The paper considers the filtering problems solved in navigation data processing underquadratic nonlinearities both in system and measurement equations. A Kalman typerecursive algorithm is proposed, where the predicted estimate and gain at each step arecalculated based on the assumption on the Gaussian posterior proba-bility density functionof the estimated vector at the previous step and minimization of estimation error covariancematrix using a linear procedure with respect to the current measurement. The similaritiesbetween this algorithm and other Kalman type algorithms such as extended and secondorderKalman filters are discussed. The procedure for estimating the performance andcomparing the algorithms is presented.