New nonlinear filtering algorithms are designed based on a receding horizon strategy, i.e., a finite impulse response (FIR) structure, and square root information filtering to achieve high accuracy and good performance in empirical error covariance tests. The new nonlinear receding horizon filters reduce approximation errors in nonlinear filtering by considering a set of recent observations with non-informative initial conditions. By applying information filtering, we are able to manage the non-informative initial conditions, and thus propose the square root version of the algorithm as a means of retaining the positive definiteness of the error covariance. Based on the proposed strategy, we then implement known nonlinear filtering frameworks. Simulation results confirm that the new nonlinear receding horizon filters outperform existing nonlinear filters in well-known nonlinear examples.