Analog to digital Convert for a bipolar Voltage

GolamMostafa:
To avoid the generation of negative voltage, one has to tie together all the zero-volt points (digital GND, analogue GND, signal GND, PWR Supply GND, and chassis GND); but, practically it is not always possible. There is always some ground loop. Under this circumstances, the sensor is to be calibrated against two known points to accommodate the offset and gain of the sensor. There is no sensor which is ideal; all sensors are real sensors, and they have gain and offset. You may follow these steps to have your sensor calibrated.

1. Apply 15V as excitation voltage.
2. Use a 4.7k + 2.2k voltage divider circuit. Voltage across of 2.2k would be fed to ADC.
3. Keep the position at 10 mm; measure the voltage across 2.2k and record it as VD1. You have the point A(d1, VD1) = A(10, VD1).

thanks for your explanation.
I try that, but it doesn't work. here is my wiring:

(link & image)
http://tinyurl.com/y834djz2
voltage divider.jpg

The voltage divider only decreases the range, it does not do anything about negative voltage.

how about an Amp?

here is the circuit that I use(in simulation):

http://tinyurl.com/ya4e3s53

It gave 1.25v (for -0.9 LVDT output) to 5V(for 10V LVDT output), so I will be able to calibrate 1.25~5V for 0~50 mm. I just wondering,is this circuit safe for LVDT and ADC? does it work practically??