Quantized innovations Kalman filter: stability and modification with scaling quantization |
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| Authors: | Jian XU Jian-xun LI Sheng XU Science Technology on Avionics Integration Laboratory Shanghai Jiao Tong University Shanghai China MOE |
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| Affiliation: | Key Laboratory of System Control and Information Processing, Shanghai Jiao Tong University, Shanghai 200240, China) (3School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China) |
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| Abstract: | The stability of quantized innovations Kalman filtering (QIKF) is analyzed. In the analysis, the correlation between quantization errors and measurement noises is considered. By taking the quantization errors as a random perturbation in the observation system, the QIKF for the original system is equivalent to a Kalman-like filtering for the equivalent state-observation system. Thus, the estimate error covariance matrix of QIKF can be more exactly analyzed. The boundedness of the estimate error covariance matrix of QIKF is obtained under some weak conditions. The design of the number of quantized levels is discussed to guarantee the stability of QIKF. To overcome the instability and divergence of QIKF when the number of quantization levels is small, we propose a Kalman filter using scaling quantized innovations. Numerical simulations show the validity of the theorems and algorithms. |
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| Keywords: | Kalman filtering Quantized innovation Stability Scaling quantization Wireless sensor network |
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