To use RSSI, the mean path loss model derived from the log-normal shadowing model is used. A good paper for that is:
S. Seidel and T. Rappaport, “914 mhz path loss prediction models for indoor wireless communications in multifloored buildings,” Antennas and Propagation, IEEE Transactions on, vol. 40, no. 2, pp. 207–217, 1992.
If your channel is LOS and the distance between Tx and Rx is small, you can get a good accuracy. But if the distance is large, at somehow point between Tx and Rx, the parameters of path loss model should be changed based on the surrounding environment, which is very challenge to be expected for all directions. In addition, the value of RSS is instantaneous and it varies over the time, therefore, it is necessary to use averaging.
Some efforts have also been made in the literature to reduce the effects of RSS variations due to channel impediments by using a compressive sensing (CS) principle such as in:
C. Feng, W. Au, S. Valaee, and Z. Tan, “Compressive sensing based positioning using rss of wlan access points,” in INFOCOM, 2010 Proceedings IEEE, 2010, pp. 1–9.
Finally, try to pay attention to the effect of the body. The orientation of user leads to the attenuation by amount of 9.3 dB due to the obstruction from the body as reported in:
K. Kaemarungsi and P. Krishnamurthy, “Properties of indoor received signal strength for wlan location fingerprinting,” in Mobile and Ubiquitous Systems: Networking and Services, 2004. MOBIQUITOUS 2004. The First Annual International Conference on, 2004, pp. 14–23.
You can use the free space propagation model. Or the two ray ground. but from your last question and since you are using chip antennas then i guess free space model should do well as long as you don't have obstacles between the both ends.
Rappaport "Wireless Communications" has a nice survey of lots of experimental data and the resulting parametric models in chapter 4. I suppose it's a little dated now, but Maxwell's Laws and the Fresnel zones don't change. I was trying to do this with robots a few years ago and lots of Black Magic RF experts said it couldn't be done. The multi-path really messes things up, but if you can stay away from walls it may be possible. Good luck!
Small scale signal variations (e.g. multipath) may greatly affect the RSS measurement. Variations of up to 30-40dB have been reported (Rappaport etc), I have measured at least 10-15dB variations in indoor deployments of low power WPAN networks. Therefore, I would suggest that instead of using a single RSS measurement to estimate distance, try using the average or median value of N measurements collected on the same spot (I'd also suggest at least N>20) so that you can reduce the effect of small scale fading. Then you can use the log-distance model with more accuracy. If you have more measurements, extract the basic characteristics of the propagation environment first (like path loss exponent etc), to achieve better results.
To use RSSI, the mean path loss model derived from the log-normal shadowing model is used. A good paper for that is:
S. Seidel and T. Rappaport, “914 mhz path loss prediction models for indoor wireless communications in multifloored buildings,” Antennas and Propagation, IEEE Transactions on, vol. 40, no. 2, pp. 207–217, 1992.
If your channel is LOS and the distance between Tx and Rx is small, you can get a good accuracy. But if the distance is large, at somehow point between Tx and Rx, the parameters of path loss model should be changed based on the surrounding environment, which is very challenge to be expected for all directions. In addition, the value of RSS is instantaneous and it varies over the time, therefore, it is necessary to use averaging.
Some efforts have also been made in the literature to reduce the effects of RSS variations due to channel impediments by using a compressive sensing (CS) principle such as in:
C. Feng, W. Au, S. Valaee, and Z. Tan, “Compressive sensing based positioning using rss of wlan access points,” in INFOCOM, 2010 Proceedings IEEE, 2010, pp. 1–9.
Finally, try to pay attention to the effect of the body. The orientation of user leads to the attenuation by amount of 9.3 dB due to the obstruction from the body as reported in:
K. Kaemarungsi and P. Krishnamurthy, “Properties of indoor received signal strength for wlan location fingerprinting,” in Mobile and Ubiquitous Systems: Networking and Services, 2004. MOBIQUITOUS 2004. The First Annual International Conference on, 2004, pp. 14–23.
Various experts have given nice theoretical ideas. These theoritical ideas prepares grtound for starting and estimating the parameters. However, practically you need to measure RSSI value at different known & convenient distances and prepare chart. This exercise to be done in various seasons (Day, night, Dry, cold, rainy).
These charts will provide you (Extrapolation or Intra-polation) the distance.
You can use an appropriate path loss model that fits the environment you are considering as already suggested by Abdo. However, you must be careful to take into consideration the noise floor level and other losses that may occur with specific reference to your application and type of environment
Can be done approximately with predefined set of condition which includes above conditions as well. So even if you reach a value with any of popular methods don't forget to add the line indicating all the assumptions and conditions.
Practically,you can not use any theoretical model to relate the distance and its respective value of RSSI .Distance and its RSSI value is linearly related to each other only in free space model if we move in longitudinal direction to transmitting antenna.