1. A method for deriving information about a propagating electromagnetic beam, the method employing a plurality of intensity images captured at parallel spaced apart planes at respective positions along a propagation path of the beam, the method comprising: (a) initializing parameters of a state space model, the parameters including at least a covariance matrix initialized with a diagonal matrix; and (b) for successive ones of the intensity images, using the previously generated parameters and the intensity image to produce new parameters giving a successively improved description of the propagating electromagnetic beam, the new parameters including at least one covariance matrix which is a diagonal matrix; wherein the parameters include the covariance matrix and a pseudo-covariance matrix, and both of the covariance matrix and the pseudo-covariance matrix are initialized with diagonal matrices.