In the case that the clutter of the polarimetric synthetic aperture radar (PolSAR) imagery follows K distribution

the existing constant false alarm rate (CFAR) detection algorithms based on multi-look polarization whitening filter (MPWF) cannot be applied to the condition that the equivalent number of looks is a non-integer.To solve the problem

a CFAR detection algorithm with analytical false alarm probability expression is proposed.After introducing the Gamma distribution texture under the product model

the probability distribution function (PDF) of the MPWF metric is integrated to obtain its cumulative distribution function (CDF)

and then the analytical form of the false alarm probability with respect to the detection threshold is obtained.The simulation results show that the new algorithm has a good false alarm fitting effect.In addition

when the target clutter ratio (TCR) is large

the new algorithm has a higher detection probability.Otherwise

the detection probability is lower than the existing algorithm.It is worth pointing out that the current false alarm probability expression of multi-look polarization matched filter (MPMF) under K distribution is wrong

so the current detection algorithm based on MPMF detection metric is modified and the correct expression of the false alarm probability is derived.