Warangps - Overview
Warangps is a graphical tool for displaying the status and coordinates of gps devices in a distributed sensor network. Among other things (to be described later), warangps can be used to display the array response function for a specific array geometry.
After starting up warangps, you should switch to the Map tab of the graphical user interface and set the radio button from Auto to Manual. Only then you are able to push the Load button to open a free format ASCII coordinate file.
After locating an appropriate file with the file browser, a file parser window will be opened. The flexibel parser is described in detail in the multi-column parser page. Here we provide an example coordinate file and a corresponding parser file.
After loading the pre-configured parser file or after specifying the different column entries by yourself for your own coordinate file, you will load the coordinates by confirming with the Ok button.
The displays in warangps will change immediately presenting the coordinates in a table (upper left) and on a map (lower left). The array response function (ARF) for the corresponding array geometry will be computed in the wavenumber domain and is displayed in the right drawing area of warangps. On top of the wavenumber map, two circles are drawn for automatically determined values of and . Details about the meaning of those quantities and the automatic computation from the array geometry are given below in the corresponding sections.
Besides the ARF, there are two more useful visualizations derived from the array response function:
- Directly below the ARF figure, 1-D cross sections along different look directions for the wave propagation are plotted. The grey lines in the background show cross sections in all directions in 2 degree steps. The black curve displays a cross section along the direction chosen in the Azimuth spin box located on the right below the drawing area. The black curve is only drawn in between the two circles for and .
- On the lower right of the drawing area, you will find a display of 4 distinct wavenumber values, , , , , as curves in frequency vs. slowness which finally provide information on the capabilities of the array geometry in terms of resolution and expected aliasing features (see below and ). The intention of this plot is to export the layer of this curve that can then be overlaid to the display of f-k analysis results in max2curve.
is used to quantify the resolution capabilities of a specific array geometry. The definitionis based on the following idea: Given two signals propagating with similar wavenumbers, what is the minimum distance between wavenumbers that will still allow to find two separated peaks in the wavenumber map?
You will most probably find several answers to this question depending on the dimensionality of the array configuration (1D, 2D or 3D) and on the signal properties (correlated or not? two or more plane waves?). One common way to look on this problem is to view the superposition of two harmonic plane waves and explore at what minimum distance the peaks of the two plane waves will merge to a single maximum in the wavenumber plane. The simple answer can be understood by assuming that the array response functions for each individual plane wave just add together. Then it becomes clear that as soon as two plane waves are separated from each other in the wavenumber domain by less than the width of the main lobe width, the two peaks can not be resolved any more. The width of the main lobe peak in the array response function is called and is related approximately to the overall array aperture by
Note that this formula stems from considering a 1-D array layout. For 2-D arrays, the type of layouts we are mostly using for ambient vibration array analysis, the main lobe width may differ with azimuth as the effective aperture of the array geometry varies with the direction of plane wave propagation.
Given just two, non-correlated (outphased) plane wave arrivals, as defined above is an appropriate approximation of the resolution capabilities of an array whereas for a single plane wave arrival (or one energetically dominant source contribution) there is no resolution limit from the array geometry. Note that, as mentioned above, the true resolution capability may be better or worse, depending on the wave field properties (number of plane waves in analysis window) and signal properties (correlated signals). You can use the graphical tool gpfksimulator allows you to do so and explore by yourself the problem of multiple plane wave arrivals. By our experience from ambient vibration experiments with synthetic (ground truth) data, the resolution capability of an array lies approximately between and .
is used to describe the proximity of grating lobes (or strong side lobes) in the array response to the main lobe position. The definition of a grating lobe is most simple for a linear (1-D) equidistant array setup. For those kind of array geometries, the array response is a fully cyclic pattern. then corresponds to the distance in wavenumber domain between any exact repetition of the main lobe pattern along the 1-D axis of propagation. can then be computed as:
where is the minimum interstation distance, i.e. the distance between neighboring stations in a 1-D linear array layout.
It is often reported that can be used to specify aliasing limits of the array settings. To a certain extent this is true, as the grating lobes are indeed aliasing patterns from the spatial sampling process implicitly performed by recording a continuous wavefield at a finite number of discrete points in space. However, spatial aliasing can not be avoided, only ameliorated by array recordings with very dense station setups.
warangps will mostly be used for determining the array limits of some particular array geometry and saving the layer file from the limit curves. Further it will allow for designing an array with desired properties or to predict the capabilities on a planned array setting in advance. warangps replaces the older tool build_array with reduced functionality with regard to the exploration of the array response function. However, the added value of warangps and its true power lies in the direct applicability for in-filed determination of station coordinates and immediate display of the array response function, thus allowing for the detection of array geometry deficiencies and improving the array capabilities by re-location of individual stations in an urban environment.
For testing, one can interactively move individual stations in the station map view (lower left figure) by right click on the figure and enabling the station edit mode (see menu to the right). The cursor will change its appearance and clicking on one of the stations symbols will cause the station position to follow the cursor. You will immediately observe the change in the array response function while moving the station.