Binary-Encoding-Based Quantized Kalman Filter: An Approximate MMSE Approach

• 成果类型: Article
• 署名作者: Liu, Qinyuan; Nie, Yao; Wang, Zidong; Dong, Hongli; Jiang, Changjun
• 署名单位: Tongji University; Tongji University; Tongji University; Brunel University; Northeast Petroleum University; Northeast Petroleum University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3496573
• 发表日期: 2025
• 页码: 3181-3196
• 关键词: Quantization (signal); Kalman filters; estimation; Probabilistic logic; encoding; sensors; Probability density function; noise; Covariance matrices; Measurement uncertainty; Binary encoding scheme (BES); iterative Bayesian estimate; Kalman filter (KF); minimum mean-square error (MMSE); networked systems; probabilistic quantizer

摘要

In this article, the Kalman filter design problem is investigated for linear discrete-time systems under binary encoding schemes. Under such a scheme, the local information is quantized into a bit string by the remote sensor based on a probabilistic quantizer, and then the bit string is transmitted via memoryless binary symmetric channels (BSCs). Due to the communication link noises, the bit flipping occurs in a random manner, and thus, the transmission of the bit string would suffer from specific bit-error rates. With the received bits, a recursive binary-encoding-based quantized Kalman filter is established in the approximate minimum mean-square error (MMSE) sense, which relies on the Gaussian approximation of the conditional probability density function at each iteration. Furthermore, the proposed estimator is shown to be of a Kalman-like type through performance analysis, which exhibits computational complexity comparable to the conventional Kalman filter. Subsequently, a posterior Cram & eacute;r-Rao lower bound is derived for the proposed binary-encoding-based quantized Kalman filter. The effectiveness of the proposed estimator is demonstrated through numerical results.