Bit-Rate Allocation for Quantized Kalman Filtering via Rate-Distortion Theory

Document Type

Article

Publication Date

1-1-2026

Abstract

The performance of Kalman filters in networked sensing systems is often limited by communication bandwidth, making quantization unavoidable. This paper studies a centralized quantized Kalman filtering framework in which a local central processor communicates state information to a remote central processor through a bandwidth-constrained channel. Motivated by sensing architectures with high-accuracy meters and local processing capabilities, the measurements are modeled as direct quantized versions of the system states. Under this setting, the proposed framework allocates a fixed communication budget among correlated state variables using the Gaussian rate–distortion function for independent sources. State correlations are exploited through a basis determined by the system dynamics and innovation covariance, enabling an analytically tractable reverse-water-filling allocation while maintaining a low-complexity scalar-quantization architecture. A steady-state analysis identifies the appropriate operating basis for four classes of dynamical systems and yields a practical covariance-aware allocation procedure. Since the allocation relies on moment-matched Gaussian approximations of the posterior and predicted prior distributions, their accuracy is assessed through Kullback-Leibler divergence analysis. Simulations show close agreement between theory and practical scalar quantization, and comparisons against uniform and random baselines demonstrate substantial distortion reductions, with improvements above 95% in the reported ill-conditioned systems. The results show that covariance-aware communication-budget allocation can significantly improve estimation performance with low implementation complexity.

Publication Title

IEEE Transactions on Signal Processing

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