The invention discloses a time
delay estimation and
distance measurement precision optimization method for entangled light
coincidence measurement. According to the method, on the basis of a Poisson
statistical model of
coincidence counting,
coincidence counting of
delay sampling points is regarded as mutually independent observation, real time
delay between
signal photons and idle photons is used as a parameter to be estimated, a joint
probability model and a log-likelihood function are constructed,
Fisher information amount and a Cramer-Rao lower bound (CRLB) corresponding to the
Fisher information amount are deduced, and the
estimation accuracy of the Cramer-Rao lower bound (CRLB) is improved. The method is used for depicting the
lower limit of variance which any unbiased estimator can reach under the observation model. In mean modeling, coincidence counting expectation is decomposed into
signal coincidence and accidental coincidence, and a
Gaussian second-order
correlation function is adopted to describe a coincidence counting peak, so that CRLB can explicitly reflect the effect of physical and statistical parameters of a
system on precision limit. On the basis,
sensitivity analysis is performed on key parameters such as
acquisition duration, two-channel single
photon counting rate, dark
counting rate, coincidence gate width, delay scanning step length and the like, a quantitative influence relationship of the key parameters on
Fisher information and CRLB is given, and the coincidence gate width shows a single-peak trend of decreasing firstly and then increasing for a precision lower bound; therefore, there is a realizable optimal gate width to minimize CRLB. And finally, mapping the time delay
estimation uncertainty into distance precision according to a
distance measurement model, and forming a parameter configuration
closed loop under the constraint of a set
acquisition duration and a
noise budget. Compared with a scheme of setting a door width depending on experience and repeated
trial and error, the method provides an explainable and reproducible lower bound driving parameter
selection criterion, and
engineering parameter design and performance optimization of
quantum distance measurement and related positioning and imaging systems can be directly supported.