In this chapter, we consider partially observed diffusion processes with small diffusion coefficients in the observation equations only. The models depend on some unknown finite-dimensional parameters, and the construction of adaptive filters is realized in three steps: first, we propose preliminary estimators of the unknown parameters based on observations over a learning interval; then, these estimators are used for the construction of the One-step MLE process; and finally, this estimator process is substituted into the equations of filtration. The preliminary estimators are based on the calculation of the asymptotics of the quadratic variation of the derivative of the observed process. First, we study the linear Gaussian model; then, we discuss the generalization of the obtained results to conditionally Gaussian models. Finally, we propose an adaptive filter for one nonlinear system.