GPS-based spatial measurements

1. A computer-implemented method, comprising:

aggregating positional signals that were received, via a network, from a plurality of device sensors, wherein each positional signal has an associated observed signal strength;

identifying a subset of the positional signals associated with a physical location, wherein each positional signal included in the subset of the positional signals was received by a given device sensor of the plurality of device sensors while the given device sensor was located within a threshold distance of the physical location;

for each positional signal included in the subset of the positional signals, generating, by an estimation device and based at least on a position of the given device sensor that received the positional signal, a corresponding approximate object height for an object located at the physical location;

for each approximate object height corresponding to the subset of the positional signals:

determining an expected signal strength for the positional signal corresponding to the approximate object height,

generating, by the estimation device, a cost value that is based on a difference between the expected signal strength and the observed signal strength associated with the positional signal corresponding to the approximate object height; and

determining, by the estimation device and based on the cost values, an estimated object height for the object.

2. The computer-implemented method of claim 1 , wherein determining the corresponding approximate object height comprises:

computing a ray associated with a direct-line path of the positional signal;

determining an object position of the object relative to the position of the given device sensor; and

determining, based on the object position, the approximate object height that would cause at least a portion of the object to intersect with the ray.

3. The computer-implemented method of claim 1 , further comprising:

determining an expected positional signal having a second expected signal strength that the given device sensor was to receive at the physical location, wherein the given device sensor did not receive the expected positional signal;

determining, for the expected positional signal and based at least on a position of the given device sensor, a corresponding approximate object height for the object; and

generating a missing cost value based on a difference between the second expected signal strength and the observed signal strength.

4. The computer-implemented method of claim 1 , further comprising:

generating, from the cost values, a cost function of approximate object heights,

wherein determining the estimated object height comprises determining an object height associated with a minimum value of the cost function.

5. The computer-implemented method of claim 1 , further comprising:

receiving positional information about one or more transmitting devices that transmitted the positional signals; and

computing a plurality of rays associated with direct-line paths of the positional signals from the transmitting devices to the plurality of device sensors.

6. The computer-implemented method of claim 5 , wherein identifying the subset of the positional signals is based at least on a set of azimuth angles of the rays associated with the subset of the positional signals.

7. The computer-implemented method of claim 1 , wherein each cost value is further based on device types of a plurality of devices that include the plurality of device sensors.

8. One or more non-transitory computer-readable media including instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of:

aggregating positional signals that were received, via a network, from a plurality of device sensors, wherein each positional signal has an associated observed signal strength;

identifying a subset of the positional signals associated with a physical location, wherein each positional signal included in the subset of the positional signals was received by a given device sensor of the plurality of device sensors while the given device sensor was located within a threshold distance of the physical location;

for each positional signal included in the subset of the positional signals, generating, by an estimation device and based at least on a position of the given device sensor that received the positional signal, a corresponding approximate object height for an object located at the physical location;

for each approximate object height corresponding to the subset of the positional signals:

determining an expected signal strength for the positional signal corresponding to the approximate object height,

generating, by the estimation device, a cost value that is based on a difference between the expected signal strength and the observed signal strength associated with the positional signal corresponding to the approximate object height; and

determining, by the estimation device and based on the cost values, an estimated object height for the object.

9. The one or more non-transitory computer-readable media of claim 8 , wherein determining the corresponding approximate object height comprises:

computing a ray associated with a direct-line path of the positional signal;

determining an object position of the object relative to the position of the given device sensor; and

determining, based on the object position, the approximate object height that would cause at least a portion of the object to intersect with the ray.

10. The one or more non-transitory computer-readable media of claim 8 , further including instructions that, when executed by the one or more processors, cause the one or more processors to perform the steps of:

determining an expected positional signal having a second expected signal strength that the given device sensor was to receive at the physical location, wherein the given device sensor did not receive the expected positional signal;

determining, for the expected positional signal and based at least on a position of the given device sensor, a corresponding approximate object height for the object; and

generating a cost value based on a difference between the second expected signal strength and the observed signal strength.

11. The one or more non-transitory computer-readable media of claim 8 , further including instructions that, when executed by the one or more processors, cause the one or more processors to perform the steps of:

generating, from the cost values, a cost function of approximate object heights,

wherein determining the estimated object height comprises determining an object height associated with a minimum value of the cost function.

12. The one or more non-transitory computer-readable media of claim 8 , further including instructions that, when executed by the one or more processors, cause the one or more processors to perform the steps of:

receiving positional information about one or more transmitting devices that transmitted the positional signals; and

computing a plurality of rays associated with direct-line paths of the positional signals from the transmitting devices to the plurality of device sensors.

13. The one or more non-transitory computer-readable media of claim 12 , wherein identifying the subset of the positional signals is based at least on a set of azimuth angles of the rays associated with the subset of the positional signals.

14. A computing system, comprising:

a plurality of device sensors that receive positional signals; and

an estimation device configured to:

aggregate the positional signals that were received, via a network, from the plurality of device sensors, wherein each positional signal has an associated observed signal strength;

identify a subset of the positional signals associated with a physical location, wherein each positional signal included in the subset of the positional signals was received by a given device sensor of the plurality of device sensors while the given device sensor was located within a threshold distance of the physical location;

for each positional signal included in the subset of the positional signals, generate, based at least on a position of the given device sensor that received the positional signal, a corresponding approximate object height for an object located at the physical location;

for each approximate object height corresponding to the subset of the positional signals:

determine an expected signal strength for the positional signal corresponding to the approximate object height,

generate a cost value that is based on a difference between the expected signal strength and the observed signal strength associated with the positional signal corresponding to the approximate object height; and

determine, based on the cost values, an estimated object height for the object.

15. The computing system of claim 14 , wherein the estimation device determines the corresponding approximate object height by:

computing a ray associated with a direct-line path of the positional signal;

determining an object position of the object relative to the position of the given device sensor; and

determining, based on the object position, the approximate object height that would cause at least a portion of the object to intersect with the ray.

16. The computing system of claim 14 , wherein the estimation device further:

determines an expected positional signal having a second expected signal strength that the given device sensor was to receive at the physical location, wherein the given device sensor did not receive the expected positional signal;

determines, for the expected positional signal and based at least on a position of the given device sensor, a corresponding approximate object height for the object; and

generates a missing cost value based on a difference between the second expected signal strength and the observed signal strength.

17. The computing system of claim 14 , further comprising: one or more transmitting devices that transmit the positional signals, wherein the estimation device: receives positional information about the one or more transmitting devices; and computes a plurality of rays associated with direct-line paths of the positional signals from the transmitting devices to the plurality of device sensors.

18. The computing system of claim 17 , wherein the one or more transmitting devices comprise one or more global navigation satellite system (GNSS) satellites.

19. The computing system of claim 17 , further comprising:

a server that communicates with at least one of the one or more transmitting devices or the plurality of device sensors,

wherein the server is separate from the plurality of device sensors, and

wherein the estimation device is included in the server.

20. The computing system of claim 14 , further comprising:

a plurality of devices that include the plurality of device sensors,

wherein the cost value is further based on device types of the plurality of devices.