Risk Sensitive Filtering for Singular Systems subject to Round-Robin Protocol

Summary · qwen2.5:32b

The paper develops a risk-sensitive Kalman filtering framework for discrete-time linear stochastic singular systems under round-robin communication constraints, transforming these systems into an augmented state space model using Weierstrass canonical form to handle periodically varying measurements. An adaptive mechanism adjusts the risk parameter online based on covariance information, ensuring robustness against uncertainties and disturbances while maintaining filter stability through established sufficient conditions. The approach demonstrates improved estimation performance compared to standard Kalman filters in numerical results.

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Exploring a new risk sensitive filtering method for singular systems in communication-constrained environments, improving real-time rendering and optimization of complex models.

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arXiv:2607.04734v1 Announce Type: new Abstract: This paper develops a risk sensitive (RS) Kalman filtering framework for discrete-time linear stochastic singular systems operating under communication constraints imposed by a round-robin protocol. Due to limited network bandwidth, only a subset of the available measurements can be transmitted at each sampling instant, resulting in a periodically varying measurement structure. By employing the Weierstrass canonical form (WCF), the singular system is transformed into an equivalent augmented state space model, yielding a round-robin induced periodic system (RRIPS). A recursive risk sensitive Kalman filter (RSKF) is then developed for the RRIPS through a Bayesian formulation and the minimization of an exponential quadratic cost function, from which the recursive filtering equations are obtained for the original singular system. To enhance robustness against modeling uncertainties and disturbances, an adaptive RS mechanism is introduced in which the risk parameter is adjusted online according to the available covariance information. This adaptive strategy guarantees the positive definiteness of the predicted covariance matrix while adjusting the degree of risk sensitivity to the prevailing estimation uncertainty. Furthermore, sufficient conditions ensuring the filter stability are established using the observability and controllability concepts of periodic systems. The proposed framework reduces to the standard KF for singular systems when the RS parameter vanishes and recovers the standard RSKF when the singular matrix reduces to the identity matrix. Finally, numerical results are presented to demonstrate the effectiveness, robustness, and improved estimation performance of the proposed approach in comparison with the standard KF.