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A navigation system determines a position by referring to artificial or natural satellites or other space objects during daylight or when the objects are in a planet's shadow. A telescope and image sensor observe and image shadows of the objects as the objects transit the sun or a sunlit surface of

A navigation system determines a position by referring to artificial or natural satellites or other space objects during daylight or when the objects are in a planet's shadow. A telescope and image sensor observe and image shadows of the objects as the objects transit the sun or a sunlit surface of a planet or moon, thereby solving problems related to the two key times during which traditional SkyMark navigation is difficult or impossible.

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1. A position determining system, comprising: a telescope having a field of view and configured to point so as to include at least a portion of a bright celestial object in the field of view, wherein the bright celestial object comprises one of: the sun or a sunlit planet or a sunlit moon;a pixelate

1. A position determining system, comprising: a telescope having a field of view and configured to point so as to include at least a portion of a bright celestial object in the field of view, wherein the bright celestial object comprises one of: the sun or a sunlit planet or a sunlit moon;a pixelated image sensor optically coupled to an output of the telescope;a telescope position estimator configured to provide an estimated position of the telescope;a telescope pointing direction estimator configured to provide an estimated pointing direction of the telescope;a data source providing ephemeral information about a plurality of satellites;a clock providing a current time;a satellite shadow detector coupled to the pixelated image sensor and configured to detect a shadow cast on the pixelated image sensor by a satellite transiting the bright celestial object;a satellite identifier coupled to the satellite shadow detector and configured to identify the satellite based on: the estimated position of the telescope, the estimated pointing direction of the telescope, the current time and the ephemeral information about the plurality of satellites;an angle estimator coupled to the satellite shadow detector and configured to estimate an estimated angle to the satellite; anda navigation filter configured to generate an updated estimated position of the telescope based on: the estimated position of the telescope, an identification of the satellite, the estimated angle to the satellite and the ephemeral information about the plurality of satellites. 2. A position determining system according to claim 1, wherein the satellite shadow detector comprises: an edge detector configured to detect pixels of the pixelated image sensor on which an edge of the bright celestial object is projected by the telescope, thereby detecting the edge of the bright celestial object in an image provided by the pixelated image sensor;a temporal median filter configured to identify pixels of the image that represent a background, based on the edge of the bright celestial object;a subtractor configured to subtract the background from the image;a threshold calculator configured to determine an adaptive threshold value for the image;a candidate shadow pixel detector configured to select pixels of the image having respective values less than the adaptive threshold value, thereby detecting candidate shadow pixels;a pixel grouper configured to group at least one candidate shadow pixel of the image, thereby detecting at least one candidate satellite shadow; anda centroid calculator configured to calculate, for each candidate satellite shadow of the at least one candidate satellite shadow, a centroid of the candidate satellite shadow. 3. A position determining system according to claim 2, wherein the satellite shadow detector further comprises: a noise filter configured to compare the image to a previous frame of the image and to delete any candidate satellite shadow from the image that is absent from the previous frame of the image. 4. A position determining system according to claim 1, wherein the navigation filter is further configured to generate a further updated estimated position of the telescope based on: the updated estimated position of the telescope, another estimated angle to another satellite, based on a subsequent transit of a second bright celestial object by the another satellite and the ephemeral information about the plurality of satellites, wherein the second bright celestial object comprises one of: the bright celestial object or another bright celestial object. 5. A position determining system, comprising: a telescope having a field of view and configured to point so as to include at least a portion of a bright celestial object in the field of view, wherein the bright celestial object comprises one of: the sun or a sunlit planet or a sunlit moon;a pixelated image sensor optically coupled to an output of the telescope;a data source providing ephemeral information about a plurality of satellites;a clock providing current time; anda navigation filter coupled to the image sensor, the data source and the clock and configured to generate an updated estimated position of the telescope based on: an estimated position of the telescope, image data captured by the image sensor as a satellite transits the bright celestial object and the ephemeral information about the plurality of satellites. 6. A position determining system according to claim 5, wherein the image data comprises an estimated angle to a satellite transiting the bright celestial object, as imaged by the pixelated image sensor. 7. A method for determining a position, the method comprising: using a telescope and an image sensor to generate image data by imaging a bright celestial object as a satellite transits the bright celestial object, wherein the bright celestial object comprises one of: the sun or a sunlit planet or a sunlit moon;estimating a position of the telescope;estimating a pointing direction of the telescope;using the image data, the estimated position of the telescope and the estimated pointing direction of the telescope, calculating an angle involving the telescope and the satellite;reading a current time from a clock;accessing ephemeral data stored in a computer memory, the ephemeral data including ephemeral data about the satellite;using a navigation filter, the current time, the angle and the ephemeral data, estimating an updated position of the telescope; andrevising the estimated position of the telescope according to the updated position of the telescope. 8. A method according to claim 7, wherein calculating the angle comprises: detecting pixels of the image sensor on which an edge of the bright celestial object is projected by the telescope, thereby detecting the edge of the bright celestial object in the image data;identifying pixels in the image data that represent a background, based on the edge of the bright celestial object;subtracting the background from the image data;determining an adaptive threshold value for the image data;selecting pixels of the image data having respective values less than the adaptive threshold value, thereby detecting candidate shadow pixels;grouping at least one candidate shadow pixel of the image data, thereby detecting at least one candidate satellite shadow; andcalculating, for each of the at least one candidate satellite shadow, a centroid of the candidate satellite shadow. 9. A method according to claim 8, further comprising: comparing the image data to a previous frame of the image data; anddeleting any candidate satellite shadow from the image data that is absent from the previous frame of the image data. 10. A method according to claim 7, further comprising: using the telescope and the image sensor to generate further image data by imaging another satellite transiting a second bright celestial object, wherein the second bright celestial object comprises one of: the bright celestial object or another bright celestial object, and the ephemeral data includes ephemeral data about the other satellite;using the further image data, calculating a second angle involving the telescope and the other satellite;using the navigation filter, the second angle and the ephemeral data, estimating a further updated position of the telescope; andfurther revising the estimated position of the telescope according to the further updated position of the telescope. 11. A method according to claim 7, further comprising: using the telescope and the image sensor to generate further image data by imaging the satellite transiting a second bright celestial object, wherein the second bright celestial object comprises one of: the bright celestial object or another bright celestial object, wherein the another bright celestial object comprises one of: the sun or a sunlit planet or a sunlit moon;using the further image data, calculating a second angle involving the telescope and the satellite;using the navigation filter, the second angle and the ephemeral data, estimating a further updated position of the telescope; andfurther revising the position of the telescope according to the further updated position of the telescope. 12. A non-transitory computer-readable medium encoded with instructions that, when executed by a processor, establish processes for performing a computer-implemented method of determining a position, the processes comprising: a process that uses a telescope and an image sensor to generate image data by imaging a bright celestial object as a satellite transits the bright celestial object, wherein the bright celestial object comprises one of: the sun or a sunlit planet or a sunlit moon;a process that estimates a position of the telescope;a process that estimates a pointing direction of the telescope;a process that uses the image data, the estimated position of the telescope and the estimated pointing direction of the telescope to calculate an angle involving the telescope and the satellite;a process that reads a current time from a clock;a process that accesses ephemeral data stored in a computer memory, the ephemeral data including ephemeral data about the satellite;a process that uses a navigation filter, the current time, the angle and the ephemeral data to estimate an updated position of the telescope; anda process that revises the estimated position of the telescope according to the updated position of the telescope.