Approximate filtering algorithms in nonlinear systems assume Gaussian prior and predictive density and remain popular due to ease of implementation as well as acceptable performance. However, these algorithms are restricted by two major assumptions: they assume no missing or delayed measurements. However, practical measurements are frequently delayed and intermittently missing. In this paper, we introduce a new extension of the Gaussian filtering to handle the simultaneous occurrence of the delay in measurements and intermittently missing measurements. Our proposed algorithm uses a novel modified measurement model to incorporate the possibility of the delayed and intermittently missing measurements. Subsequently, it redesigns the traditional Gaussian filtering for the modified measurement model. Our algorithm is a generalized extension of the Gaussian filtering, which applies to any of the traditional Gaussian filters, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF). A further contribution of this paper is that we study the stochastic stability of the proposed method for its EKF-based formulation. We compared the performance of the proposed filtering method with the traditional Gaussian filtering (particularly the CKF) and three extensions of the traditional Gaussian filtering that are designed to handle the delayed and missing measurements individually or simultaneously.INDEX TERMS Delayed measurements, Gaussian filtering, missing measurements, nonlinear Bayesian filtering.

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This article addresses the Gaussian filtering problem under the environment of jointly occurring delayed and missing measurements. In this work, the former irregularity is incorporated (in the measurement model) using a Bernoulli random variable (BRV) and a geometric random variable, while the latter is subsumed with the help of the BRV; thereby, it enables to take account of large delay extents efficiently. Specifically, a modified measurement model, which incorporates the concerned irregularities, is introduced. Accordingly, the measurement‐related statistical parameters, that is, measurement estimate, covariance, and cross‐covariance, are rederived with respect to the modified measurement model. The rederived parameters replace the corresponding ones in the traditional Gaussian filtering algorithm, resulting in the proposed Gaussian filter. The simulation results conclude the superior performance of the proposed filter over the existing filters in handling the coexisting delay and missing measurement irregularities.