System and Method for Integer-Less GNSS Positioning

A method for tracking a state of a receiver of a global navigational satellite system (GNSS), wherein the method uses a processor coupled to a memory storing a motion model transitioning a previous state of the receiver to a current state of the receiver according to the motion data, wherein the motion model is a probabilistic model subject to process noise, and a measurement model relating a subset of the measurements of satellite signals to the current state of the receiver, and wherein the measurement model is a probabilistic model subject to measurement noise, and a state estimator configured to track the state of the receiver using a joint probability of the state of the receiver estimated by the motion model and the measurement model, wherein the processor is coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor carry out steps of the method, comprising:

• accepting motion data indicative of a change of a state of the receiver;
• accepting measurements of satellite signals including a combination of carrier signals and code signals transmitted from a set of GNSS satellites, wherein a measurement for each satellite signal includes a single difference between the satellite signal transmitted by a satellite and another satellite signal to include a relative position of the receiver of the satellite signal with respect to a position of the satellite subject to integer ambiguity of the carrier signal of the satellite and noise, such that all possible measurements for each satellite signal form a set of measurements;
• selecting the subset of measurements, wherein each measurement in the subset of measurements is formed by a weighted combination of multiple different measurements from the set of measurements;
• and
• executing the state estimator with the motion model using the motion data and the measurement model using the selected subset of measurements to estimate the state of the receiver.

A non-transitory computer readable storage medium embodied thereon a program executable by a processor for performing a method, wherein the medium stores a motion model transitioning a previous state of the receiver to a current state of the receiver according to the motion data, wherein the motion model is a probabilistic model subject to process noise, and a measurement model relating a subset of the measurements of satellite signals to the current state of the receiver, and wherein the measurement model is a probabilistic model subject to measurement noise, and a state estimator configured to track the state of the receiver using a joint probability of the state of the receiver estimated by the motion model and the measurement model, the method comprising:

• accepting motion data indicative of a change of a state of the receiver;
• accepting measurements of satellite signals including a combination of carrier signals and code signals transmitted from a set of GNSS satellites, wherein a measurement for each satellite signal includes a single difference between the satellite signal transmitted by a satellite and another satellite signal to include a relative position of the receiver of the satellite signal with respect to a position of the satellite subject to integer ambiguity of the carrier signal of the satellite and noise, such that all possible measurements for each satellite signal form a set of measurements;
• selecting the subset of measurements, wherein each measurement in the subset of measurements is formed by a weighted combination of multiple different measurements from the set of measurements;
• and
• executing the state estimator with the motion model using the motion data and the measurement model using the selected subset of measurements to estimate the state of the receiver.