Sensor Query Schedule and Sensor Noise Covariances for Accuracy-constrained Trajectory Estimation

2026-02-18

AI Summary

This work addresses the critical challenge of jointly designing sensor query rates and noise covariance under resource and cost constraints to meet prescribed trajectory estimation accuracy requirements. It presents the first formalization of this problem as a unified optimization model, leveraging semidefinite programming (SDP) within the Kalman filter error covariance framework to simultaneously optimize measurement scheduling and noise parameters. The proposed approach efficiently determines whether a given accuracy target is achievable and, when feasible, synthesizes a corresponding implementation strategy. Experimental validation demonstrates that the computed sensor configurations consistently attain the desired accuracy in both simulated and real-world scenarios, while also reliably identifying infeasible accuracy demands.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Trajectory estimation involves determining the trajectory of a mobile robot by combining prior knowledge about its dynamic model with noisy observations of its state obtained using sensors. The accuracy of such a procedure is dictated by the system model fidelity and the sensor parameters, such as the accuracy of the sensor (as represented by its noise covariance) and the rate at which it can generate observations, referred to as the sensor query schedule. Intuitively, high-rate measurements from accurate sensors lead to accurate trajectory estimation. However, cost and resource constraints limit the sensor accuracy and its measurement rate. Our work's novel contribution is the estimation of sensor schedules and sensor covariances necessary to achieve a specific estimation accuracy. Concretely, we focus on estimating: (i) the rate or schedule with which a sensor of known covariance must generate measurements to achieve specific estimation accuracy, and alternatively, (ii) the sensor covariance necessary to achieve specific estimation accuracy for a given sensor update rate. We formulate the problem of estimating these sensor parameters as semidefinite programs, which can be solved by off-the-shelf solvers. We validate our approach in simulation and real experiments by showing that the sensor schedules and the sensor covariances calculated using our proposed method achieve the desired trajectory estimation accuracy. Our method also identifies scenarios where certain estimation accuracy is unachievable with the given system and sensor characteristics.

Problem

• trajectory estimation
• sensor noise covariance
• sensor query schedule
• accuracy constraint
• mobile robot

Innovation

• sensor scheduling
• noise covariance estimation
• trajectory estimation
• semidefinite programming
• accuracy-constrained optimization