# Locating Image Sources from Multiple Spatial Room Impulse Responses
## 2 Methods
### Measurements  
The image source detection algorithm uses multiple SRIR measurements between different source and receiver positions. As in a single-microphone RIR measurement, a sound source plays a logarithmic sweep that is recorded by a receiver microphone array. The recorded signals are then convolved with the time-inverted sweep [8] in order to obtain a set of RIRs from the array. One SRIR measurement therefore contains a set of RIRs between one source and one receiver position, which we call source-receiver measurement.  
In the presented case studies (Section 3), SRIRs have been measured with a GRAS 50 VI-1 intensity probe. It consists of six omnidirectional capsules in a symmetric layout,  
Figure 1: Image source detection method. Room impulse responses are measured between \(S\) sources and \(R\) receivers where the latter consists of \(M\) microphones. Each set of \(M\) impulse responses is analyzed for direction-of-arrival (DoA), resulting in a set of directional parameters for each source-receiver pair. These responses are extracted for the direct sound and \(E\) early reflections that are stored in their corresponding objects. The direct sound objects are utilized to align the receivers to a common coordinate frame. Using this frame, early reflection objects can be combined across measurements to form \(N\) image sources. Finally, the image sources can further be aligned with each other to find more accurate location estimates for first order image sources.  
with one pair of capsules on each coordinate axis. The probe is well suited for directional estimation based on the time difference of arrival (TDoA). The later processing stages also require an omnidirectional pressure response. The intensity probe obtains this response from the topmost microphone, although the most optimal solution would be to acquire it from the center of the array [9].  
Apart from performing the impulse response measurements themselves, one needs to perform a few geometrical measurements to establish the absolute frame of reference for geometry calibration (Section 2.4). For the method described here, we use manually measured source positions and determine the receiver positions automatically from the direct sound estimates. If the source positions are kept static, one can move around the space with the receiver array freely. Best results have been observed when the loudspeaker is rotated to always point towards the microphone array. The geometry calibration algorithm used here can compensate for small inaccuracies in the receiver array orientation, but generally one should orient the microphone array consistently w.r.t. the frame of reference between measurements.  
The geometry calibration algorithm does not require sample-wise synchronization of source and receiver. Anyhow, one can determine the measurement system delay (Section 2.4.1) by measuring the input-output delay of the audio card, using a loop-back connection. But even after compensating this, there can still be some uncompensated system delay left, for example, due to digital signal processing in the amplifier and mechanical group delay in the loudspeaker. For this reason, the presented geometry calibration algorithm (Section 2.4.2) does not use the measured time information directly, but attempts to estimate any constant delay. While even other methods could be used to improve synchronization during measurement, using legacy datasets clearly demands for the algorithm to solve this problem. To avoid another bias, one can approximate the speed of sound accurately enough from measuring the air temperature.