Matched-filter mismatch loss from within-pulse time-varying platform motion

In active sonar, own-Doppler nullification is used to remove the effect of motion of the source and receiver platforms. The process generally assumes a constant radial velocity throughout pulse transmission and during echo reception. When the platform motion does not satisfy the constant-radial-velocity assumption, the matched filter suffers a mismatch loss from time-varying own-Doppler (TVOD). The average TVOD signal-to-noise-ratio loss for velocity variations represented by a Gaussian random process is derived and approximated to show its dependence on the velocity variance, pulse duration and center frequency. The results provide a quantitative assessment of the common lore that platform velocity variations arising from wave motion are negligible for low frequencies or short pulses, but can produce significant losses as pulse duration and frequency or velocity variation increase.