Efficient Sensor Fusion Through Covariance-Constrained Observation Decimation (CCOD)
Observation decimation is frequently employed in state estimation to reduce sensing, communication, and computational requirements, but decreasing the measurement assimilation frequency increases estimation uncertainty. Selecting an appropriate observation decimation factor therefore requires accurately predicting the resulting estimator performance. While the discrete algebraic Riccati equation (DARE) provides the steady-state estimation-error covariance for standard linear time-invariant Kalman filters, it is not directly applicable to estimators employing decimated measurement updates. Existing approaches address this limitation through lifted system representations or periodic Riccati equation formulations, both of which incur additional computational complexity. This paper presents a covariance-constrained observation decimation (CCOD) framework that reformulates the DARE inputs using equivalent decimated system and process-noise matrices that capture covariance growth between measurement updates. The proposed reformulation enables direct prediction of the steady-state estimation-error covariance through a single DARE evaluation without increasing the system dimension or solving coupled periodic Riccati equations. The resulting covariance prediction is used to determine the maximum observation decimation factor that satisfies a prescribed estimation uncertainty bound. Validation using a high dimensional linear time-invariant system and a space object tracking application demonstrates that the proposed approach accurately predicts steady-state estimator performance while reducing the measurement assimilation frequency required to satisfy specified covariance constraints.