Mobile platform positioning using satellite positioning system and visual-inertial odometry

1. A method of determining a trajectory of a mobile platform, the method comprising:

obtaining a satellite positioning system (SPS) measurement from one or more SPS signals acquired by an SPS receiver of the mobile platform;

obtaining a visual-inertial odometry (VIO) measurement of the mobile platform from a VIO system of the mobile platform;

determining a first position estimate of the mobile platform based, at least in part, on the SPS measurement and the VIO measurement;

adjusting the first position estimate to generate a smoothed position estimate based, at least in part, on a smoothing parameter that controls a smoothness of the trajectory,

wherein the smoothing parameter is a fixed nonnegative number that is not a function of time and

the amount that the first position is adjusted is limited by a fixed threshold that controls a maximum difference between the smoothed position estimate and a previous smoothed position estimate; and

determining the trajectory of the mobile platform, at least in part, using the smoothed position estimate.

2. The method of claim 1 , wherein the difference between the smoothed position estimate and the previous smoothed position estimate is less than a difference between the first position estimate and the previous smoothed position estimate.

3. The method of claim 1 , wherein adjusting the first position estimate to generate the smoothed position estimate comprises:

determining a difference between the smoothed position estimate and the first position estimate;

determining the smoothness of the trajectory based, in part, on the smoothed position estimate and the smoothing parameter; and

minimizing a cost function that determines a trade-off between:

the difference between the smoothed position estimate and the first position estimate, and

the smoothness of the trajectory.

4. The method of claim 3 , wherein determining the smoothness of the trajectory comprises:

applying the smoothing parameter to a difference between the smoothed position estimate and a previous smoothed position estimate.

5. The method of claim 4 , wherein the cost function is represented by ∥s t −x t ∥ 2 +λ∥s t −s t−1 ∥ 2 , wherein s t is the smoothed position estimate, x t is the first position estimate, s t−1 is the previous smoothed position estimate, and λ is the smoothing parameter.

6. The method of claim 3 , wherein determining the smoothness of the trajectory comprises:

applying the smoothing parameter to a difference between:

a difference between the smoothed position estimate and a previous smoothed position estimate; and

a VIO displacement measurement included in the VIO measurement.

7. The method of claim 6 , wherein the cost function is represented by ∥s t −x t ∥ 2 +λ∥s t −s t−1 −v t ∥ 2 , wherein s t is the smoothed position estimate, x t is the first position estimate, s t−1 is the previous smoothed position estimate, v t is the VIO displacement measurement, and λ is the smoothing parameter.

8. The method of claim 1 , further comprising:

obtaining a predicted future position estimate of the mobile platform, wherein generating the smoothed position estimate is based, in part, on the predicted future position estimate.

9. The method of claim 1 , wherein:

the SPS measurement indicates a range-rate value, a pseudorange value, a velocity value, or some combination thereof corresponding to the mobile platform; and

the VIO measurement indicates a VIO-based velocity measurement, a VIO-based displacement value, or both corresponding to the mobile platform.

10. An apparatus for determining a trajectory of a mobile platform, the apparatus comprising:

means for obtaining a satellite positioning system (SPS) measurement from one or more SPS signals acquired by an SPS receiver of the mobile platform

means for obtaining a visual-inertial odometry (VIO) measurement of the mobile platform from a VIO system of the mobile platform;

means for determining a first position estimate of the mobile platform based, at least in part, on the SPS measurement and the VIO measurement;

means for adjusting the first position estimate to generate a smoothed position estimate based, in part, on a smoothing parameter that controls a smoothness of the trajectory,

wherein the smoothing parameter is a fixed nonnegative number that is not a function of time and

the amount that the first position is adjusted is limited by a fixed threshold that controls a maximum difference between the smoothed position estimate and a previous smoothed position estimate; and

means for determining the trajectory of the mobile platform, at least in part, using the smoothed position estimate.

11. The apparatus of claim 10 , wherein the difference between the smoothed position estimate and the previous smoothed position estimate is less than a difference between the first position estimate and the previous smoothed position estimate.

12. The apparatus of claim 10 , wherein the means for adjusting the first position estimate to generate the smoothed position estimate comprises:

means for determining a difference between the smoothed position estimate and the first position estimate;

means for determining the smoothness of the trajectory based, in part, on the smoothed position estimate and the smoothing parameter; and

means for minimizing a cost function that determines a trade-off between:

the difference between the smoothed position estimate and the first position estimate, and

the smoothness of the trajectory.

13. The apparatus of claim 12 , wherein the means for determining the smoothness of the trajectory comprises:

means for applying the smoothing parameter to a difference between the smoothed position estimate and a previous smoothed position estimate, wherein the cost function is represented by ∥s t −x t ∥ 2 +λ∥s t −s t−1 ∥ 2 , wherein s t is the smoothed position estimate, x t is the first position estimate, s t−1 is the previous smoothed position estimate, and λ is the smoothing parameter.

14. The apparatus of claim 12 , wherein the means for determining the smoothness of the trajectory comprises:

means for applying the smoothing parameter to a difference between:

a difference between the smoothed position estimate and a previous smoothed position estimate; and

a VIO displacement measurement included in the VIO measurement, wherein the cost function is represented by ∥s t −x t ∥ 2 +λ∥s t −s t−1 −v t ∥ 2 , wherein s t is the smoothed position estimate, x t is the first position estimate, s t−1 is the previous smoothed position estimate, v t is the VIO displacement measurement, and λ is the smoothing parameter.

15. The apparatus of claim 10 , further comprising:

means for obtaining a predicted future position estimate of the mobile platform, wherein generating the smoothed position estimate is based, in part, on the predicted future position estimate.

16. An apparatus for determining a trajectory of a mobile platform, the apparatus comprising:

at least one processor; and

at least one memory coupled to the at least one processor, the at least one processor and the at least one memory being configured to direct the apparatus to:

obtain a satellite positioning system (SPS) measurement from one or more SPS signals acquired by an SPS receiver of the mobile platform;

obtain a visual-inertial odometry (VIO) measurement of the mobile platform from a VIO system of the mobile platform;

determine a first position estimate of the mobile platform based, at least in part, on the SPS measurement and the VIO measurement;

adjust the first position estimate to generate a smoothed position estimate based, in part, on a smoothing parameter that controls a smoothness of the trajectory,

wherein the smoothing parameter is a fixed nonnegative number that is not a function of time and

the amount that the first position is adjusted is limited by a fixed threshold that controls a maximum difference between the smoothed position estimate and a previous smoothed position estimate; and

determine the trajectory of the mobile platform, at least in part, using the smoothed position estimate.

17. The apparatus of claim 16 , wherein the difference between the smoothed position estimate and the previous smoothed position estimate is less than a difference between the first position estimate and the previous smoothed position estimate.

18. The apparatus of claim 16 , wherein the at least one processor and the at least one memory are configured to direct the apparatus to:

determine a difference between the smoothed position estimate and the first position estimate;

determine the smoothness of the trajectory based, in part, on the smoothed position estimate and the smoothing parameter; and

minimize a cost function that determines a trade-off between:

the difference between the smoothed position estimate and the first position estimate, and the smoothness of the trajectory.

19. The apparatus of claim 16 , wherein the at least one processor and the at least one memory are configured to direct the apparatus to:

obtain a predicted future position estimate of the mobile platform; and

generate the smoothed position estimate based, in part, on the predicted future position estimate.