If one was to attempt dead reckoning, one would follow this path:
1: The inertial sensor provides acceleration with respect to its body-fixed coordinate system. This must be transformed into a coordinate system fixed to the earth. In order to accomplish this, it is necessary to know the orientation of the inertial sensor relative to the earth-fixed coordinate system.
2. Subtract the gravity vector.
3. Double integrate (WRT time) the acceleration.
Note that any small errors in either the orientation estimate, or the sensor’s acceleration bias, or the knowledge of the gravity vector will result in exponentially increasing errors. The size of these errors has no bounds.
We generally do not recommend our sensors for applications involving position measurement due the exceptional difficultly of such computations.
Even the best systems, costing hundreds of thousands of dollars, are subject to error accumulation on the order of 1 kilometer per hour.
The bias errors of the industrial grade accelerometers used in the inertial sensor will produce errors of many kilometers within seconds.
This assumes that the orientation is known perfectly.
Uncertainty in the orientation measurement will make the errors even larger.
These inertial instruments use MEMS sensors (accelerometers, gyroscopes).
These MEMS sensors are classified as 'automotive' or ‘industrial’ grade.
They are not 'tactical' or 'navigational' grade.
The bottom line is that the inertial sensor cannot directly provide a displacement measurement.
Let us also be very clear that this statement is not meant to dissuade you; it is meant to set the tone for the complexity involved in this application.
Papers such as this discuss the science involved in great detail: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwiCsraTjO3RAhWj24MKHXIvBIAQFggaMAA&url=https%3A%2F%2Fsciforum.net%2Fconference%2Fecsa-1%2Fpaper%2F2395%2Fdownload%2Fpdf&usg=AFQjCNEqcxQZFt3dmpiyKJOTzcNXiwgnzA&cad=rja[na01.safelinks.protection.outlook.com]