Bound on range precision for shot-noise limited ladar systems

The precision of ladar range measurements is limited by noise. The fundamental source of noise in a laser signal is the random time between photon arrivals. This phenomenon, called shot noise, is modeled as a Poisson random process. Other noise sources in the system are also modeled as Poisson processes. Under the Poisson-noise assumption, the Cramer-Rao lower bound (CRLB) on range measurements is derived. This bound on the variance of any unbiased range estimate is greater than the CRLB derived by assuming Gaussian noise of equal variance. Finally, it is shown that, for a ladar capable of dividing a fixed amount of energy into multiple laser pulses, the range precision is maximized when all energy is transmitted in a single pulse.