Optimal and robust shockwave detection and estimation

We consider detection and estimation of aeroacoustic shockwaves generated by supersonic projectiles. The shockwave is an N-shaped acoustic wave. The optimal detection/estimation scheme is considered based on an additive white Gaussian noise model. The introduction of an invertible linear transformation, such as the Fourier transform or the wavelet transform, does not improve detection performance under this model. However, if unknown interference and/or model mismatch is present, linear transforms may be of use. In addition, they may significantly reduce complexity at the cost of sub-optimality. We consider the use of the wavelet transform as a means of detecting the very fast rise and fall times of the shockwave, resulting in a l-D edge detection problem. This method is effective at moderate to high SNR and is robust with respect to unknown environmental interference that will generally not exhibit singularities as sharp as the N-wave edges