On The Accuracy Limit of Joint Time-Delay/Doppler/Acceleration Estimation with a Band-Limited Signal

The derivation of estimation lower bounds is paramount to design and assess the performance of new estimators. A lot of effort has been devoted to the joint distance-velocity estimation problem, but very few works deal with acceleration, being a key aspect in several high-dynamics applications. Considering a generic band-limited signal formulation, in this contribution we derive a new closed-form Cramér-Rao bound (CRB) expression for joint time-delay/Doppler/acceleration estimation. This new formulation, especially easy to use, depends only on the baseband signal samples, and can be exploited for several purposes including estimator assessment (i.e., for signal design or to derive performance loss metrics with respect to the best (lowest) CRB). These results are illustrated and validated with two representative band-limited signals, namely, a GPS L1 C/A signal and a linear frequency modulated chirp signal.