**Author details**

Ying Shen *China Mobile Group, Zhejiang Co., Ltd. Huzhou Branch, Huzhou, China* 

Hui Zhang\*

270 Stochastic Modeling and Control

**Figure 2.** (a) Actual state and estimate of b(k), *N*=2, (b) Estimation error of b(k), *N*=2,

This paper discusses the parameter identifiability of quantized linear systems with Gauss-Markov parameters from information theoretic point of view. The existing definition concerning this property is reviewed and new definition is proposed for quantized systems. Criterion function, the Gramian of parameter identifiability for quantized systems is analyzed based on the quantity of mutual information. The derived conclusions consist with our intuition very well and also provide us with intrinsic perspective for the quantizer design. The analysis shows that the Gramian of quantized systems converge to that of unquantized systems when the quantization intervals turn to zero, and a well designed quantizer can preserve the identifiability of the original system even if the quantizer is as

(c)

k

0 10 20 30 40 50 60 70 80 90 100

Prior error entropy Posterior error entropy

coarse as one bit. The analytical analysis is verified by the illustrative simulation.

(c) Prior and posterior error entropy, *N*=2

**6. Conclusion** 

0.7

0.8

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1

1.1

Prior and posterior error entropy

1.2

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*State Key Laboratory of Industrial Control Technology, Institute of Industrial Process Control, Department of Control Science and Engineering, Zhejiang University, Hangzhou, China* 
