A robust filter for sensors with partial measurement Loss and random multi-step delay

For nonlinear state estimation in wireless sensor networks (WSNs) with partial measurement loss and random multi-step delay (PML-RMD), a new robust loss and delay Variational Bayesian cubature Kalman filter (LDVBCKF), is proposed in this paper. The proposed filter integrates the VB framework into CKF to address scenarios where measurement anomalies arise from independently operating sensors. First, PML-RMD is modeled using diagonal Bernoulli matrices to characterize partial loss in each measurement dimension and categorical distribution variables to represent random multi-step delay, establishing an integrated measurement framework. Building upon this, the conjugate prior distributions for the uncertain measurement loss probabilities and multi-step delay probabilities are modeled as Beta and Dirichlet distributions, respectively, forming a joint prior distribution. By leveraging VB inference, approximate posterior probability distributions of the system state, latent variables, and anomaly probabilities are derived, facilitating their adaptive joint estimation. Finally, the resulting filter integrates VB updated parameters into the cubature Kalman filter structure, target tracking simulations in WSNs demonstrate the filter’s superior robustness and accuracy in handling PML-RMD, significantly outperforming conventional methods constrained by fixed prior assumptions.