Amplitude calibration with pointing correction

A system for estimating calibration for ground based beam forming in a satellite communications network, the system comprising:

• a processor;
• one or more instructions encoded in a non-transitory computer-readable storage medium for execution by the processor, the one or more instructions when executed by the processor operable to:
• obtain measurements of gain of a first calibration signal retransmitted by one or more satellite elements, the first calibration signal being communicated by a first calibration station located at a first geographic location, the measurements of gain including a first measurement of gain for a first element of the one or more satellite elements retransmitting the first calibration signal;
• compute weights indicative of a confidence in the obtained measurements of gain for the one or more satellite elements retransmitting the first calibration signal, wherein computing the weights includes computing a first weight indicative of a confidence in the first measurement;
• access a first geodetic radiation gain pattern of the first element, the first geodetic radiation gain pattern being a function of a roll, a pitch, and a yaw of a satellite;
• compute partial derivatives of the first geodetic radiation pattern with respect to roll, pitch and yaw at a point in the first geodetic radiation pattern corresponding to the first geographic location;
• obtain measurements of gain of a second calibration signal retransmitted by one or more satellite elements, the second calibration signal being communicated by a second calibration station located at a second geographic location that is different from the first geographic location;
• compute weights indicative of a confidence in the obtained measurements of gain for the one or more satellite elements retransmitting the second calibration signal;
• compute partial derivatives of the first geodetic radiation pattern with respect to roll, pitch and yaw at a point in the first geodetic radiation pattern corresponding to the second geographic location;
• generate a first cost function using at least the obtained measurements of gain for the one or more satellite elements retransmitting the first calibration signal, the obtained measurements of gain for the one or more satellite elements retransmitting the second calibration signal, the computed weights indicative of the confidence in the obtained measurements of gain for the one or more satellite elements retransmitting the first calibration signal, the computed weights indicative of the confidence in the obtained measurements of gain for the one or more satellite elements retransmitting the second calibration signal, the computed partial derivatives of the first geodetic radiation pattern with respect to roll, pitch and yaw at a point in the first geodetic radiation pattern corresponding to the first geographic location, and the computed partial derivatives of the first geodetic radiation pattern with respect to roll, pitch and yaw at a point in the first geodetic radiation pattern corresponding to the second geographic location;
• compute values for one or more unknown variables by reducing the first cost function with respect to the one or more unknown variables, the one or more unknown variables being selected from a group consisting of an estimated change in roll error, an estimated change in pitch error, and an estimated change in yaw error;
• determine a pointing error of the satellite using the computed values;
• and
• store the pointing error.

A method for estimating calibration for ground based beam forming in a satellite communications network, the method comprising:

• obtaining, from multiple calibration stations, measurements of gain of a calibration signal that is retransmitted by a first element of one or more satellite elements and then received by the calibration stations, wherein the calibration stations include a first calibration station located at a first geographic location and a second calibration station located at a second geographic location that is different from the first geographic location, the measurements of gain including a first measurement of gain received from the first station and a second measurement of gain received from the second station;
• accessing a geodetic radiation gain pattern of the first element, the geodetic radiation gain pattern being a function of a roll, a pitch, and a yaw of a satellite;
• computing weights indicative of a confidence in the obtained measurements of gain obtained from the multiple calibration stations, wherein computing the weights includes computing a first weight indicative of a confidence in the first measurement and a second weight indicative of a confidence in the second measurement, the first weight being computed, at least in part, by calculating a first gradient of the geodetic radiation gain pattern of the first element and the second weight being computed, at least in part, by calculating a second gradient of the geodetic radiation gain pattern of the first element;
• computing partial derivatives of the geodetic radiation pattern with respect to roll, pitch and yaw at multiple points in the geodetic radiation pattern corresponding to the locations of the multiple calibration stations, wherein computing the partial derivatives includes computing a first partial derivative of the geodetic radiation pattern with respect to roll, pitch and yaw at a point in the geodetic radiation pattern corresponding to the first geographic location and computing a second partial derivative of the geodetic radiation pattern with respect to roll, pitch and yaw at a point in the geodetic radiation pattern corresponding to the second first geographic location;
• generating a first cost function using at least the measurements of gain obtained from the multiple calibration stations, the computed weights indicative of the confidence in the measurements of gain obtained from the multiple calibration stations, and the computed partial derivatives of the geodetic radiation pattern with respect to roll, pitch and yaw at the multiple points in the geodetic radiation pattern corresponding to the locations of the multiple calibration stations;
• computing values for one or more unknown variables by reducing the cost function with respect to the one or more unknown variables, the one or more unknown variables being selected from a group consisting of an estimated change in roll error, an estimated change in pitch error, and an estimated change in yaw error;
• determining a pointing error of the satellite using the computed values;
• and
• storing the pointing error.

A system for estimating calibration for ground based beam forming in a satellite communications network, the system comprising:

• a processor;
• one or more instructions encoded in a non-transitory computer-readable storage medium for execution by the processor, the one or more instructions when executed by the processor operable to:
• obtain, from multiple calibration stations, measurements of gain of a calibration signal that is retransmitted by a first element of one or more satellite elements and then received by the calibration stations, wherein the calibration stations include a first calibration station located at a first geographic location and a second calibration station located at a second geographic location that is different from the first geographic location, the measurements of gain including a first measurement of gain received from the first station and a second measurement of gain received from the second station;
• access a geodetic radiation gain pattern of the first element, the geodetic radiation gain pattern being a function of a roll, a pitch, and a yaw of a satellite;
• compute weights indicative of a confidence in the obtained measurements of gain obtained from the multiple calibration stations, wherein computing the weights includes computing a first weight indicative of a confidence in the first measurement and a second weight indicative of a confidence in the second measurement, the first weight being computed, at least in part, by calculating a first gradient of the geodetic radiation gain pattern of the first element and the second weight being computed, at least in part, by calculating a second gradient of the geodetic radiation gain pattern of the first element;
• compute partial derivatives of the geodetic radiation pattern with respect to roll, pitch and yaw at multiple points in the geodetic radiation pattern corresponding to the locations of the multiple calibration stations, wherein computing the partial derivatives includes computing a first partial derivative of the geodetic radiation pattern with respect to roll, pitch and yaw at a point in the geodetic radiation pattern corresponding to the first geographic location and computing a second partial derivative of the geodetic radiation pattern with respect to roll, pitch and yaw at a point in the geodetic radiation pattern corresponding to the second first geographic location;
• generate a first cost function using at least the measurements of gain obtained from the multiple calibration stations, the computed weights indicative of the confidence in the measurements of gain obtained from the multiple calibration stations, and the computed partial derivatives of the geodetic radiation pattern with respect to roll, pitch and yaw at the multiple points in the geodetic radiation pattern corresponding to the locations of the multiple calibration stations;
• compute values for one or more unknown variables by reducing the cost function with respect to the one or more unknown variables, the one or more unknown variables being selected from a group consisting of an estimated change in roll error, an estimated change in pitch error, and an estimated change in yaw error;
• determine a pointing error of the satellite using the computed values;
• and
• store the pointing error.

A method for estimating delay calibration for ground based beam forming in a satellite communications network, the method comprising:

• obtaining measurements of delay of a first calibration signal retransmitted by one or more satellite elements, the first calibration signal being communicated by a first calibration station located at a first geographic location, the measurements of delay including a first measurement of delay for a first element of the one or more satellite elements retransmitting the first calibration signal;
• computing weights indicative of a confidence in the obtained measurements of delay for the one or more satellite elements retransmitting the first calibration signal, wherein computing the weights includes computing a first weight indicative of a confidence in the first measurement;
• accessing a first geodetic radiation pattern of the first element, the first geodetic radiation pattern being a function of a roll, a pitch, and a yaw of a satellite;
• computing partial derivatives of the first geodetic radiation pattern with respect to roll, pitch and yaw at a point in the first geodetic radiation pattern corresponding to the first geographic location;
• obtaining measurements of delay of a second calibration signal retransmitted by one or more satellite elements, the second calibration signal being communicated by a second calibration station located at a second geographic location that is different from the first geographic location;
• computing weights indicative of a confidence in the obtained measurements of delay for the one or more satellite elements retransmitting the second calibration signal;
• computing partial derivatives of the first geodetic radiation pattern with respect to roll, pitch and yaw at a point in the first geodetic radiation pattern corresponding to the second geographic location;
• generating a first cost function using at least the obtained measurements of delay for the one or more satellite elements retransmitting the first calibration signal, the obtained measurements of delay for the one or more satellite elements retransmitting the second calibration signal, the computed weights indicative of the confidence in the obtained measurements of delay for the one or more satellite elements retransmitting the first calibration signal, the computed weights indicative of the confidence in the obtained measurements of delay for the one or more satellite elements retransmitting the second calibration signal, the computed partial derivatives of the first geodetic radiation pattern with respect to roll, pitch and yaw at a point in the first geodetic radiation pattern corresponding to the first geographic location, and the computed partial derivatives of the first geodetic radiation pattern with respect to roll, pitch and yaw at a point in the first geodetic radiation pattern corresponding to the second geographic location;
• computing values for one or more unknown variables by reducing the first cost function with respect to the one or more unknown variables that are selected from a group consisting of an estimated change in roll error, an estimated change in pitch error, and an estimated change in yaw error;
• determining a pointing error of the satellite using the computed values;
• and
• storing the pointing error.

A method for estimating delay calibration for ground based beam forming in a satellite communications network, the method comprising:

• obtaining, from multiple calibration stations, measurements of delay of a calibration signal that is retransmitted by a first element of one or more satellite elements and then received by the calibration stations, wherein the calibration stations include a first calibration station located at a first geographic location and a second calibration station located at a second geographic location that is different from the first geographic location, the measurements of delay including a first measurement of delay received from the first station and a second measurement of delay received from the second station;
• accessing a geodetic radiation pattern of the first element, the geodetic radiation pattern being a function of a roll, a pitch, and a yaw of a satellite;
• computing weights indicative of a confidence in the obtained measurements of delay obtained from the multiple calibration stations, wherein computing the weights includes computing a first weight indicative of a confidence in the first measurement and a second weight indicative of a confidence in the second measurement, the first weight being computed, at least in part, by calculating a first gradient of the geodetic radiation pattern of the first element and the second weight being computed, at least in part, by calculating a second gradient of the geodetic radiation pattern of the first element;
• computing partial derivatives of the geodetic radiation pattern with respect to roll, pitch and yaw at multiple points in the geodetic radiation pattern corresponding to the locations of the multiple calibration stations, wherein computing the partial derivatives includes computing a first partial derivative of the geodetic radiation pattern with respect to roll, pitch and yaw at a point in the geodetic radiation pattern corresponding to the first geographic location and computing a second partial derivative of the geodetic radiation pattern with respect to roll, pitch and yaw at a point in the geodetic radiation pattern corresponding to the second first geographic location;
• generating a first cost function using at least the measurements of delay obtained from the multiple calibration stations, the computed weights indicative of the confidence in the measurements of delay obtained from the multiple calibration stations, and the computed partial derivatives of the geodetic radiation pattern with respect to roll, pitch and yaw at the multiple points in the geodetic radiation pattern corresponding to the locations of the multiple calibration stations;
• computing values for one or more unknown variables by reducing the cost function with respect to the one or more unknown variables, the one or more unknown variables being selected from a group consisting of an estimated change in roll error, an estimated change in pitch error, and an estimated change in yaw error;
• determining a pointing error of the satellite using the computed values;
• and
• storing the pointing error.