In the soft-input soft-output Viterbi algorithm (SOVA), the log-likelihood ratio (LLR) of each bit is determined by the minimum metric difference between the ML path and its competitive paths. This paper proposes to trim large metric differences in order to reduce the complexity of SOVA. By trimming the metric differences, only a small number of backtracking operations are carried out, while many LLRs may be omitted as the result of the lack of metric differences. By revealing the relationship among neighboring LLRs, the omitted LLRs are estimated from its neighoring LLRs as well as intrinsic information. The extrinsic information transfer chart analysis demonstrates that the proposed algorithm has similar convergence behavior as the Log-MAP algorithm, if the trimming factor M is moderate. Other analyses verify that our approach provides good LLR quality with only at most 1/M backtracking operations of SOVA. Simulation results show that it outperforms SOVA and performs as well as its variants and the Log-MAP algorithm.

This paper proposed a two‐stage robust extended Kalman filter (TREKF) for state estimation of non‐linear uncertain system with unknown inputs. In engineering practice, the extended Kalman filter (EKF) with unknown inputs of the non‐linear uncertain system may be degraded or even diverged. The optimal two‐stage EKF (TEKF) is designed to solve the unknown inputs. The robust EKF (REKF) is considered to solve the non‐linear uncertain system for a long time. However, the information about the non‐linear uncertain system with unknown inputs is always incorrect. To solve this problem, the TREKF is designed by using the advantages of the TEKF and REKF, furthermore, its stability is proved. Finally, the performances of the TREKF, which are compared with the results of the REKF, TEKF and EKF, are verified by illustrating a numerical example of the powered descent phase of Mars EDL (entry, descent and landing). These also verify that the unfavourable effects of the model uncertainties and the unknown inputs are reduced efficiently by using the TREKF for the miniature coherent altimeter and velocimeter and inertial measurement unit integrated navigation during the powered descent phase of Mars EDL.