Systems and methods for low latency 3-axis accelerometer calibration

1. A telematics system, comprising:

a processor;

an acceleration sensor connected to the processor, wherein the acceleration sensor is a 3-axis accelerometer configured to determine an acceleration sensor vector comprising forward acceleration information along a forward axis, lateral acceleration information along a lateral axis, and vertical acceleration information along a vertical axis, wherein the forward axis, the lateral axis, and the vertical axis are defined by a first orientation of the acceleration sensor;

a velocity sensor mounted to a vehicle and connected to the processor and configured to determine velocity information along a vehicular forward axis and heading information, wherein the vehicular forward axis is defined by a second orientation of the vehicle and the heading information is relative to the second orientation of the vehicle; and

a memory connected to the processor and configured to store an acceleration alignment application;

wherein the acceleration alignment application configures the processor to:

determine vehicular forward acceleration information along the vehicular forward axis using the velocity information;

determine vehicular lateral acceleration information using the velocity information and the heading information;

determine a lateral incline vector as a difference of the acceleration sensor vector and a dot product of the vehicular lateral acceleration information with a normalized cross product of a calibrated forward vector and the acceleration sensor vector;

calculate a lateral acceleration vector as a normalized cross product of the calibrated forward vector and the lateral incline vector;

determine a forward incline vector as a difference of the acceleration sensor vector and a dot product of the vehicular forward acceleration information and a normalized cross product of the lateral incline vector and the lateral acceleration vector;

calculate a forward acceleration vector as a normalized cross product of the forward incline vector and the lateral acceleration vector;

calculate a vertical acceleration vector as a normalized cross product of the lateral acceleration vector and the forward acceleration vector;

compute lateral alignment information as a dot product of the lateral acceleration vector and the acceleration sensor vector;

compute forward alignment information as a dot product of the forward acceleration vector and the acceleration sensor vector; and

compute vertical alignment information as a dot product of the vertical acceleration vector and the acceleration sensor vector;

wherein the lateral alignment information, the forward alignment information, and the vertical alignment information calibrate the first orientation of the acceleration sensor to the second orientation of the vehicle.

2. The telematics system of claim 1 , wherein the calibrated forward vector aligns the vehicular forward axis with the forward axis.

3. The telematics system of claim 2 , wherein:

the acceleration alignment application further configures the processor to determine a vehicular lateral axis using the heading information and the vehicular forward acceleration information; and

the calibrated forward vector further aligns the vehicular lateral axis with the lateral axis.

4. A method for calibrating axes of an acceleration sensor using a telematics system, where the telematics system is mounted in a vehicle having a vehicular forward axis, a vehicular lateral axis, and a vehicular vertical axis, the method comprising:

determining, by the telematics system, vehicular forward acceleration information along the vehicular forward axis using a velocity sensor of the telematics system;

determining, by the telematics system, vehicular lateral acceleration information along the vehicular lateral axis using the velocity sensor of the telematics system;

determining, by the telematics system, a lateral incline vector as a difference of an acceleration sensor vector and a dot product of the vehicular lateral acceleration information with a normalized cross product of a calibrated forward vector and the acceleration sensor vector, wherein the acceleration sensor vector is determined by an acceleration sensor of the telematics system, and wherein the acceleration sensor vector comprises forward acceleration information along a forward axis, lateral acceleration information along a lateral axis, and vertical acceleration information along a vertical axis;

calculating, by the telematics system, a lateral acceleration vector as a normalized cross product of the calibrated forward vector and the lateral incline vector;

determining, by the telematics system, a forward incline vector as a difference of the acceleration sensor vector and a dot product of the vehicular forward acceleration information and a normalized cross product of the lateral incline vector and the lateral acceleration vector;

calculating, by the telematics system, a forward acceleration vector as a normalized cross product of the forward incline vector and the lateral acceleration vector;

calculating, by the telematics system, a vertical acceleration vector as a normalized cross product of the lateral acceleration vector and the forward acceleration vector;

computing, by the telematics system, lateral alignment information as a dot product of the lateral acceleration vector and the acceleration sensor vector;

computing, by the telematics system, forward alignment information as a dot product of the forward acceleration vector and the acceleration sensor vector; and

computing, by the telematics system, vertical alignment information as a dot product of the vertical acceleration vector and the acceleration sensor vector, wherein the lateral alignment information, the forward alignment information, and the vertical alignment information calibrate axes of the acceleration sensor to axes of the vehicle.

5. The method of claim 4 , wherein the calibrated forward vector aligns the vehicular forward axis with the forward axis using the telematics system.

6. The method of claim 5 , further comprising:

aligning the vehicular lateral axis with the lateral axis using the calibrated forward vector using the telematics system.