Systems and methods for autonomous operations of ground station networks

A method for providing control vectors to a ground station network comprising:

• receiving information on one or more ground stations, where every individual ground station has a location, and where the every ground station comprises an aperture and further comprises a pointing system in mechanical communication with the aperture, where the pointing system establishes the aperture at a specific azimuth and a specific elevation in accordance with a control vector uj(t) provided to the every ground station;
• receiving a time horizon, where the time horizon comprises an initial time t0 and a final time tf;
• receiving position data, where the position data establishes a position for every satellite comprising a plurality of satellites at one or more time periods comprising the time horizon;
• establishing one or more time marks tk, where each time mark tk is a time later than or equal to the initial time t0 and earlier than or equal to the final time tf;
• formulating a cost function, where the cost function comprises an addend Aj(tk) for each specific ground station j comprising the one or more ground stations at each time mark tk, where the addend Aj(tk) comprises:
• a Benefit Value Function for each particular satellite i comprising the plurality of satellites, where the Benefit Value Function comprises:
• a value vij(tk) where the value vij (tk) is dependent on a slant range rij(tk) between the each specific ground station j and the each particular satellite i, where the slant range rij(tk) is based on the location of the each specific ground station j and a position pi(tk) for the each particular satellite i at the each time mark tk, where the position pi(tk) is determined using the position data;
• and
• a target size Tij(tk) where the target size Tij(tk) is dependent on a potential orientation Oj(tk) over at least an interval of the potential orientation Oj(tk) and dependent on the position pi(tk), where the potential orientation Oj(tk) defines an elevation angle and an azimuth angle of the aperture of the each specific ground station j at the each time mark tk;
• and
• a slewing cost Gij(tk), where the slewing cost Gij(tk) is dependent on the potential orientation Oj(tk) over at least the interval of the potential orientation Oj(tk) and dependent on the direction of the slant range rij(tk), thereby formulating the cost function where the cost function comprises a plurality of potential orientations Oj(tk);
• optimizing the cost function and quantifying each potential orientation Oj(tk) in the plurality of potential orientations Oj(tk), thereby generating a plurality of operational orientations Oj(tk);
• providing the control vector uj(t) to the every individual ground station, where the control vector uj(t) provided to the every individual ground station defines at least one operational orientation Oj(tk) comprising the plurality of operational orientations Oj(tk), thereby providing control vectors to the ground station network;
• operating the each specific ground station j in accordance with the control vector uj(t) at one or more of the one of the one or more time marks;
• and
• exchanging communications between at least one ground station comprising the one or more ground stations and at least one satellite comprising the plurality of satellites.

An apparatus for communicating with a plurality of satellites using one or more ground stations comprising:

• the one or more ground stations, where every individual ground station has a location, and where the every individual ground station comprises an aperture and further comprises a pointing system in mechanical communication with the aperture, and the pointing system configured to establish the aperture at a specific azimuth and a specific elevation in accordance with a control vector uj(t);
• and
• a digital processor in communication with each of the one or more ground stations, the digital processor comprising a memory and the memory storing instructions executable by the digital processor, the instructions comprising:
• receiving a time horizon where the time horizon defines an elapsed time from an initial time t0 to a final time tf;
• receiving position data, where the position data establishes a position for every satellite comprising the plurality of satellites at one or more time periods comprising the time horizon;
• establishing one or more time marks tk, where each time mark tk is a time later than or equal to the initial time t0 and earlier than or equal to the final time tf;
• determining a target size Tij(tk) by evaluating a target size equation Tij(t) at the each time mark tk, where an absolute value of the target size equation Tij(t) increases over at least an interval of a potential orientation Oj(tk) as a vector dot product of the potential orientation Oj(tk) and a unit vector of a slant range rij(tk) increases;
• determining a slewing cost Gij(tk) by evaluating a slewing cost equation Gij(t) at the each time mark tk, where an absolute value of the slewing cost equation Gij(t) decreases over at least the interval of the potential orientation Oj(tk) as the vector dot product of the potential orientation Oj(tk) and the unit vector of the slant range rij(tk) increases;
• formulating a cost function, where the cost function comprises an addend Aj(tk) for each specific ground station j comprising the one or more ground stations at each time mark tk, where the addend Aj(tk) comprises:
• a Benefit Value Function for each particular satellite i comprising the plurality of satellites, where the Benefit Value Function comprises:
• a value vij(tk) where the value vij(tk) is dependent on the slant range rij(tk) between the each specific ground station j and the each particular satellite i, where the slant range rij(tk) is based on the location of the each specific ground station j and a position pi(tk) for the each particular satellite i at the each time mark tk, where the position pi(tk) is determined using the position data;
• and
• the target size Tij(tk) where the target size Tij(tk) is dependent on the potential orientation Oj(tk) over at least an interval of the potential orientation Oj(tk) and dependent on the position pi(tk), where the potential orientation Oj(tk) defines an elevation angle and an azimuth angle of the aperture of the each specific ground station j at the each time mark tk;
• and
• the slewing cost Gij(tk), where the slewing cost Gij(tk) is dependent on the potential orientation Oj(tk) over at least the interval of the potential orientation Oj(tk) and dependent on the direction of the slant range rij(tk), thereby formulating the cost function where the cost function comprises a plurality of potential orientations Oj(tk);
• optimizing the cost function and quantifying each potential orientation Oj(tk) in the plurality of potential orientations Oj(tk), thereby generating a plurality of operational orientations Oj(tk);
• and
• communicating the control vector uj(t) to the pointing system of the every individual ground station, where the control vector uj(t) provided to the pointing system of the every individual ground station defines at least one operational orientation Oj(tk) comprising the plurality of operational orientations Oj(tk).