Converting accelerometer readings to center of IMU

Question

I recently purchased 3 single axis accelerometers for tracking acceleration of a vehicle. I have used a box like structure to mount each accelerometer orthogonal to each other ( As much as possible) to calculate 3d space acceleration of the vehicle.

Below is a system diagram to represent clarity

This setup is done for experimental purpose only I understand that buying a 3axis accelerometer would have been easier for execution, Also the vehicle is able to rotate on it's own axis and travel forward backward only currently

As you all can see that IMU itself is placed away from center of gravity of the vehicle and Inside IMU accelerometer is placed away from center of IMU.

Hence 2 compensations needs to be performed for converting IMU accelerometer readings to with respect to center of gravity of Vehicle.

1. Represent accelerometer readings with respect to center of IMU
2. Represent accelerometer readings with respect to center of gravity of vehicle

I have found out the solution for the 2nd part which is done using rigid body dynamics formula used in the below link https://www.basicairdata.eu/knowledge-center/compensation/inertial-measurement-unit-placement/

Question

The problem I am facing right now is that each accelerometer gives readings based on their respective center which is away from center of the box I have placed them in. I would like to get readings with respect to centre of the box.

Is there any way I could offset the accelerometer readings to center of the box. I have obtained the distance from center of the box to each accelerometers by experimental practices.

Any reference/Links would be helpfull

GOAL

The goal of the experiment is to obtain precise and accurate data of acceleration readings of the accelerometer and gyroscope. The goal is not to calculate current position of the vehicle however accelerometer readings will be used to predict the position of the vehicle w.r.t current position.

UPDATE

1. I have seemingly forgot to mention that the setup also contains 3-axis gyroscope, however I am unsure as how to use this for solving the above problem
2. Question is modified to add more detail/picture.

Thanks & Regards

Answer 1

A rigid object moves in one piece; all of its locations have the same velocity.

So, you need to do nothing, if you can assume your rotation velocity (so, pitch, yaw and roll) to be zero, or if you can assume your translation derivative to be zero (i.e., vehicle rotates only, doesn't move away at changing speed).

If your vehicle can do both, you're basically out of luck: Looking at a single sensor, you cannot tell how much of its reading is due to translational acceleration and how much is from rotation (i.e., taking a turn).

But you need to know that: translation applies to all parts of your rigid vehicle the same, but rotation rotates "outer" parts faster than "inner" parts.

Even combining two sensors' individual readings won't take you far: Both are just numbers, and you can't know how much of their readings can be explained by a rotation and what by a diagonal translational acceleration.

The only way out here is to take history and a system model into account to make a good-as-possible guess on how much you're in a curve or sliding.

Typical use case of the Kalman filter, to be honest. You'll need to read up on that, and come up with a system and observer model. Have fun!

Note that this is always worse than actually having gyro readings! (I just mention that because your question – incorrectly as far as we can tell – is tagged with imu and gyro, which three single-axis accelerometers are not. You're missing three axes of rotational acceleration measurement.)