequential images (Nmin = 2). For this study, we assume that pattern ambiguity is not a limiting factor and define the availability of an attitude solution by Nmin = 3. One problem with this definition is that it conflates stochastic effects (star detection) with non-stochastic effects (star distribution, slew rates, tracking modes, etc.
) and, therefore, is difficult to quantify over a range of operating conditions.Throughout the design and development process of a star tracker, several different models are used to predict the availability performance of the sensor. The lowest fidelity models generally assume idealized (static) imaging conditions and are useful for examining the top level performance of candidate optical systems [1,4]. These models are typically based on a fixed stellar detection threshold, mt, which is used in conjunction with the sensor field of view (FOV) to determine the number of detectable stars for a given sensor orientation. Repeating this calculation over a large number of orientations, equally spaced across the celestial sphere, yields an idealized measure of star tracker availability.
The fixed mt is typically defined by a minimum SNR set by the noise of the image detector and the size of the sensor’s point spread function (PSF). This type of model is summarized by the first row of Figure 1.Figure 1.Commonly used types Anacetrapib of availability testing.A step up from the lowest fidelity are various models that explicitly include the effects of slew rate. These models utilize a dynamic stellar detection threshold that is based on the slew rate, mt = f (��), and a minimum star SNR [10,11].