Positioning determinations of receivers
The disclosed method and system is used to determine the position of a user device. The user device can receive data signals and/or carrier signals from orbiting space vehicles. These data signals can be used for positioning calculation and/or track maintenance of the user device. The disclosed method and system can account for time and frequency biases of the user device. For the track maintenance, a Kalman filter state estimator can be extended to include a velocity of the user device.
1. A method for track maintenance of a user device comprising:
receiving a signal from at least one space vehicle;
obtaining a position of the user device based on the received signal;
applying an extended Kalman filter state estimator including the position of the user device and a velocity of the user device; and
obtaining an estimate of a state of the user device for the track maintenance,
wherein obtaining the position of the user device includes a snapshot calculation, and
wherein performing at least one of the snapshot calculation and the extended Kalman filter state estimator includes a pseudo range measurement model and a pseudo range rate measurement model.
2. The method of claim 1 , wherein computing the pseudo range measurement model and the pseudo range rate measurement model includes a nonlinear least squares method.
3. The method of claim 1 , wherein performing at least one of the snapshot calculation and the extended Kalman filter state estimator includes a time bias and a frequency bias.
4. The method of claim 3 , wherein computing the time bias and the frequency bias includes a linear least squares method.
5. The method of claim 3 , wherein computing the time bias includes approximating the time bias with a polynomial.
6. The method of claim 3 , wherein computing the frequency bias includes taking a derivative of the time bias with respect to time.
7. The method of claim 3 , wherein the time bias and the frequency bias are expressed as explicit functions of a position of the user device.
8. The method of claim 3 , wherein expressions of the time bias and the frequency bias modify a nonlinear least squares cost function by removing the biases as independent states, thereby reducing the number of independent variables to those of a position of the user device alone.
9. The method of claim 1 , wherein the signal is received from a low earth orbit (LEO) satellite.
10. The method of claim 9 , wherein the LEO satellite is part of the Iridium system.
11. The method of claim 1 , wherein the state of the user device includes a position of the user device, a velocity of the user device, a time bias, and a frequency bias.
12. The method of claim 1 , wherein obtaining the estimate of the state of the user device includes evaluating a latitude and a longitude of the position of the user device.