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This study is concerned with the problem of state estimation for networked systems with a Markov plant considering the measurement uncertainties. The measurements suffer from both the randomly occurring missing phenomenon and the quantisation effects. Taking into account the statistical knowledge of the quantised measurements, an approximate minimum mean square error estimate algorithms is derived based on Gaussian assumption, which is referred to as interacting multiple model Monte Carlo (IMMMC) algorithm. A quantised measurement expectation calculated by Monte Carlo sampling method is embedded into the Kalman filter under the IMM framework. A simulation example is provided demonstrating that IMMMC is computationally appealing and presents better estimate performance than the previous algorithms. Moreover, IMMMC has better mode following ability and can clearly distinguish the occurrence of measurements missing. [ABSTRACT FROM AUTHOR]