Systems and methods with dead-reckoning
In an embodiment, a method for determining a speed of a vehicle in a dead-reckoning system includes measuring a centripetal acceleration, using an accelerometer, of the vehicle traversing a curved path on a plane of travel. The method also includes measuring an angular velocity, using a gyroscope, of the vehicle. The speed of the vehicle is calculated from the centripetal acceleration and the angular velocity.
1. A method comprising:
continuously monitoring a change in a direction of a vehicle using a gyroscope; and
detecting the change in the direction of the vehicle, and, based thereon:
measuring a centripetal acceleration of the vehicle using an accelerometer,
measuring an angular velocity of the vehicle using the gyroscope, and
calculating a linear velocity of the vehicle from the centripetal acceleration and the angular velocity.
2. The method of claim 1 , further comprising calibrating the accelerometer and the gyroscope prior to the measuring.
3. The method of claim 1 , wherein calculating the linear velocity comprises dividing the centripetal acceleration by the angular velocity.
4. The method of claim 1 , wherein calculating the linear velocity comprises using the formula:
V
=
360
×
Accel
2
π
×
Gyro
where Accel is the centripetal acceleration measured by the accelerometer and Gyro is an angular velocity measured by the gyroscope in accordance with the change in the direction of the vehicle.
5. The method of claim 1 , wherein the method further comprises detecting a weak or an absence of a global positioning satellite (GPS) reception.
6. The method of claim 1 , further comprising powering up the accelerometer in response to detecting the change in the direction of the vehicle.
7. The method of claim 1 , further comprising:
periodically storing the angular velocity and the centripetal acceleration in a memory; and
reading the angular velocity and the centripetal acceleration from the memory upon detecting the change in the direction of the vehicle.
8. The method of claim 1 , wherein measuring the centripetal acceleration comprises measuring the centripetal acceleration in each of a x-y plane, z-x plane, and y-z plane of the vehicle traveling in a three-dimensional coordinate system.
9. The method of claim 8 , wherein measuring the angular velocity comprises measuring a pitch angular velocity, a yaw angular velocity, and a roll angular velocity.
10. The method of claim 9 , wherein calculating the linear velocity of the vehicle comprises:
calculating an instantaneous velocity in the x-y plane comprising dividing y-axis centripetal acceleration and the yaw angular velocity;
calculating an instantaneous velocity in the z-x plane comprising dividing z-axis centripetal acceleration and the roll angular velocity; and
calculating an instantaneous velocity in the y-z plane comprising dividing the z-axis centripetal acceleration and the pitch angular velocity.
11. The method of claim 10 , further comprising determining a total instantaneous velocity, wherein the total instantaneous velocity is calculated by taking square root of a sum of the instantaneous velocity in the x-y plane squared, instantaneous velocity in the z-x plane squared, and instantaneous velocity in the y-z plane squared.
12. A vehicle comprising:
an accelerometer configured to be rigidly mounted to the vehicle;
a gyroscope configured to be rigidly mounted to the vehicle and being proximate to the accelerometer;
a processor; and
a memory storing a program to be executed in the processor, the program comprising instructions to:
continuously monitor a change in a direction of the vehicle using the gyroscope; and
detect the change in the direction of the vehicle, and, based thereon:
measure a centripetal acceleration of the vehicle using the accelerometer,
measure an angular velocity of the vehicle using the gyroscope, and
calculate a linear velocity of the vehicle from the centripetal acceleration and the angular velocity.
13. The vehicle of claim 12 , wherein calculating the linear velocity is calculated by dividing the centripetal acceleration by the angular velocity.
14. The vehicle of claim 12 , wherein calculating the linear velocity is calculated using the formula:
V
=
360
×
Accel
2
π
×
Gyro
where Accel is the centripetal acceleration measured by the accelerometer and Gyro is an angular velocity measured by the gyroscope in accordance with the change in the direction of the vehicle.
15. The vehicle of claim 12 , wherein measuring the centripetal acceleration comprises measuring the centripetal acceleration in each of a x-y plane, z-x plane, and y-z plane of the vehicle traveling in a three-dimensional coordinate system.
16. The vehicle of claim 15 , wherein measuring the angular velocity comprises measuring a pitch angular velocity, a yaw angular velocity, and a roll angular velocity.
17. The vehicle of claim 16 , wherein calculating the linear velocity of the vehicle comprises:
calculating an instantaneous velocity in the x-y plane comprising dividing y-axis centripetal acceleration and the yaw angular velocity;
calculating an instantaneous velocity in the z-x plane comprising dividing z-axis centripetal acceleration and the roll angular velocity; and
calculating an instantaneous velocity in the y-z plane comprising dividing z-axis centripetal acceleration and the pitch angular velocity.
18. A fleet of vehicles comprising a master vehicle and a plurality of slave vehicles, wherein the master vehicle and each of the slave vehicles operate in accordance with the vehicle of claim 12 .
19. The fleet of vehicles of claim 18 , wherein a coordinated movement between the master vehicle and the slave vehicles is in accordance with an updated speed and position calculated at each slave vehicle in reference to the master vehicle.
20. An apparatus comprising:
an accelerometer configured to be rigidly mounted to a vehicle;
a gyroscope configured to be rigidly mounted to the vehicle proximate to the accelerometer;
a processor; and
a memory storing a program to be executed in the processor, the program comprising instructions to:
continuously monitor a change in a direction of the vehicle using the gyroscope; and
detect the change in the direction of the vehicle, and based thereon:
measure a centripetal acceleration of the vehicle using the accelerometer,
measure an angular velocity of the vehicle using the gyroscope, and
calculate a linear velocity of the vehicle from the centripetal acceleration and the angular velocity.
21. The apparatus of claim 20 , wherein calculating the linear velocity comprises dividing the centripetal acceleration by the angular velocity.
22. The apparatus of claim 20 , wherein calculating the linear velocity comprises using the formula:
V
=
360
×
Accel
2
π
×
Gyro
where Accel is the centripetal acceleration measured by the accelerometer and Gyro is an angular velocity measured by the gyroscope in accordance with the change in the direction of the vehicle.
23. The apparatus of claim 20 , wherein measuring the centripetal acceleration comprises measuring the centripetal acceleration in each of a x-y plane, z-x plane, and y-z plane of the vehicle that the vehicle is traveling in a three-dimensional coordinate system; wherein the angular velocity comprises a pitch angular velocity, a yaw angular velocity, and a roll angular velocity; and wherein calculating the linear velocity of the vehicle comprises:
calculating an instantaneous velocity in the x-y plane comprises dividing y-axis centripetal acceleration and the yaw angular velocity;
calculating an instantaneous velocity in the z-x plane comprising dividing z-axis centripetal acceleration and the roll angular velocity; and
calculating an instantaneous velocity in the y-z plane comprising dividing z-axis centripetal acceleration and the pitch angular velocity.
24. A non-transitory computer-readable medium storing computer instructions for determining a speed of a vehicle in a dead-reckoning system, that when executed by a processor, causes the processor to perform the steps of:
continuously monitoring a change in a direction of the vehicle using a gyroscope; and
detecting the change in the direction of the vehicle, and, based thereon:
measuring a centripetal acceleration of the vehicle using an accelerometer,
measuring an angular velocity of the vehicle using the gyroscope, and
calculating a linear velocity of the vehicle from the centripetal acceleration and the angular velocity.
25. The non-transitory computer-readable medium of claim 24 , wherein calculating the linear velocity comprises using the formula:
V
=
360
×
Accel
2
π
×
Gyro
where Accel is the measured centripetal acceleration by the accelerometer and Gyro is the angular velocity measured by the gyroscope in accordance with the change in the direction of the vehicle.