From Equation 11, the delay-Doppler function S v,τ) consisted of the Dirac function in delay-Doppler point (τ q,v q ) which corresponds to reflecting path q and is supposed to be sparse.
When T1 is set as an ultrasound transmitter, the received signal of R1 consists of the signal propagated from a directly transmitted path, a reflecting path from the bubble and the inner pipe wall, and an arc path in the pipe wall.
The acoustic localization/communication is affected by many environmental factors like reflected paths, transmission losses and speed of sound.
Reflected paths result into absorption and scattering of the transmitted signal that reduces the intensity of sound energy.
The calibration consists in extracting relevant multipath components (MPCs), for instance once reflected paths, simultaneously from the model and measurement.
The maximal speed is 15 m/s, the Rician factor dB, and the reflected paths come uniformly, resulting in the classical Jakes DPP (31), with and.
The algorithm is designed in such a way that it overcomes the ambiguous nodes errata and reflected paths and therefore makes the algorithm more robust.
The existing algorithms does not consider the effect of realistic condition namely, (a) reflected paths, (b) watch circles, and (c) node displacement, which increases the localization error exponentially.
However, we overcome the problem of reflected paths and watch circles in our scheme, and the proposed scheme does not require time synchronization in the network.
Whereas authors in [5] uses the time synchronization between the two nodes without considering the notion of reflected paths, which increases the error exponentially.
