In this paper, we consider the tracking of a radar target with unknown range and range rate at low signal-to-noise ratio (SNR). For this nonlinear estimation problem, the Cramér-Rao lower bound (CRLB) provides a bound on an unbiased estimator's mean-squared error (MSE). However, there exists a threshold SNR at which the estimator variance deviates from the CRLB. We consider the Barankin bound (BB) on the range and range-rate variance in order to obtain a tighter lower bound at low SNR, and we use the BB to predict the SNR threshold for a transmitted signal. We demonstrate that the BB with the additional information provided by the threshold SNR has an advantage over the CRLB in selecting the optimal transmit waveform at low SNRs. We also develop a waveform parameter configuration method that uses the BB and the ambiguity function resolution cell measurement model to optimize the SNR threshold.