This article designs an advanced Gaussian filtering algorithm for improving accuracy in the presence of time-delay in measurements. The proposed method uses a Bernoulli random variable and a geometric random variable to reformulate the delay modeling strategy. Subsequently, the traditional Gaussian filtering method for the modified measurement model is rederived. The proposed method precludes two major drawbacks of the existing delay filtering methods, including a priori knowledge of many delay probabilities and an ambiguous selection of an upper bound of delay. Thus, the proposed method outperforms the existing delay filtering methods and the same is validated from the simulation results. The proposed method is a general modification of the traditional Gaussian filtering and applies to all conventionally popular Gaussian filters.