Doppler GNSS systems and methods

1. A system comprising:

a position sensor coupled to a mobile structure and configured to provide a Doppler-derived velocity corresponding to motion of the position sensor; and

a logic device configured to communicate with the position sensor in an assisted or autonomous navigation operation, wherein the logic device is configured to:

initialize an estimated relative position of the mobile structure to a preselected value irrelevant to an absolute position of the mobile structure on earth;

receive the Doppler-derived velocity from the position sensor at consecutive time points during the navigation operation; and

determine an estimated relative position of the mobile structure corresponding to each said time point based, at least in part, on the received Doppler-derived velocity for the time point and a prior estimated relative position of the mobile structure.

2. The system of claim 1 , wherein:

the determining the estimated relative position of the mobile structure comprises determining, for each position component, the sum of the prior estimated relative position with a product of the Doppler-derived velocity and a time interval between the receiving the Doppler-derived velocity and the receiving the prior Doppler-derived velocity.

3. The system of claim 1 , wherein:

the prior estimated relative position comprises non-vertical position components; and

the determining the estimated relative position of the mobile structure comprises determining, for each non-vertical position component, the sum of the prior estimated relative position with a product of the Doppler-derived velocity and a time interval between the receiving the Doppler-derived velocity and the receiving the prior Doppler-derived velocity while disregarding a vertical position component of the mobile structure.

4. The system of claim 1 , wherein:

the mobile structure comprises a watercraft; and

time intervals between the consecutive time points are approximately equal to each other.

5. The system of claim 1 , wherein the preselected value has only zero components as denoting a position of the mobile structure at a start of the navigation operation.

6. The system of claim 1 , wherein the mobile structure is a watercraft, and the navigation operation is at most 1400 seconds in duration.

7. The system of claim 1 , wherein the navigation operation is an assisted docking operation.

8. The system of claim 1 , wherein the navigation operation is an autonomous docking operation.

9. A system comprising:

a position sensor coupled to a mobile structure and configured to provide an absolute position of the position sensor;

an orientation sensor coupled to the mobile structure and configured to provide an absolute orientation of the mobile structure; and

a logic device configured to communicate with the position sensor and the orientation sensor, wherein the logic device is configured to:

receive the absolute orientation of the mobile structure from the orientation sensor and the absolute position of the position sensor from the position sensor;

determine a transformation matrix based, at least in part, on the received absolute orientation of the mobile structure;

determine an absolute position offset associated with the position sensor based, at least in part, on the received absolute orientation of the mobile structure, the determined transformation matrix, and a relative position vector from a center of mass of the mobile structure to a mounting position of the position sensor on the mobile structure; and

determine an estimated absolute position of the mobile structure based, at least in part, on the absolute position received from the position sensor and the determined absolute position offset.

10. The system of claim 9 , wherein:

the position sensor is configured to provide an absolute linear velocity corresponding to motion of the position sensor;

the orientation sensor is configured to provide an angular velocity of the mobile structure; and

the logic device is configured to:

receive the absolute linear velocity of the position sensor from the position sensor and the angular velocity of the mobile structure from the orientation sensor;

determine a relative linear velocity of the position sensor, relative to the center of mass of the mobile structure, based, at least in part, on the relative position vector and the received angular velocity; and

determine an estimated linear velocity of the mobile structure based, at least in part, on the received absolute linear velocity of the position sensor and the determined relative linear velocity of the position sensor.

11. The system of claim 10 , wherein the logic device is configured to:

set a vertical component of the absolute position received from the position sensor to a preselected constant value prior to the determining the estimated absolute position of the mobile structure; and/or

set a vertical component of the absolute linear velocity received from the position sensor to zero prior to the determining the estimated linear velocity of the mobile structure.

12. The system of claim 9 , wherein:

the position sensor is configured to provide a time series of absolute linear velocities corresponding to motion of the position sensor;

the orientation sensor is configured to provide a time series of angular velocities of the mobile structure; and

the logic device is configured to:

receive the absolute linear velocities of the position sensor from the position sensor and the angular velocities of the mobile structure from the orientation sensor; and

determine an estimated linear velocity of the mobile structure based, at least in part, on the received absolute linear velocities of the position sensor and the received angular velocities of the mobile structure.

13. The system of claim 12 , wherein the determining the estimated linear velocity of the mobile structure comprises:

determining a cross-correlation of the received angular velocities of the mobile structure and the received absolute linear velocities of the position sensor, and determining an amplitude scalar and a measurement delay corresponding to an angular velocity component of the received absolute linear velocities of the position sensor based on a first peak identified in the determined cross-correlation; or

downsampling the received angular velocities of the mobile structure and the received absolute linear velocities of the position sensor to a preselected sample rate above a Nyquist frequency for an expected dominant frequency of the angular velocity component of the received absolute linear velocity of the position sensor, and determining the amplitude scalar and the measurement delay corresponding to the angular velocity component based on a spectral analysis of the downsampled angular velocities of the mobile structure and/or the downsampled absolute linear velocities of the position sensor; and

determining the estimated linear velocity of the mobile structure by removing the angular velocity component from the received absolute linear velocities of the position sensor based, at least in part, on the determined amplitude scalar and measurement delay.

14. The system of claim 9 , further comprising a spatial measurement sensor coupled to the mobile structure and configured to provide spatial data corresponding to an environment about the mobile structure, wherein the logic device is configured to:

receive the absolute orientations of the mobile structure from the orientation sensor and the spatial data from the spatial measurement sensor;

determine a set of relative orientations of a water plane represented within the spatial data corresponding to a set of measurement times, relative to a sensor orientation corresponding to the spatial measurement sensor;

identify a set of absolute orientations of the mobile structure corresponding to the set of measurement times based, at least in part, on the received absolute orientations of the mobile structure; and

determine a relative sensor orientation corresponding to the spatial measurement sensor, relative to the orientation sensor, based, at least in part, on the determined set of relative orientations of the water plane, the identified set of absolute orientations of the mobile structure, and a known absolute orientation of the water plane.

15. The system of claim 14 , wherein the logic device is configured to:

receive absolute positions of the position sensor from the position sensor; and

determine a relative sensor position corresponding to the spatial measurement sensor, relative to the position sensor, based, at least in part, on the determined relative sensor orientation corresponding to the spatial measurement sensor and the received absolute positions of the position sensor.

16. A method comprising:

receiving a Doppler-derived velocity corresponding to motion of a position sensor coupled to a mobile structure;

determining an estimated relative position of the mobile structure based, at least in part, on the received Doppler-derived velocity and a prior estimated relative position of the mobile structure;

receiving an absolute orientation of the mobile structure from an orientation sensor coupled to the mobile structure and an absolute position of the position sensor coupled to the mobile structure;

determining a transformation matrix based, at least in part, on the received absolute orientation of the mobile structure;

determining an absolute position offset associated with the position sensor based, at least in part, on the received absolute orientation of the mobile structure, the determined transformation matrix, and a relative position vector from a center of mass of the mobile structure to a mounting position of the position sensor on the mobile structure; and

determining an estimated absolute position of the mobile structure based, at least in part, on the absolute position received from the position sensor and the determined absolute position offset.

17. The method of claim 16 , further comprising:

receiving an absolute linear velocity of the position sensor from the position sensor and an angular velocity of the mobile structure from the orientation sensor;

determining a relative linear velocity of the position sensor, relative to the center of mass of the mobile structure, based, at least in part, on the relative position vector and the received angular velocity; and

determining an estimated linear velocity of the mobile structure based, at least in part, on the received absolute linear velocity of the position sensor and the determined relative linear velocity of the position sensor.

18. A method of claim 16 , further comprising:

receiving absolute linear velocities of a position sensor coupled to a mobile structure and angular velocities of the mobile structure from an orientation sensor coupled to the mobile structure; and

determining an estimated linear velocity of the mobile structure based, at least in part, on the received absolute linear velocities of the position sensor and the received angular velocities of the mobile structure.

19. The method of claim 18 , wherein the determining the estimated linear velocity of the mobile structure comprises:

determining a cross-correlation of the received angular velocities of the mobile structure and the received absolute linear velocities of the position sensor, and determining an amplitude scalar and a measurement delay corresponding to an angular velocity component of the received absolute linear velocities of the position sensor based on a first peak identified in the determined cross-correlation; or

downsampling the received angular velocities of the mobile structure and the received absolute linear velocities of the position sensor to a preselected sample rate above a Nyquist frequency for an expected dominant frequency of the angular velocity component of the received absolute linear velocity of the position sensor, and determining the amplitude scalar and the measurement delay corresponding to the angular velocity component based on a spectral analysis of the downsampled angular velocities of the mobile structure and/or the downsampled absolute linear velocities of the position sensor; and

determining the estimated linear velocity of the mobile structure by removing the angular velocity component from the received absolute linear velocities of the position sensor based, at least in part, on the determined amplitude scalar and measurement delay.

20. The method of claim 16 , further comprising:

receiving absolute orientations of the mobile structure from the orientation sensor coupled to the mobile structure and spatial data from a spatial measurement sensor coupled to the mobile structure;

determining a set of relative orientations of a water plane represented within the spatial data corresponding to a set of measurement times, relative to a sensor orientation corresponding to the spatial measurement sensor;

identifying a set of absolute orientations of the mobile structure corresponding to the set of measurement times based, at least in part, on the received absolute orientations of the mobile structure; and

determining a relative sensor orientation corresponding to the spatial measurement sensor, relative to the orientation sensor, based, at least in part, on the determined set of relative orientations of the water plane, the identified set of absolute orientations of the mobile structure, and a known absolute orientation of the water plane.

21. The method of claim 20 , further comprising:

receiving absolute positions of the position sensor coupled to the mobile structure; and

determining a relative sensor position corresponding to the spatial measurement sensor, relative to the position sensor, based, at least in part, on the determined relative sensor orientation corresponding to the spatial measurement sensor and the received absolute positions of the position sensor.