We study the Continuous-Discrete Kalman Filter (CD-KF) for State-Space Models (SSMs) where continuous-time dynamics are observed via multiple sensors with discrete, irregularly timed measurements. Our focus extends to scenarios in which the measurement process is coupled with the states of an auxiliary SSM. For instance, higher measurement rates may increase energy consumption or heat generation, while a sensor’s accuracy can depend on its own spatial trajectory or that of the measured target. Each sensor thus carries distinct costs and constraints associated with its measurement rate and additional constraints and costs on the auxiliary state. We model measurement occurrences as independent Poisson processes with sensor-specific rates and derive an upper bound on the mean posterior covariance matrix of the CD-KF along the mean auxiliary state. The bound is continuously differentiable with respect to the measurement rates, which enables efficient gradient-based optimization. Exploiting this bound, we propose a finite-horizon optimal control framework to optimize measurement rates and auxiliary-state dynamics jointly. We further introduce a deterministic method for scheduling measurement times from the optimized rates. Empirical results in state-space filtering and dynamic temporal Gaussian process regression demonstrate that our approach achieves improved trade-offs between resource usage and estimation accuracy.

Many physical quantities change continuously over time (e.g., blood pressure, ocean temperature, radiation). To track these quantities, we often rely on multiple devices with different accuracies and operating conditions. For instance, imagine a low‐Earth‐orbit satellite observing terrestrial phenomena. Its sensors’ accuracy depends on the satellite’s orbital position. This satellite might carry high‐resolution sensors that perform best in sunlight and radar sensors that can operate anytime with consistent accuracy, but consume more energy and are less accurate. In our paper, we introduce an efficient method to decide both when to take measurements and which sensor to use, while also accounting for other changing factors (e.g., daylight, orbital position, and stored energy). We demonstrate our approach on several examples and show how it effectively balances measurement needs with resource constraints in this type of setting.