Real-time high-accuracy determination of integer ambiguities in a kinematic GPS receiver

A satellite receiver and processor unit, comprising:

• (a) a satellite tracker, said satellite tracker tracking satellite signals from a first plurality of satellites, said satellite signals including a satellite code modulated by a carrier signal;
• (b) a navigation processor in circuit communication with said tracker, at least one of said tracker and said navigation processor determining for each satellite of said first plurality of satellites the satellite code and phase of the carrier signal;
• (c) a telemetry receiver in circuit communication with said navigation processor, said telemetry receiver receiving a telemetry signal from a reference receiver, the telemetry signal including for each satellite of a second plurality of satellites the satellite code and phase of the associated carrier signal, said first and second pluralities of satellites having associated therewith at least one overlapping subset of satellites;
• (1) wherein said navigation processor determines an estimated double difference integer ambiguity for each satellite of said at least one overlapping subset of satellites using a Kalman filter with double difference integer ambiguities added as additional states;
• and
• (2) wherein said navigation processor determines an integer ambiguity for each satellite of said at least one overlapping subset of satellites using said estimated double difference integer ambiguity for each satellite of said at least one overlapping subset of satellites.

A method of determining that a cycle slip has occurred during tracking of a carrier signal from a satellite, comprising the steps of:

• (a) measuring a plurality of actual phase data points for the carrier signal associated with the satellite;
• (b) fitting a polynomial to the plurality of actual phase data points for the satellite;
• (c) extrapolating a predicted next phase measurement data point from the polynomial;
• (d) measuring a next phase data point for the carrier signal associated with the satellite;
• and
• (e) comparing the predicted next phase measurement data point with the measured next phase data point.

A method of determining integer ambiguities in the distances between a plurality of satellites and a receiver, the satellites transmitting a satellite signal comprising a satellite code modulated by a carrier signal, comprising the steps of:

• (a) receiving satellite signals with a participant receiver from a first plurality of satellites;
• (b) converting the carrier signals from said satellites of said first plurality of satellites into computer-readable participant carrier phase data;
• (c) determining participant satellite code from the signals from said satellites of said first plurality of satellites;
• (d) storing time-correlated participant satellite code and participant carrier phase data for each satellite from the first plurality of satellites;
• (e) receiving satellite signals with a reference receiver from a second plurality of satellites, said first and second pluralities of satellites having associated therewith at least one overlapping subset of satellites;
• (f) converting the carrier signals from said satellites of said second plurality of satellites into computer-readable reference carrier phase data;
• (g) determining reference satellite code from the signals from said satellites of said second plurality of satellites;
• (h) storing time-correlated reference satellite code and reference carrier phase data for each satellite from said second plurality of satellites;
• (i) determining estimated integer ambiguities for each satellite of at least one overlapping subset of satellites of said first and second pluralities of satellites using a Kalman filter with double difference integer ambiguities added as additional states;
• and
• (j) determining an integer ambiguity for each satellite of said at least one overlapping subset of satellites using said estimated double difference integer ambiguity for each satellite of said at least one overlapping subset of satellites.

A method of determining a course correction for a participant receiver, comprising the steps of:

• (a) receiving satellite position data with a participant receiver from a first plurality of satellites;
• (b) receiving with a telemetry receiver reference position data for a second plurality of satellites, said reference position data being telemetered from a reference receiver;
• (c) determining estimated integer ambiguities for each satellite of at least one overlapping subset of satellites of said first and second pluralities of satellites using a Kalman filter, the satellite position data, and the reference position data;
• (d) determining integer ambiguities for each satellite of the at least one overlapping subset of satellites from said estimated integer ambiguities by searching along double difference lines of sight between the satellites and the receivers;
• (e) determining the present location of the participant receiver using the determined integer ambiguities;
• (f) comparing the present location of the participant receiver with a predetermined desired location;
• and
• (g) displaying a course correction associated with the difference between the present location and the predetermined desired location of the participant receiver.

A computer-readable computer program product comprising a computer readable medium having computer program logic recorded thereon for enabling a processor in a computer system to determine integer ambiguities in the distances between a plurality of satellites and a receiver, the satellites transmitting a satellite signal comprising a satellite code modulated by a carrier signal, said computer program product comprising:

• (a) means for determining that a cycle slip has occurred during tracking of the carrier signal from at least one satellite of said first plurality of satellites;
• (b) means for sorting the satellites of said at least one overlapping subset of satellites to maximize the angular difference between double difference pairs;
• (c) means for performing a Kalman filter innovations test to determine whether at least one measurement from at least one satellite of said at least one overlapping subset of satellites improves an estimated double difference integer ambiguity or not;
• (d) means for determining whether there is at least one satellite in a double difference pair whose signal is no longer being tracked and, if so, compressing a covariance matrix associated with said Kalman filter thereby removing the at least one satellite whose signal is no longer being tracked;
• (e) means for determining estimated integer ambiguities for each satellite said plurality of satellites using a Kalman filter with double difference integer ambiguities added as additional states;
• (f) means for processing estimated double difference integer ambiguities in said Kalman filter until their error estimates are determined to within a predetermined variance;
• (g) means for determining an integer ambiguity for each satellite of said plurality of satellites using said estimated double difference integer ambiguity for each satellite of said plurality of satellites;
• (h) means for sequentially selecting at least one set of candidate double difference integer ambiguities by searching said candidate double difference integer ambiguities along the double difference line of sight for each satellite of said at least one overlapping subset of satellites;
• (i) means for determining after-the-fit residuals for the at least one selected set of candidate double difference integer ambiguities;
• and
• (j) means for, if the after-the-fit residuals for the at least one selected set of candidate double difference integer ambiguities are below a predetermined threshold, deeming the selected set of candidate double difference integer ambiguities to be the double difference integer ambiguities.