Cooperative Positioning
The JAVA applet below calculates the CramérRao lower bound for 2dimensional positioning. Pseudorange measurements between base stations (BSs) and a mobile terminal (MT) are obtained using a Gaussian error model having zero mean and a configurable standard deviation. For cooperative positioning, additional range measurements between MTs are obtained. The error model for these measurements is Gaussian again with zero mean and a standard deviation which is configurable. The color plot shows the CramérRao lower bound for the positioning root mean squared error (RMSE) in m. In black colored regions, the positioning RMSE is greater or equal than the maximum color bar value.
With the initial parameters, most indoor areas show a positioning RMSE ≥10m for TDOA positioning. Nevertheless, if several cooperative MTs are located within this poorly covered area, there is a significant gain due to cooperation by exploiting additional ranging measurements between MTs.
Applet Manual
Main Window
Click on tab Main to switch to the main window.
Scenario Panel
The main window shows the distribution of BSs, MTs and walls.

Base Stations
are represented by white markers "B0, B1, ...".
Double left click on the panel to add a BS. The applet supports up to 10 BSs. 
Mobile Terminals
are represented by gray markers "M".
Double right click on the panel to add a MT. The applet supports up to 20 MTs. Note, the applet calculation time increases significantly with the number of MTs.  Double left click on a BS and MT marker to remove.

Walls/Buildings
are represented by white lines. With the shift key pressed left click on the panel to add walls. With the shift key pressed use drag&drop (left mouse button) to move walls.
 With the shift key pressed double left click on a wall to open a dialog for setting an individual penetration loss or for removing that wall. Type a negative value in order to use the default wall penetration loss (see description of parameters below).
 In order to speed up calculation a subarea within the scenario panel can be defined. The color plot is calculated and shown only for this area. For the definition of this calculation area draw a rectangular window using the mouse (left mouse button) with the ctrl key pressed. Use ctrl single left click to remove the calculation area.
 Press alt and drag the mouse pointer (left mouse button) over the scenario panel. You'll see error ellipses for 1σ, 2σ and 3σ.
Control Buttons
 Press the Exec button to start the calculation of the CramerRao lower bound color plot.
 Press the Stop button to stop the calculation thread.
 Pressing Clear removes all components from the scenario panel.
 Reset sets the scenario panel to its initial state. Three BSs are plotted on fixed positions. 5 MTs are randomly distributed within a building.
Positioning
 TDOA ("Time Differences of Arrival") or hyperbolic positioning is based on the measurement of pseudoranges. The time bases (clocks) of the BSs are assumed to be synchronized. The clock of the MT is not synchronized to the BSs' clocks. In two dimensions, a TDOA value represents positions of equal distance difference of the MT and both involved BSs. Geometrically these positions describe a hyperbola with it's foci at the two BSs' positions. To calculate a MT position, at least two hyperbolas or TDOAs for intersection are required, which means that we need at least three BSs.
 Cooperative TDOA works like hyperbolic positioning. There are additional mobile terminals to which the considered MT performs a range (distance) measurement. Distance measurements are obtained if MTs are within the communication range of each other.
 Cooperative Gain shows the RMSE difference of the TDOA and Cooperative TDOA
 Pairwise TDOA (PTDOA) is similar to TDOA except that BS clocks are not fully synchronized. Only pairs of BSs are synchronous. Synchronous BS pairs are 01, 23, 45, etc. To calculate a MT position, at least two hyperbolas or TDOAs (in 2D) for intersection are required, which means that we need at least four BSs.
Parameter Window
Click on tab Parameters to switch to the parameter window.
Generic Parameters

Color Bar Max
The maximum value of the color bar scale.
Value range: 0...∞ [m] 
Scale Factor
Vertical resp. horizontal dimension of the layout in meters per pixel. The size of the panel is 400x300 pixels.
Value range: > 0 [m/pixel] 
Deafault Wall Penetration Loss
Allows to set a default value for the wall penetration loss, i.e., the attenuation for a wavefront travelling through a wall.
Value range: 0...∞ [dB]
Ranging Parameters

Pseudo Ranging RMSE
The root mean squared error (RMSE) for determination of pseudo ranges between BSs and MTs at a given reference distance (see parameter below).
Value range: 0.01...∞ [m] 
Reference Distance (d_{r})
The distance between BS and MT at which the pseudo ranging RMSE given above appears.
Value range: 1...∞ [m] 
Pseudo Ranging Decay Factor (γ)
The mean squared error (MSE) increases by 10 x γ x log(d/d_{r}) dB, where d is the distance between BS and MT.
Value range: 0...5
Cooperation Parameters

Coop. Communication Range
A range measurement between two MTs is obtained only if the MTs are within the communications range of each other.
Value range: 0...∞ [m] 
Coop. Ranging RMSE
The root mean squared error (RMSE) for determination of pseudo ranges between MTs at a given reference distance (see parameter below).
Value range: 0.01...∞ [m] 
Coop. Reference Distance (d_{c})
The distance between MTs at which the coop. ranging RMSE given above appears.
Value range: 1...∞ [m] 
Coop. Ranging Decay Factor (γ_{c})
The mean squared error (MSE) increases by 10 x γ_{c} x log(d/d_{c}) dB, where d is the distance between MTs.
Value range: 0...5
There is another version of this applet which provides a larger scenario panel and allows to load/save scenarios from and to files. However, for file loading and saving the applet requires the permission to go out of the browser's sandbox. For that you have to trust this applet. Your browser should ask you about that.

Note:
 You trust this applet on your own risk.
 There is no warranty and liability on our part.