Simulation for Micro-controller algorithm

I am developing a project which is related to detection of the hand movement when the users are using a product. In the device there is micro-controller and a 6-DOF IMU (accelerometer and gyroscope) for this purpose.

I am planing to create a firmware on the micro-controller which will output the data from the IMU through serial communication and the data will be stored in a spreadsheet in the computer. Then I will ask the users to use the product normally so that I have the user data during normal usage. After that I will try to test the hand movement detection algorithm in a computer simulation software to verify the algorithm. At last I will implement these algorithm into the micro-controller. Is this process good?

Can you recommend any computer simulation software that could do the job? Prefer to have one with cheaper cost :)

Thank you very much.

still needs some more info on what you intend to do.
Does the device you are going to make is embedded in the product or outside, in the study phase ?

testing your algorithm can be done at the design stage by writing a c or cpp code .
You must give more insight into your product to be designed.

Yes the device is embedded inside the product.

In short, in general for testing firmware the Proteus is the most accurate, and for testing algorithms, one of my preference is the MATLAB (Simulink), anyway the question as posed, does not give enough detail to have a more exact dimension of the problem and / or a clue of the appropriate solution.