Techniques for using satellites to aid in geographical position determination

A non-transitory computer readable medium storing a program causing at least one processor to execute a process to determine a position of a body, the process comprising:

• counting an atomic clock derived time starting at a current global navigation satellite system (GNSS) time and incremented by a periodic time count from an atomic clock;
• attempting to receive a later current GNSS time occurring after the current GNSS time;
• determining whether the later current GNSS time is received and valid;
• determining that the later current GNSS data is at least one of not received and not valid, then causing provision of an estimated geographical position of the body to a navigation system;
• receiving beacon data of each of a plurality of satellites, wherein the beacon data comprises a unique satellite identifier of one of the plurality of satellites and a signal strength of a beacon signal including the unique satellite identifier;
• extracting a satellite identifier from each received beacon data;
• using each extracted satellite identifier and most recently received orbital data for a plurality of satellites, obtaining orbital data of each satellite whose satellite identifier was extracted;
• obtaining a reference time from the most recently received orbital data for the plurality of satellites;
• determining a difference time equal to an absolute value of a difference between another current atomic clock derived time and the reference time;
• based on a radiation pattern of an antenna array of a satellite receiver configured to receive each beacon signal and minimum detectable signal threshold level of the satellite receiver, defining a bounded area;
• using the difference time and an obtained orbital data, generating an estimated probability density function (PDF) of absolute geographical position of each satellite in the bounded area and whose satellite identifier was extracted;
• using each estimated PDF of absolute geographical position, generating a representation of estimated PDFs of relative geographical position of each satellite in the bounded area, wherein each such relative geographical position is relative to a most recently (a) estimated position of the body or (b) received valid GNSS position;
• using yet another current atomic clock derived time and received beacon data of each satellite whose satellite identifier was extracted, determining (a) angles of arrival of the beacon signal of each satellite, whose satellite identifier was extracted, with respect to the body, and (b) a signal strength of each beacon signal received from a satellite whose satellite identifier was extracted;
• using each determined angles of arrival, determining a representation of measured PDFs of relative geographical position for each satellite whose identifier was extracted;
• using inertial measurement unit (IMU) data, the representation of the measured PDFs of relative geographical position for each satellite, and the representation of estimated PDFs of relative geographical position of each satellite, determining the estimated geographical position of the body;
• determining a measured entry time and a measured exit time of each satellite, and a gradient, over the bounded area, of a strength of the beacon signal of each satellite whose identifier was extracted over the bounded area;
• and
• for each satellite whose identifier was extracted, adding the measured entry time, the measured exit time, and the gradient of a strength of the beacon signal of each satellite whose identifier was extracted to the representation of measured PDFs of relative position of each satellite.

An apparatus for determining a position of a body, the apparatus comprising:

• a satellite receiver on or in the body, wherein the satellite receiver comprises an antenna array on or in the body;
• an atomic clock on or in the body and configured to provide a periodic time count;
• a global navigation satellite system (GNSS) receiver on or in the body;
• an inertial measurement unit on or in the body and comprising at least one of:
• at least one accelerometer and at least one gyroscope,
• a processing circuitry on or in the body and communicatively coupled to each of the satellite receiver, the atomic clock, the GNSS receiver, and the inertial measurement unit;
• wherein the processing circuitry is configured to:
• count an atomic clock derived time starting at a current GNSS time from the GNSS receiver and incremented by the periodic time count received from the atomic clock;
• attempt to receive a later current GNSS time occurring after the current GNSS time;
• determine whether the later current GNSS time is received and valid;
• determining that the later current GNSS time is at least one of not received and not valid, then use an estimated geographical position of the body to provide information about the position of the body with respect to an intended destination of the body;
• receive beacon data of each of a plurality of satellites, wherein the beacon data comprises a unique satellite identifier of one of the plurality of satellites and a signal strength of a beacon signal including the unique satellite identifier;
• extract a satellite identifier from each received beacon data;
• using each extracted satellite identifier and most recently received orbital data for a plurality of satellites, obtain orbital data of each satellite whose satellite identifier was extracted;
• obtain a reference time from the most recently received orbital data for the plurality of satellites;
• determine a difference time equal to an absolute value of a difference between another current atomic clock derived time and the reference time;
• based on a radiation pattern of an antenna array of a satellite receiver configured to receive each beacon signal and minimum detectable signal threshold level of the satellite receiver, define a bounded area;
• using the difference time and an obtained orbital data, generate an estimated probability density function (PDF) of absolute geographical position of each satellite in the bounded area and whose satellite identifier was extracted;
• using each estimated PDF of absolute geographical position, generate a representation of estimated PDFs of relative geographical position of each satellite in the bounded area, wherein each such relative geographical position is relative to a most recently (a) estimated position of the body or (b) received valid GNSS position;
• using yet another current atomic clock derived time and received beacon data of each satellite whose satellite identifier was extracted, determine (a) angles of arrival of the beacon signal of each satellite, whose satellite identifier was extracted, with respect to the body, and (b) a signal strength of each beacon signal received from a satellite whose satellite identifier was extracted;
• using each determined angles of arrival, determine a representation of measured PDFs of relative geographical position for each satellite whose identifier was extracted;
• using inertial measurement unit (IMU) data, the representation of the measured PDFs of relative geographical position for each satellite, and the representation of estimated PDFs of relative geographical position of each satellite, determine the estimated geographical position of the body;
• determine a measured entry time and a measured exit time of each satellite, and a gradient, over the bounded area, of a strength of the beacon signal of each satellite whose identifier was extracted over the bounded area;
• and
• for each satellite whose identifier was extracted, adding the measured entry time, the measured exit time, and the gradient of a strength of the beacon signal of each satellite whose identifier was extracted to the representation of measured PDFs of relative position of each satellite.