State estimation problems for systems involving small parameters are treated by both analytical and Lie algebraic approximation techniques. Specific classes of nonlinear filtering problems, which are perturbations of the Kalman problem, are considered. Asymptotic expansions of the unnormalized conditional density are presented, and in the case of observations of a Gauss-Markov process through polynominal (weak) nonlinearities a convergence result is derived. These expansions are related to certain approximations and deformations of the associated estimation Lie algebra.