## Wireless Sensor Network Localization Measurement Repository

This page provides electronic access to data collected in the
measurement campaign reported in [1]. Please see the reference
for a detailed description of the measurement experiments. This
page describes only the files which contain the data.

### Acknowledgements

Data was collected by Neal Patwari while supported by Motorola Labs'
Florida Communications Research Lab, in Plantation, FL. All
measurement equipment was also provided by Motorola Labs.

### Files

The data is contained within a Matlab file (binary file) that can be
opened in Matlab with the `load' command.

### Description

There are three channel measurement experiments presented in [1], the
first in Section IV, and the next two in Section V. This data
corresponds to the measurement campaign in Section IV. This
campaign measured both TOA and RSS between sensors in a 44-sensor
network in an office environment. The variables contained
in the Matlab file are as follows:

- P_dB_RSS:
Measured received power between sensors in dBm (a 44 by 44
matrix). The (i,j) element is the dB average of 10 measurements,
5 with the transmitter at i and receiver at j, and 5 with the
transmitter at j and receiver at i. (The diagonal elements are
not used, and the matrix is symmetric.)
- n_p_RSS: The
estimated path loss exponent
- P_0_RSS: The
received power at the reference distance of 1m, in dBm.
- tilde_d_RSS:
The ML distance estimate from P_dB_RSS, n_p_RSS, and P_0_RSS, as given
in Equation (7) in reference [1].
- deviceLocs: Actual
coordinates of the 44 devices, in units of meters as shown in the plot
on this page.
- T_TOA: Time
delay between sensors, in seconds (a 44 by 44 matrix). The (i,j)
element is the T
_{i,j} reported in Section IV of [1], i.e., the average of 10 measured
time delays, 5 with the
transmitter at i and receiver at j, and 5 with the transmitter at j and
receiver at i. (The diagonal elements are not used, and the matrix is
symmetric.)

- mu_T_TOA: mean
time delay error. This, as described in Section IV of [1], has
already been subtracted out of T_TOA.
If you want the original TOA measurements you should add it back in to
each element.

- v_p_TOA: Speed
of propagation (speed of light) in m/s.

### Further Information

Please contact Neal Patwari
by email: npatwari _at_ umich.edu, or visit the Sensing and Processing Across Networks (SPAN) web site.

### References

[1] Neal Patwari, Alfred O. Hero III, Matt Perkins, Neiyer
Correal, and Robert J. O'Dea,"Relative Location Estimation in Wireless
Sensor Networks", IEEE Transactions
on Signal Processing, vol. 51, no. 8, Aug. 2003, pages
2137-2148. Available: [pdf].

### New! Matlab Localization Code

We now make a set of Matlab localization code freely available. This code encompasses two main components:

- simMLE.m:
Simulation script and accompanying functions which run simulation
trials for sensor localization when measurements are RSS and TOA.
The simulation generates a sensor network geometry, selects reference
devices, generates measurements based on the statistical models
presented in [1], and then estimates sensor coordinates by maximizing
the likelihood function. Many trials are run, and afterwards, the
1-standard deviation uncertainty ellipse of the simulations is
ouput. The Cramér-Rao bound (CRB) is also calculated and
displayed.
- calcLocalizationCRB.m:
Function for calculation of the CRB on unbiased location
estimators. This code calculates the bound when measurements are
either RSS, Quantized RSS, Proximity (Connectivity), TOA, or AOA.
This function is based on the work presented in several papers (see publications page).
Arbitrary sensor geometries, channel measurement parameters, and sets
of measurements can be set.

Download Matlab localization simulation and Cramer-Rao Bound calculation code. Please contact Neal Patwari for further information.

Last Modified 18 Oct 2006 by Neal Patwari