GNSS tracking using cascaded probabilistic estimators

1 . A method for tracking a state of a device based on transmissions from a global navigation satellite system (GNSS), wherein the method is executed by a processor coupled with stored instructions implementing the method, wherein the stored instructions, when executed by the processor to carry out steps of the method, comprising:

collecting GNSS measurement data of satellite signals transmitted from multiple satellites, wherein the GNSS measurement data include code measurements, carrier phase measurements and doppler measurements of the satellite signals;

executing multiple probabilistic estimators concurrently tracking the state of the device using at least two measurement models relating the GNSS measurement data with the state of the device, wherein the multiple probabilistic estimators include a first estimator tracking the state of the device based on a first measurement model using the code measurements, and wherein the multiple probabilistic estimators include a second estimator tracking the state of the device based on a second measurement model using the GNSS measurement data masked by a binary mask blocking a subset of GNSS measurement data of a subset of the satellite signals based on values of coefficients of the binary mask, wherein the number of measurements in the first measurement model is smaller than the number of measurements in the second measurement model;

determining the values of coefficients of the binary mask based on outputs of the first estimator;

determining the state of the device based on outputs of the second estimator;

outputting the state of the device determined by the second estimator, wherein the device is a GNSS receiver of a vehicle, such that the state of the device indicates a state of the vehicle; and

controlling movement of the vehicle based on the state of the vehicle.

2 . The method of claim 1 , wherein each of the coefficients of the binary mask corresponds to one of the satellite signals of one of the multiple satellites, and wherein the values of coefficients of the binary mask are determined based on a statistical relationship of the code measurements of each of the satellite signals with a state estimate indicated by the outputs of the first estimator.

3 . The method of claim 1 , further comprising:

generating a plurality of measurement models, each corresponding to a different subset of the code measurements;

estimating the state of the device using each of the plurality of measurement models of code measurements to produce multiple state estimates;

comparing the multiple state estimates with each other to determine one or multiple outlier code measurements of outlier satellite signals causing deviation in the multiple state estimates; and

determining the values of coefficients of the binary mask blocking the code measurements and the phase measurements of the outlier satellite signals.

4 . The method of claim 3 , further comprising:

removing the outlier code measurements from the plurality of measurement models.

5 . The method of claim 3 , further comprising:

associating the outlier code measurements with measurement noise larger than measurement noise of nonoutlier code measurements, resulting in the same number of measurements being used in each measurement model, but different noise statistics associated with each measurement.

6 . The method of claim 3 , further comprising:

transitioning between the plurality of measurement models based on transition probabilities that are constant or determined as a function of one or a combination of signal-to-noise ratio of the GNSS measurement data, elevation angles of the satellites, and world geometries.

7 . The method of claim 1 , wherein the first measurement model of the first estimator includes a parametric covariance noise matrix with elements defining noise of the code measurements or differenced residuals of code measurements from multiple satellites, further comprising:

updating different elements of the noise covariance matrix based on a difference between a prediction of a state estimate by a prediction model of the first estimator and a measurement of the state estimate indicated by the measurement model processing the corresponding code measurements; and

determining the values of the coefficients of the binary mask based on estimated parameters of the noise covariance matrix.

8 . The method of claim 7 , further comprising:

designating each of the satellite signals as being subject to outlier measurements based on an indicator function defined with the parameters of noise covariance matrix; and

setting the values of the coefficients of the binary mask corresponding to each outlier satellite signal to zero based on indicator signals.

9 . The method of claim 7 , further comprising for each time step:

predicting a state estimate of the device using the prediction model subject to process noise; and

iteratively updating, until a termination condition is met, the predicted state estimate and noise covariance matrix based on the first measurement model processing the code measurements of the satellite signals, wherein for each iteration, the first estimator updates the predicted state estimate and updates the noise covariance matrix with respect to the updated prediction of the position estimate.

10 . The method of claim 9 , further comprising:

iteratively updating parameters of an inverse Wishart or inverse gamma distribution over the noise covariance matrix and its elements.

11 . The method of claim 10 , further comprising:

designating each of the satellite signals as being subject to outlier measurements based on an indicator function defined as a threshold on statistical mean, statistical mode, or statistical quantile functions of the estimated inverse Wishart or the inverse gamma distribution over the noise covariance matrix.

12 . The method of claim 9 , wherein the noise covariance matrix is a joint covariance noise matrix of the GNSS measurements of the satellite signals updated by solving to a variational inference problem.

13 . The method of claim 1 , wherein the probabilistic estimators include one or a combination of a probabilistic filter and a probabilistic smoother.

14 . The method of claim 13 , wherein the probabilistic filter includes an approximate Gaussian filter using statistical linearization techniques to resolve nonlinearities of the estimation model.

15 . The method of claim 1 , wherein the first estimator tracks the state of the device, and wherein the second estimator jointly tracks state of multiple devices including the device, and a larger estimation problem is formed to jointly estimate the state trajectories of multiple receivers.

16 . The method of claim 1 , wherein the measurement model included in the first estimator describes a set of measurements that are a subset of the measurements used in the second estimator.

17 . The method of claim 1 , wherein the device is a GNSS receiver mounted to an aquatic buoy, further comprising:

determining changes of water level based on the state of the device.

18 . A system for tracking a state of a device based on transmissions from a global navigation satellite system (GNSS), the system comprising a processor coupled with stored instructions, wherein the stored instructions, when executed by the processor cause the system to:

collect GNSS measurement data of satellite signals transmitted from multiple satellites, wherein the GNSS measurement data include code measurements, carrier phase measurements, and doppler measurements of the satellite signals;

execute multiple probabilistic estimators concurrently tracking the position state of the object device using different measurement models connecting the GNSS measurement data with the state of the device, wherein the multiple probabilistic estimators include a first estimator tracking the position state of the object device based on a first measurement model using the code measurements, and wherein the multiple probabilistic estimators include a second estimator tracking the state of the device based on a second measurement model using the GNSS measurement data masked by a binary mask blocking a subset of the GNSS measurement data formed in a subset of the satellite signals based on values of coefficients of the binary mask, wherein the first measurement model is smaller than the second measurement model;

determine the values of coefficients of the binary mask based on outputs of the first estimator;

determine the state of the device based on outputs of the second estimator;

output the state of the device determined by the second estimator, wherein the device is a GNSS receiver of a vehicle, such that the state of the device indicates a state of the vehicle; and

control movement of the vehicle based on the state of the vehicle.

19 . A non-transitory computer-readable storage medium embodied thereon a program executable by a processor for performing a method for estimating movement of a device based on a state of the device tracked using transmissions from a global navigation satellite system (GNSS), the method comprising: collecting GNSS measurement data of satellite signals transmitted from multiple satellites, wherein the GNSS measurement data code measurements, and carrier phase measurements of the satellite signals;

executing multiple probabilistic estimators concurrently tracking the position state of the object device using different measurement models connecting the GNSS measurement data with the state of the device, wherein the multiple probabilistic estimators include a first estimator tracking the position state of the object device based on a first measurement model using the code measurements, and wherein the multiple probabilistic estimators include a second estimator tracking the state of the device based on a second measurement model using the GNSS measurement data masked by a binary mask blocking a subset of the GNSS measurement data formed in a subset of the satellite signals based on values of coefficients of the binary mask, wherein the first measurement model is smaller than the second measurement model;

determining the values of coefficients of the binary mask based on outputs of the first estimator;

determining the state of the device based on outputs of the second estimator;

outputting the state of the device determined by the second estimator, wherein the device is a GNSS receiver of a vehicle, such that the state of the device indicates a state of the vehicle; and

controlling movement of the vehicle based on the state of the vehicle.