The Army is currently developing systems of acoustic sensors to provide target tracking and identification in battlefield environments. The acoustic signatures of vehicles of interest, such as tanks and trucks, often contain tones that are harmonically related to a fundamental frequency and produce a pattern that can help identify the target. Target ID is very challenging however, because the signals are highly nonstationary and dependent on the weather and terrain as well as the vehicle's range, velocity, aspect, and operating mode. Methods to efficiently implement maximum likelihood estimates of the harmonic amplitudes, phases, and fundamental frequency have been developed and demonstrated on real data. Asymptotic Cramer-Rao bounds CRB for the parameters are readily available for both the white and colored noise case and give insight into practical issues for real-time implementation. A simple (but sometimes overlooked) observation that arises in these problems is the effect of defining the phase in the middle of the time window which both simplifies the CRB calculations and analysis and speeds up the MLE implementations.