Using data point integration or basic kinematics for postion tracking

Soo I'm looking at trying to calculate position out of an accelerometer. What I'm curious is there any benefit to data point integration for calculating out position or would using basic ground fixed kinematics do an equivalent job.

How many axis? If more than one and rotation is possible, you will have dramas.
You could try and integrate the readings, but noise and lack of sensitivity will make this tricky.

This is the sort of problem no one has solved yet because the technology isn't good enough. You need some kind of external reference to make it reliable. I.e. the amount of money poured into headset tracking, or aircraft inertial navigation.

I'm using two degrees of freedom from the accelerometer to determine rotation about the z axis and longitudinal offset. I'm using the x and y axis which run perpendicular to the ground.

I know drift is going to be a big issue with this but I'm trying to make my device drive in a straighter line. The other thing is that I'm running large averages so I'm accurate to a calibration bias assuming a mostly level floor.

The device just runs wall to wall and I'm hoping to avoid an aircraft accelerometer so I can keep using a simple analog accelerometer. Although that 9 degrees of freedom would be really helpful to running in a straight line.

Z axis being the vertical?
What chip are you using?

I assume you are using an accelerometer that measures acceleration about an axis, like a single axis on a gyroscope.

Linear accelerometers won't help you measure rotation around an axis though, imagine if something is stationary but rotating about its center of mass. I'm not saying your project can spin on its axis, just that it won't measure correctly under all circumstances.

You can get chips that have 3x linear accelerometers, 3x axis gyro, 2x axis magnetic sensor in a small package you can wire up to a raspberry pi or something similar.

Z axis is vertical. I'm using an ADXL335.

This method won't be accurate if the moment of turning isn't centered between the two wheels. The accelermoter is postiined far from the point I'm forcing it to rotate around this will let a linear axis detect acceleration.

Well, only one way to find out!
I would probably try integration first, not sure what you mean by ground kinematics, or how that differs from the first option.

At the end of the day I imagine you will want to implement some kind of kalman filter to get rid of noise and track movement better.

There are plenty of guides on the net, and code in various languages for various micros.
This is a link i found ages ago:

How a Kalman filter works, in pictures