Observer-based discrete Markov jump systems (D-MJSs) are random, but their faults to be estimated are deterministic signals, so it is difficult to directly study the fault estimation of the system.Here, an approach of constructing auxiliary systems is proposed, which constructs deterministic intermediate variables by taking expectations of random variables, and then the established intermediate estimator can estimate the system state and faults at the same time.In addition, based on a new scaling method, the uncertainty of the Transition Probability Matrix (TPM) is considered.All conditions are given by Linear Matrix Inequalities (LMIs), and the state error is ensured by stable input state.Numerical simulation examples are provided to prove the effectiveness and superiority of the proposed approach.