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

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...

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Vydáno v:IEEE transactions on automatic control Ročník 70; číslo 5; s. 3181 - 3196
Hlavní autoři: Liu, Qinyuan, Nie, Yao, Wang, Zidong, Dong, Hongli, Jiang, Changjun
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.05.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Binary encoding scheme (BES)
Bit error rate
Codes
Coding
Conditional probability
Covariance matrices
Discrete time systems
Encoding
Estimation
Filter design (mathematics)
Information systems
iterative Bayesian estimate
Kalman filter (KF)
Kalman filters
Lower bounds
Measurement uncertainty
minimum mean-square error (MMSE)
networked systems
Noise
Probabilistic logic
probabilistic quantizer
Probability density function
Probability density functions
Quantization (signal)
Remote sensors
Sensors
Statistical analysis
Strings
ISSN:0018-9286, 1558-2523
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Popis
Shrnutí: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 Cramér-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.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2024.3496573