Imaging system and method for attitude determination
The subject matter disclosed herein is generally directed towards systems and methods for estimating vehicle attitude information using position data of stars and astronomical objects in the sky. Considerable advantages may be realized by equipping vehicles with low-cost star trackers adequate for filtering images based on statistical-based techniques, which could provide a robust and reliable attitude determination. The methods described herein provide algorithms to reduce the amount of processing capacity and memory for finding stars and astronomical objects. In some instances, the provided systems and methods allow the prediction of the next location of the stars and/or other astronomical objects to enhance the search by looking for them at the predicted location. The algorithms may be applied in real-time and are suitable for movable platforms with limited resources such as satellites and spacecraft.
1 . An imaging system for attitude determination, the imaging system comprising:
one or more imaging sensors comprising a plurality of pixel sensors and configured to capture at least one image having a plurality of pixels; and
one or more processors configured to:
instruct the one or more imaging sensors to capture the at least one image having a plurality of pixels;
filter the at least one image, based at least in part on statistical-based techniques, to detect one or more centroid candidates, by filtering some or all the pixels of the plurality of pixels of the at least one image based at least in part on a hypothesis test;
identify, based at least in part on the one or more centroid candidates, one or more stars;
generate a mapping between the one or more stars and the one or more centroid candidates; and
estimate an attitude, based on the mapping;
wherein the hypothesis test comprises computing statistical values in a window of the at least one image to test one or more hypotheses to determine the one or more centroid candidates, the window having a size of one or more pixels, and determining whether a likelihood metric is above, equal or below a threshold value; and
wherein the threshold value is a variable threshold value adjusted based on a priori information;
wherein the window is slid over the at least one image to compute the statistical values in selected one or more sub-regions of the at least one image;
wherein the one or more sub-regions are determined based at least in part on a hint, the hint including an attitude hint or a centroid hint; and
wherein the attitude hint is determined by the steps comprising:
before capturing the at least one image, capturing a plurality of subsequent images;
determining, based at least in part on a first image and a second image of the plurality of subsequent images, a first order angular velocity estimate; and
determining, based at least in part upon the first order angular velocity estimate, an attitude estimate associated to the at least one image, to obtain the attitude hint.
2 . The imaging system according to claim 1 ,
wherein the one or more processors are configured to slide the window over the at least one image to compute the statistical values in all the pixels of the at least one image, and
wherein preferably the one or more processors are configured to slide the window over the at least one image from a first position to a second position by one pixel at a time such that the relative displacement from the first position to the second position is the size of a pixel or a multiple thereof, and the one or more pixels of the window in the first position overlap by at least one pixel the pixels of the window in the second position.
3 . The imaging system according to claim 1 , wherein, for computing the statistical values, the one or more processors are further configured to perform at least one of: computing a likelihood of occurrence of a hypothesis, or computing the likelihood metric.
4 . The imaging system according to claim 3 , wherein computing the likelihood metric comprises weighting or relating the likelihood of occurrence of two or more hypotheses.
5 . The imaging system according to claim 3 , wherein computing the likelihood of occurrence of a hypothesis comprises:
setting a hypothesis model;
estimating statistical parameters of the hypothesis model based at least in part on a pixel parameter, wherein the statistical parameters are estimated so that the hypothesis has a maximum likelihood of occurrence;
computing the likelihood of occurrence of the hypothesis based at least in part on the statistical parameters.
6 . The imaging system according to claim 5 ,
wherein a first hypothesis is set as a null hypothesis and is modeled based on a statistical distribution; and a second hypothesis is set as an alternative hypothesis and is modeled based at least in part on a star characteristic including star shape, star quantity or star magnitude,
wherein preferably the statistical distribution represents image noise and comprises at least one of a Gaussian distribution, a Poisson distribution, or a statistical distribution modeling stray light; and
wherein preferably a model of the second hypothesis comprises a combination of a function representing a star shape and a statistical distribution representing image noise; the function representing the star shape comprising at least one of a Gaussian bell, a saturated Gaussian bell, a sinc function, a square waveform, a rectangular waveform, a sawtooth waveform, or a triangle waveform.
7 . The imaging system according to claim 6 , wherein the one or more processors are further configured to compute the likelihood metric, comprising calculating a quotient of the likelihood of occurrence of the second hypothesis divided by the likelihood of occurrence of the first hypothesis.
8 . The imaging system according to claim 1 , wherein the variable threshold value is different for different pixels or windows in the at least one image.
9 . The imaging system according to claim 8 , wherein the variable threshold value is determined based at least in part on a Bayesian interpretation associated with the likelihood metric, and wherein computing the likelihood metric comprises calculating a quotient between two a priori probabilities associated with the presence of a centroid candidate.
10 . The imaging system according to claim 1 , wherein the imaging system is all or partially on-board a movable platform including a manned or unmanned aerial, spatial, maritime or terrestrial vehicle.
11 . A method for attitude determination of a vehicle, the method comprising:
detecting one or more centroid candidates in at least one image by filtering the at least one image based at least in part on statistical-based techniques, wherein the filtering comprises filtering some or all of the pixels of a plurality of pixels of the at least one image based at least in part on a hypothesis test;
matching the one or more centroid candidates to astronomical objects to obtain matches;
determining, based on the matches, a transformation factor; and
determining, based on the transformation factor, the attitude of the vehicle;
wherein the hypothesis test comprises computing statistical values in a window of the at least one image to test one or more hypotheses to determine the one or more centroid candidates, the window having a size of one or more pixels, and determining whether a likelihood metric is above, equal or below a threshold value;
wherein the threshold value is a variable threshold value adjusted based on a priori information;
wherein the window is slid over the at least one image to compute the statistical values in selected one or more sub-regions of the at least one image;
wherein the one or more sub-regions are determined based at least in part on a hint, the hint including an attitude hint or a centroid hint; and
wherein the attitude hint is determined by the steps comprising:
before capturing the at least one image, capturing a plurality of subsequent images;
determining, based at least in part on a first image and a second image of the plurality of subsequent images, a first order angular velocity estimate; and
determining, based at least in part upon the first order angular velocity estimate, an attitude estimate associated to the at least one image, to obtain the attitude hint.
12 . The method according to claim 11 , further comprising at least one of removing background noise from the at least one image, clustering pixels from the at least one image to obtain clusters, and determining cluster centroids to obtain centroid candidates.
13 . The method according to claim 11 , further comprising capturing at least one image by an imaging system on-board the vehicle, the vehicle a manned or unmanned aerial, spatial, maritime or terrestrial vehicle.
14 . The method according to claim 11 , wherein matching the one or more centroid candidates to astronomical objects to obtain matches comprises searching for the astronomical objects in an astronomical objects catalog, and the method further comprises predicting, based on the attitude hint, a position of the astronomical objects in a subsequently captured image, to obtain one or more centroid hints for the subsequently captured image.
15 . The method according to claim 14 , wherein the method further comprises searching for the matches in a portion of the astronomical objects catalog based, at least in part, on the one or more centroid hints and on a field-of-view of an imaging sensor, the imaging sensor configured to capture the at least one image and the subsequently captured image.
16 . The method according to claim 14 , wherein the method further comprises:
predicting, based on the one or more centroid hints, additional astronomical objects within a field-of-view of an imaging sensor;
projecting the additional astronomical objects into the field-of-view of the imaging sensor;
and matching the one or more centroid candidates to the additional astronomical objects to obtain matches.