calculation algorythm in three-dimensional linear system of equations

Hello! First information to this project: You should be a professional in mathematics if you want to bid for this project. Second information to this project: I do not care about the language in which you build a solution for this mathematical job. Indeed a clear mathematical structure would be best for me. Please find the complete project description page down... ## Deliverables Here is my mathematical challenge for you: I hold a mobile gps system in my hand. This gps system also contains three position sensors for the thee dimensions. (the gps feature is not important for this project) So, every sensor tells me every 0.01 seconds the acceleration force of its axis. Example: I hold the device absolute horizontal and then let it fall. Now two sensors are measuring a g force of 0 and on sensor measures a g force of 1. Because the last one measures that the device accelerates with 1 g to the earth. (if this up to here contains new informations for you, please do not go on reading this project description ;-) Okay, now the user of this device holds it straight and static into any direction and press a button. This is the moment your mathematical method should start. The user now turns himself with the device in his hand to the left site. At a special moment the user stops his turning movement to the left and turns now back to the right site. Now your method should find out three informations: 1. What are the x,y coordinates of the turning point on the left side relative to the starting point when the user pressed the button? The z-coordinate (the altitude) is not interesting. 2. What are the x,y coordinates of the point when the device passes again the x-coordinate from that point when the user pressed the button? So of course the x-coordinate will be the same than at the timepoint when the button was pressed but the y-coordinate may be different because it is not a machine which makes this movements, it is a man. The z-coordinate (the altitude) is not interesting. 3. How fast is the device when it passes the original x-coordinate? The very important comment to this project is that the three accelarations do affect themselves because the user will not be able to hold the device for example in perfect horizontal position. So, if he accelerates the device for example with 1 g to the left but holds the device with a 10 degree angle to the horizontal, the x sensor wound not mess 1 g, it would mess a bit less or more. May be +/-0.95 g. And the z sensor would not mess 0, it would mess +/-0.05 g or kind of that. So you always must consider all three measurings in the three dimensional linear system of equations. The dataset of the measurings would look like that. Every 0.01 seconds a new line: [X]: -0.02 [Y]: -0.29 [Z]: -0.91 [X]: -0.05 [Y]: -0.27 [Z]: -1.07 [X]: -0.09 [Y]: -0.31 [Z]: -1.03 [X]: +0.00 [Y]: -0.33 [Z]: -0.92 [X]: +0.20 [Y]: -0.27 [Z]: -0.98 and so on... I will give you the complete dataset after you bid and get this project.