Wide area positioning system
Positioning systems and methods for estimating an altitude of a receiver. In some embodiments, pressure and temperature information from a network of sensors is received by the receiver, and the pressure and temperature information from the network of sensors is used along with pressure information measured at a position of the receiver to estimate the altitude of the receiver.
1. A method for estimating an altitude of a receiver, the method comprising:
identifying
(a) a measurement of pressure measured by a pressure sensor of the receiver at a location of the receiver,
(b) a measurement of temperature not measured at the location of the receiver,
(c) a first reference pressure determined for a reference altitude using (i) a first pressure measurement measured by a first atmospheric reference sensor at a first known reference location and (ii) a first altitude of the first known reference location, and
(d) a second reference pressure determined for the reference altitude using (i) a second pressure measurement measured by a second atmospheric reference sensor at a second known reference location and (ii) a second altitude of the second known reference location;
determining, using one or more processors, a reference pressure estimate by: (i) combining two or more reference pressures that include the first reference pressure and the second reference pressure using a weighted average approach in which the weighting for the first reference pressure is a function of distance between the first known reference location and a point of interest, and the weighting for the second reference pressure is a function of distance between the second known reference location and the point of interest, or (ii) generating a second order surface that best fits at least two reference pressures that include the first reference pressure and the second reference pressure, and using the second order surface to determine the reference pressure estimate; and
determining, using the one or more processors, an estimated altitude of the receiver using the measurement of pressure, the measurement of temperature, and the reference pressure estimate.
2. The method of claim 1 , wherein the first altitude, the second altitude, and the reference altitude are different.
3. The method of claim 1 , wherein the reference pressure estimate is determined by combining the two or more reference pressures that include the first reference pressure and the second reference pressure using the weighted average approach in which the weighting for the first reference pressure is the function of distance between the first known reference location and the point of interest, and the weighting for the second reference pressure is the function of distance between the second known reference location and the point of interest.
4. The method of claim 1 , wherein the reference pressure estimate is determined by generating the second order surface that best fits the at least two reference pressures that include the first reference pressure and the second reference pressure, and using the second order surface to determine the reference pressure estimate.
5. The method of claim 1 , wherein the reference altitude is sea level, and the first altitude is a height of the first known reference location above sea level.
6. The method of claim 1 , said first reference pressure determined using the measurement of temperature, wherein the measurement of temperature specifies a temperature measured at the first reference location.
7. The method of claim 1 , wherein the measurement of temperature specifies a temperature measured at a third reference location that is different than the first reference location.
8. The method of claim 1 , the method comprising:
determining a second estimated altitude of the receiver using
(a) a second measurement of pressure measured by the pressure sensor of the receiver at a second location of the receiver,
(b) a second measurement of temperature not measured at the second location of the receiver, and
(c) a third reference pressure determined using (i) another pressure measurement measured at the first reference location and (ii) the first altitude.
9. The method of claim 8 , the method comprising:
receiving the second measurement of temperature from the first reference location.
10. The method of claim 1 , the method comprising:
determining a second estimated altitude of the receiver using
(a) a second measurement of pressure measured by the pressure sensor of the receiver at the location of the receiver,
(b) a second measurement of temperature not measured at the location of the receiver, and
(c) a third reference pressure determined using (i) another pressure measurement measured at the first reference location and (ii) the first altitude.
11. The method of claim 1 , said first reference pressure sent from a first transmitter.
12. The method of claim 1 , said first pressure measurement and said first altitude sent from a first transmitter, wherein the method comprises:
determining the first reference pressure using the first pressure measurement and the first altitude.
13. The method of claim 1 , wherein the estimated altitude of the receiver is determined using any of the following mathematical relationships:
(i) −(R*T/g)*ln(P/P_0), where P is the measurement of pressure measured by the pressure sensor of the receiver, P_0 is the reference pressure estimate, T is the measurement of temperature, g is acceleration due to gravity, and R is a gas constant value, wherein the reference pressure estimate is an estimated pressure at sea-level; or
(ii) z_2−(R*T/g)*ln(P_1/P_2), where P_1 is the measurement of pressure measured by the pressure sensor of the receiver, P_2 is the reference pressure estimate, z_2 is the reference altitude, T is the measurement of temperature, g is the acceleration due to gravity, and R is the gas constant, wherein the reference pressure estimate is an estimated pressure at the reference altitude.
14. A positioning system comprising:
a terrestrial transmitter network including transmitters;
a reference sensor array comprising a first atmospheric reference sensor at a first known reference location, and further comprising a second atmospheric reference sensor at a second known reference location; and
a receiver with an atmospheric sensor that collects atmospheric pressure data at a location of the receiver,
wherein the system is operable to:
identify
(a) a measurement of pressure measured by a pressure sensor of the receiver at the location of the receiver,
(b) a measurement of temperature not measured at the location of the receiver,
(c) a first reference pressure determined for a reference altitude using (i) a first pressure measurement measured by the first atmospheric reference sensor at the first known reference location and (ii) a first altitude of the first known reference location, and
(d) a second reference pressure determined for the reference altitude using (i) a second pressure measurement measured by the second atmospheric reference sensor at the second known reference location and (ii) a second altitude of the second known reference location;
determine, using one or more processors, a reference pressure estimate by: (i) combining two or more reference pressures that include the first reference pressure and the second reference pressure using a weighted average approach in which the weighting for the first reference pressure is a function of distance between the first known reference location and a point of interest, and the weighting for the second reference pressure is a function of distance between the second known reference location and the point of interest, or (ii) generating a second order surface that best fits at least two reference pressures that include the first reference pressure and the second reference pressure, and using the second order surface to determine the reference pressure estimate; and
determine, using the one or more processors, an estimated altitude of the receiver using the measurement of pressure, the measurement of temperature, and the reference pressure estimate.
15. One or more non-transitory computer-readable media embodying program instructions that, when executed by one or more processors, cause the one or more processors to perform a method for estimating an altitude of a receiver, the method comprising:
identifying
(a) a measurement of pressure measured by a pressure sensor of the receiver at a location of the receiver,
(b) a measurement of temperature not measured at the location of the receiver,
(c) a first reference pressure determined for a reference altitude using (i) a first pressure measurement measured by a first atmospheric reference sensor at a first known reference location and (ii) a first altitude of the first known reference location, and
(d) a second reference pressure determined for the reference altitude using (i) a second pressure measurement measured by a second atmospheric reference sensor at a second known reference location and (ii) a second altitude of the second known reference location;
determining, using one or more processors, a reference pressure estimate by: (i) combining two or more reference pressures that include the first reference pressure and the second reference pressure using a weighted average approach in which the weighting for the first reference pressure is a function of distance between the first known reference location and a point of interest, and the weighting for the second reference pressure is a function of distance between the second known reference location and the point of interest, or (ii) generating a second order surface that best fits at least two reference pressures that include the first reference pressure and the second reference pressure, and using the second order surface to determine the reference pressure estimate; and
determining, using the one or more processors, an estimated altitude of the receiver using the measurement of pressure, the measurement of temperature, and the reference pressure estimate.
16. The one or more non-transitory computer-readable media of claim 15 , wherein the first altitude, the second altitude, and the reference altitude are different.
17. The one or more non-transitory computer-readable media of claim 15 , wherein the reference pressure estimate is determined by combining the two or more reference pressures that include the first reference pressure and the second reference pressure using the weighted average approach in which the weighting for the first reference pressure is the function of distance between the first known reference location and the point of interest, and the weighting for the second reference pressure is the function of distance between the second known reference location and the point of interest.
18. The one or more non-transitory computer-readable media of claim 15 , wherein the reference pressure estimate is determined by generating the second order surface that best fits the at least two reference pressures that include the first reference pressure and the second reference pressure, and using the second order surface to determine the reference pressure estimate.
19. The one or more non-transitory computer-readable media of claim 15 , wherein the reference altitude is sea level, and the first altitude is a height of the first known reference location above sea level.
20. The one or more non-transitory computer-readable media of claim 15 , said first reference pressure determined using the measurement of temperature, wherein the measurement of temperature specifies a temperature measured at the first reference location.
21. The one or more non-transitory computer-readable media of claim 15 , wherein the measurement of temperature specifies a temperature measured at a third reference location that is different than the first reference location.
22. The one or more non-transitory computer-readable media of claim 15 , the method comprising:
determining a second estimated altitude of the receiver using
(a) a second measurement of pressure measured by the pressure sensor of the receiver at a second location of the receiver,
(b) a second measurement of temperature not measured at the second location of the receiver, and
(c) a third reference pressure determined using (i) another pressure measurement measured at the first reference location and (ii) the first altitude.
23. The one or more non-transitory computer-readable media of claim 22 , the method comprising:
receiving the second measurement of temperature from the first reference location.
24. The one or more non-transitory computer-readable media of claim 15 , the method comprising:
determining a second estimated altitude of the receiver using
(a) a second measurement of pressure measured by the pressure sensor of the receiver at the location of the receiver,
(b) a second measurement of temperature not measured at the location of the receiver, and
(c) a third reference pressure determined using (i) another pressure measurement measured at the first reference location and (ii) the first altitude.
25. The one or more non-transitory computer-readable media of claim 15 , said first reference pressure sent from a first transmitter.
26. The one or more non-transitory computer-readable media of claim 15 , said first pressure measurement and said first altitude sent from a first transmitter, wherein the method comprises:
determining the first reference pressure using the first pressure measurement and the first altitude.
27. The one or more non-transitory computer-readable media of claim 15 , wherein the estimated altitude of the receiver is determined using any of the following mathematical relationships:
(i) −(R*T/g)*ln(P/P_0), where P is the measurement of pressure measured by the pressure sensor of the receiver, P_0 is the reference pressure estimate, T is the measurement of temperature, g is acceleration due to gravity, and R is a gas constant value, wherein the reference pressure estimate is an estimated pressure at sea-level; or
(ii) z_2−(R*T/g)*ln(P_1/P_2), where P_1 is the measurement of pressure measured by the pressure sensor of the receiver, P_2 is the reference pressure estimate, z_2 is the reference altitude, T is the measurement of temperature, g is the acceleration due to gravity, and R is the gas constant, wherein the reference pressure estimate is an estimated pressure at the reference altitude.