A new algorithm for the accurate estimation of the specific differential phase shift on propagation (K-dp) from noisy total differential phase shift (Psi(dp)) measurements is presented for data acquired with a polarimetric weather radar. The new approach, which is based on the compilation of ensembles of Kalman filter estimates, does not rely on additional data like the reflectivity or the differential reflectivity in order to constrain the solution, and it is based on Psi(dp) only. The dependence of the solution on Psi(dp) only allows one to apply the algorithm in various environmental conditions without reducing its performance. Drawbacks that are usually inherent in algorithms of this kind (like the loss of the small-scale structure and the smoothing of high peak values) are partially overcome by a two-step algorithm design, which first determines an ensemble of possible solutions and then selects and averages the ensemble members such that the estimated K-dp profile has a better agreement with the truth. The algorithm is thoroughly evaluated and compared with a commonly used algorithm on stochastically simulated profiles of raindrop size distribution. It is found that the accuracy of the K-dp values estimated with the new algorithm significantly increases. The algorithm is also experimentally evaluated by applying it on X-band radar data that were acquired in northern Brazil during the CHUVA campaign and at a high alpine site in Switzerland during snowfall. Results show that the spatial fine structure and the high values of precipitation are better represented with the new method.