State estimation is the core function of distribution management system, and its estimation accuracy directly affects the operation of other advanced application functions of distribution management system. However, the access of a large number of distributed generation brings non‐Gaussian noise and bad data problems, which affect the accuracy of state estimation. Therefore, based on the conventional cubature particle filter (CPF), two new state estimation operators, robust cubature filter 1 (RCPF1) and robust cubature filter 2 (RCPF2), are proposed by introducing the Huber's M‐estimation theory into the CPF algorithm and integrating a time‐varying, multi‐dimensional scale factor with the CPF, respectively. The simulation results based on IEEE33 bus system showed that: (1) RCPF has better estimation accuracy and robustness than conventional cubature particle filter and cubature Kalman filter; (2) RCPF2 has better estimation performance than RCPF1 in the case of non‐Gaussian noise and bad data.