ICML 2025

Optimal Sensor Scheduling and Selection for Continuous-Discrete Kalman
Filtering with Auxiliary Dynamics
Mohamad Al Ahdab 1 2 John Leth 1 Zheng-Hua Tan 1 2
Abstract
We study the Continuous-Discrete Kalman Filter
(CD-KF) for State-Space Models (SSMs) where
continuous-time dynamics are observed via multi-
ple sensors with discrete, irregularly timed mea-
surements. 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 trajec-
tory or that of the measured target. Each sensor
thus carries distinct costs and constraints asso-
ciated 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 co-
variance matrix of the CD-KF along the mean
auxiliary state. The bound is continuously differ-
entiable with respect to the measurement rates,
which enables efficient gradient-based optimiza-
tion. Exploiting this bound, we propose a finite-
horizon optimal control framework to optimize
measurement rates and auxiliary-state dynam-
ics 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.
1Department of Electronic Systems, Aalborg University, Aal-
borg Øst 9220, Denmark. 2Pioneer Centre for Artificial Intelli-
gence, Copenhagen 1350, Denmark.. Correspondence to: Mo-
hamad Al Ahdab <maah@es.aau.dk>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025
by the author(s).
1. Introduction
State-space...