Optimal Sensor Scheduling and Selection for Continuous-Discrete Kalman Filtering with Auxiliary Dynamics

TL;DR

This paper develops an optimization framework for sensor scheduling in continuous-discrete Kalman filtering, accounting for auxiliary dynamics and resource constraints, leading to improved estimation accuracy and resource efficiency.

Contribution

It introduces a differentiable upper bound on the posterior covariance for joint optimization of measurement rates and auxiliary states in complex sensor scenarios.

Findings

Enhanced estimation accuracy with optimized sensor scheduling.

Reduced resource consumption while maintaining performance.

Effective joint control of measurement timing and auxiliary dynamics.

Abstract

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.