Amplitude calibration estimation

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 a measurement of gain of a first calibration signal retransmitted from one or more satellite elements, the first calibration signal being communicated by a first calibration station located at a first geographic location, the measurement of gain of the first calibration signal including a first measurement of gain for a first element of the one or more satellite elements retransmitting the first calibration signal;
• access a first expected gain for the first element retransmitting the first calibration signal;
• compute a first weight indicative of a confidence in the first measurement, at least in part, by calculating a gradient of a first geodetic radiation gain pattern of the first element;
• obtain a measurement 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, the measurement of gain of the second calibration signal including a second measurement of gain for a second element of the one or more satellite elements retransmitting the second calibration signal;
• access a second expected gain for the one or more satellite elements retransmitting the second calibration signal;
• compute a second weight indicative of a confidence in the second measurement, at least in part, by calculating a gradient of a first geodetic radiation gain pattern of the second element;
• generate a cost function using at least the obtained measurement of gain for the one or more satellite elements retransmitting the first calibration signal, the obtained measurement of gain for the one or more satellite elements retransmitting the second calibration signal, the accessed first expected gain for the first element retransmitting the first calibration signal and the accessed second expected gain for the second element retransmitting the second calibration signal, the computed weights indicative of the confidences in the first and second measurements;
• 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 including at least a satellite element relative gain or at least a calibration station relative gain;
• and
• store the values.

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 expected gains for the calibration signal retransmitted by the first element to the multiple calibration stations, wherein accessing the expected gains includes accessing a first expected gain for the calibration signal after being retransmitted by the first element and then received by the first calibration station and a second expected gain for the calibration signal after being retransmitted by the first element and then received by the second calibration station;
• computing weights indicative of a confidence in the 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 a 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;
• generating a cost function using at least the measurements of gain obtained from the multiple calibration stations, the accessed expected gains for the calibration signal after being retransmitted by the first element to the multiple calibration stations, and the computed weights indicative of the confidence in the measurements of gain obtained from 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 including at least a satellite element relative gain or at least a calibration station relative gain;
• and
• storing the values.

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 expected gains for the calibration signal retransmitted by the first element to the multiple calibration stations, wherein accessing the expected gains includes accessing a first expected gain for the calibration signal after being retransmitted by the first element and then received by the first calibration station and a second expected gain for the calibration signal after being retransmitted by the first element and then received by the second calibration station;
• compute weights indicative of a confidence in the 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 a 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;
• generate a cost function using at least the measurements of gain obtained from the multiple calibration stations, the accessed expected gains for the calibration signal after being retransmitted by the first element to the multiple calibration stations, and the computed weights indicative of the confidence in the measurements of gain obtained from 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 including at least a satellite element relative gain or at least a calibration station relative gain;
• and
• store the values.

A method for computing confidence weights for calibration earth station measurements in a satellite communications network, the method comprising:

• identifying a calibration earth station located at a first geographic location;
• identifying a satellite antenna element that is being calibrated through communications of one or more calibration signals between a gateway and the calibration earth station through the satellite antenna element;
• accessing a geodetic radiation gain pattern for the satellite antenna element, the geodetic radiation gain pattern being a function of an orientation of a satellite that includes the satellite antenna element;
• calculating a gradient of the geodetic radiation gain pattern;
• computing a measurement confidence weight for one or more measurements of the one or more calibration signals using the calculated gradient;
• and
• applying the measurement confidence weight to the one or more measurements of the one or more calibration signals for calibrating the satellite antenna element.

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

• obtaining a measurement of delay of a first calibration signal retransmitted from one or more satellite elements, the first calibration signal being communicated by a first calibration station located at a first geographic location, the measurement of delay of the first calibration signal including a first measurement of delay for a first element of the one or more satellite elements retransmitting the first calibration signal;
• accessing a first expected delay for the first element retransmitting the first calibration signal;
• computing a first weight indicative of a confidence in the first measurement, at least in part, by calculating a gradient of a first geodetic radiation pattern of the first element;
• obtaining a measurement 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, the measurement of delay of the second calibration signal including a second measurement of delay for a second element of the one or more satellite elements retransmitting the second calibration signal;
• accessing a second expected delay for the one or more satellite elements retransmitting the second calibration signal;
• computing a second weight indicative of a confidence in the second measurement, at least in part, by calculating a gradient of a first geodetic radiation pattern of the second element;
• generating a cost function using at least the obtained measurement of delay for the one or more satellite elements retransmitting the first calibration signal, the obtained measurement of delay for the one or more satellite elements retransmitting the second calibration signal, the accessed first expected delay for the first element retransmitting the first calibration signal and the accessed second expected delay for the second element retransmitting the second calibration signal, the computed weights indicative of the confidences in the first and second measurements;
• 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 including at least a satellite element relative delay or at least a calibration station relative gain;
• and
• storing the values.

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 expected gains for the calibration signal retransmitted by the first element to the multiple calibration stations, wherein accessing the expected gains includes accessing a first expected delay for the calibration signal after being retransmitted by the first element and then received by the first calibration station and a second expected delay for the calibration signal after being retransmitted by the first element and then received by the second calibration station;
• computing weights indicative of a confidence in the 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 a 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;
• generating a cost function using at least the measurements of delay obtained from the multiple calibration stations, the accessed expected gains for the calibration signal after being retransmitted by the first element to the multiple calibration stations, and the computed weights indicative of the confidence in the measurements of delay obtained from 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 including at least a satellite element relative delay or at least a calibration station relative gain;
• and
• storing the values.