Stochastic Event-triggered Sensor Schedule for Remote State Estimation (1402.0599v1)

Abstract: We propose an open-loop and a closed-loop stochastic event-triggered sensor schedule for remote state estimation. Both schedules overcome the essential difficulties of existing schedules in recent literature works where, through introducing a deterministic event-triggering mechanism, the Gaussian property of the innovation process is destroyed which produces a challenging nonlinear filtering problem that cannot be solved unless approximation techniques are adopted. The proposed stochastic event-triggered sensor schedules eliminate such approximations. Under these two schedules, the MMSE estimator and its estimation error covariance matrix at the remote estimator are given in a closed-form. Simulation studies demonstrate that the proposed schedules have better performance than periodic ones with the same sensor-to-estimator communication rate.

• The paper introduces a stochastic event-triggered sensor schedule that preserves the Gaussian property, enabling robust MMSE state estimation.
• It derives straightforward recursive forms for the MMSE estimator and error covariance, ensuring stability without critical communication thresholds.
• The study provides analytical bounds on communication rates and estimation errors, offering practical insights for resource-constrained networked systems.

Stochastic Event-triggered Sensor Schedule for Remote State Estimation

The paper presents a novel approach to remote state estimation by introducing two types of stochastic event-triggered sensor schedules: open-loop and closed-loop. These schedules are designed to address the limitations of existing approaches in state estimation, particularly when dealing with nonlinear filtering problems under resource constraints.

The proposed sensor schedules leverage a stochastic event-triggering mechanism as opposed to deterministic approaches, allowing the retention of the Gaussian property of the innovation process. This crucial feature eliminates the need for approximations tied to computational intractability, thereby simplifying the estimation problem. In both schedules, the Minimum Mean Squared Error (MMSE) estimator and its associated estimation error covariance are derived in straightforward recursive forms, facilitating ease of analysis.

Main Contributions

1. General Stochastic Decision Rule: The paper introduces a decision-making policy for sensor scheduling in both open-loop and closed-loop configurations. In the open-loop case, decisions rely solely on local observations, while in the closed-loop case, decisions incorporate feedback information. This stochastic design preserves mathematical tractability by maintaining Gaussian properties.
2. MMSE Estimator Stability: The paper demonstrates that the MMSE estimator under these stochastic schedules remains stable, unlike some traditional methods with critical thresholds for stability conditions. Notably, for the closed-loop scheduler, there is no minimum communication rate required to ensure estimator stability.
3. Performance Bounds: Analytical results are provided for both the upper and lower bounds of average communication rates and estimation error covariance, offering an insightful comparative analysis with periodic schedules. This feature enables optimization of sensor energy use and communication bandwidth, crucial for applications with resource constraints.
4. Optimization Framework: The paper formulates an optimization problem to balance trade-offs between communication rate and estimation quality. This framework supports the design of system parameters to meet specific operational goals within constrained environments.

Practical and Theoretical Implications

The stochastic approach to event-triggered scheduling proposed in this paper has significant implications for the design of networked control systems (NCSs), especially in applications across aerospace, healthcare, and industrial automation. By reducing reliance on deterministic sampling, the new schedules offer improved flexibility and efficiency in resource utilization.

From a theoretical standpoint, the retention of Gaussian properties simplifies the design of optimal estimators, which is vital for advancing state estimation techniques. The combination of rigorous mathematical foundations and practical insights makes the paper a substantial contribution to the field of remote state estimation under constraints.

Future Developments

Looking forward, this research opens several avenues for future exploration. Potential developments could include the extension of this stochastic scheduling framework to multi-sensor settings, where complexities introduced by inter-sensor dependencies could be investigated. Additionally, exploring enhanced integration with modern communication protocols, such as IoT frameworks, could amplify the practical applications of this research.

With its strong foundational results and forward-looking implications, this paper represents a substantial step towards smarter, more efficient networked estimation strategies in environments constrained by resources. As such, it provides a robust platform for future advancements in remote sensing and estimation techniques.