Accelerometer data integration (MMSE)

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  1. Based on the raw accelerometer measurements use simple integration on the raw $X$ and $Y$ axis data to determine the velocity and position.
  2. If we assume a linear model $Y = aX + b$ for determine the MMSE of $X$ (where $X$ is acceleration along one of the $x$ or $y$ acceleration axes), how does it compare with the results in part 1?

The first part is relatively easy, but I am not sure about second part.