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A chaotic signal in an observation area of network nodes is sent to a fusion center for reconstruction. As the communication bandwidth is limited, the signal must be quantified before sending to the fusion center, which will add quantization noise to the observed signal, which makes the signal reconstruction more difficult. A chaotic signal reconstruction algorithm is proposed in this paper based on square-root cubature Kalman filter. Firstly the probability density function of the observed signal is estimated, and then the optimal quantizer is used to quantify the observed signal. Under the limited budget of quantization bits, the best performance can be achieved. Compared with the unscented Kalman filter counterpart, our algorithm has fewer cubature points and has the merit of small computation load; meanwhile, it uses the square root of error variance for iteration, this will be more stable and accurate when iterating for parameter estimation. Simulation results show that the algorithm can reconstruct the observed signal quickly and effectively, with consuming less computation time and being more accurate than the one based on unscented Kalman filter.
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Keywords:
- cubature rule /
- probability density function /
- signal reconstruction /
- chaotic signal
[1] Zhang C, Fei S M, Zhou X P 2012 Chin. Phys. B 21 120101
[2] Qi H, Wang F B, Deng H 2013 Acta Phys. Sin. 62 104301 (in Chinese) [祁浩, 王福豹, 邓宏 2013 62 104301]
[3] Liu H R, Yin W X, Han T, Dong M R 2014 Acta Phys. Sin. 63 040509 (in Chinese) [刘浩然, 尹文晓, 韩涛, 董明如 2014 63 040509]
[4] Liu X L, Li Z, Hu Y S 2013 Acta Phys. Sin. 62 070201 (in Chinese) [刘向丽, 李赞, 胡易俗 2013 62 070201]
[5] de Senneville B D, Roujol S, Hey S, Moonen C, Ries M 2013 IEEE Trans. Medical Imaging 32 711
[6] Feng J C 2012 Chaotic Signal and Information Process (Beijing: Tsinghua University Press) p101 (in Chinese) [冯久超 2012 混沌信号与信息处理 (北京: 清华大学出版社)第101页]
[7] Feng J C, Tse C K, Lau F C M 2003 IEEE Trans. Circuits and Systems-I 50 954
[8] Ribeiro A, Giannakis G B, Roumeliotis S 2006 IEEE Trans. Signal Process. 54 4782
[9] Chen H B, Feng J C 2010 J. Southwest Univ. (Natural Science Edition) 32 124 (in Chinese) [陈宏滨, 冯久超 2010 西南大学学报 (自然科学版) 32 124]
[10] Roseveare N, Natarajan B 2012 IEEE Trans. Aerosp. Electron. Syst. 48 3494
[11] Chandra K P B, Gu D W, Postlethwaite I 2013 IEEE Sensors J. 13 750
[12] Wang S Y, Feng J C 2012 Acta Phys. Sin. 61 170508 (in Chinese) [王世元, 冯久超 2012 61 170508]
[13] Zhou J, Liu Y A, Wu F, Zhang H G, Zu Y X 2011 Acta Phys. Sin. 60 090504 (in Chinese) [周杰, 刘元安, 吴帆, 张洪光, 俎云霄 2011 60 090504]
[14] Walpole R E, Myers R H, Myers S L, Ye K 2012 Probability & Statistics for Engineers & Scientists (9th Ed.) (Boston: Pearson Education Inc.) pp84-86
[15] Maaref A, Aissa S 2009 IEEE Trans. Commun. 57 214
[16] Shi J, Yang D S, Shi S G 2011 Acta Phys. Sin. 60 064301 (in Chinese) [时洁, 杨德森, 时胜国 2011 60 064301]
[17] Yu X, Wang H Q, Yang E H 2010 IEEE Trans. Inform. Theory 56 5796
[18] Bianchi P, Jakubowicz J 2013 IEEE Trans. Signal Process. 61 3119
[19] Cui S, Xiao J J, Goldsmith A J, Luo Z Q, Poor H V 2007 IEEE Trans. Signal Process. 55 4683
[20] Chen H B, Feng J C, Fang Y 2008 Chin.Phys.Lett. 25 405
[21] Yu S M, Yu Z D 2008 Acta Phys. Sin. 57 6859 (in Chinese) [禹思敏, 禹之鼎 2008 57 6859]
[22] Gao G R, Liu Y P, Pan Q 2012 Acta Phys. Sin. 61 139701 (in Chinese) [高国荣, 刘艳萍, 潘琼 2012 61 139701]
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[1] Zhang C, Fei S M, Zhou X P 2012 Chin. Phys. B 21 120101
[2] Qi H, Wang F B, Deng H 2013 Acta Phys. Sin. 62 104301 (in Chinese) [祁浩, 王福豹, 邓宏 2013 62 104301]
[3] Liu H R, Yin W X, Han T, Dong M R 2014 Acta Phys. Sin. 63 040509 (in Chinese) [刘浩然, 尹文晓, 韩涛, 董明如 2014 63 040509]
[4] Liu X L, Li Z, Hu Y S 2013 Acta Phys. Sin. 62 070201 (in Chinese) [刘向丽, 李赞, 胡易俗 2013 62 070201]
[5] de Senneville B D, Roujol S, Hey S, Moonen C, Ries M 2013 IEEE Trans. Medical Imaging 32 711
[6] Feng J C 2012 Chaotic Signal and Information Process (Beijing: Tsinghua University Press) p101 (in Chinese) [冯久超 2012 混沌信号与信息处理 (北京: 清华大学出版社)第101页]
[7] Feng J C, Tse C K, Lau F C M 2003 IEEE Trans. Circuits and Systems-I 50 954
[8] Ribeiro A, Giannakis G B, Roumeliotis S 2006 IEEE Trans. Signal Process. 54 4782
[9] Chen H B, Feng J C 2010 J. Southwest Univ. (Natural Science Edition) 32 124 (in Chinese) [陈宏滨, 冯久超 2010 西南大学学报 (自然科学版) 32 124]
[10] Roseveare N, Natarajan B 2012 IEEE Trans. Aerosp. Electron. Syst. 48 3494
[11] Chandra K P B, Gu D W, Postlethwaite I 2013 IEEE Sensors J. 13 750
[12] Wang S Y, Feng J C 2012 Acta Phys. Sin. 61 170508 (in Chinese) [王世元, 冯久超 2012 61 170508]
[13] Zhou J, Liu Y A, Wu F, Zhang H G, Zu Y X 2011 Acta Phys. Sin. 60 090504 (in Chinese) [周杰, 刘元安, 吴帆, 张洪光, 俎云霄 2011 60 090504]
[14] Walpole R E, Myers R H, Myers S L, Ye K 2012 Probability & Statistics for Engineers & Scientists (9th Ed.) (Boston: Pearson Education Inc.) pp84-86
[15] Maaref A, Aissa S 2009 IEEE Trans. Commun. 57 214
[16] Shi J, Yang D S, Shi S G 2011 Acta Phys. Sin. 60 064301 (in Chinese) [时洁, 杨德森, 时胜国 2011 60 064301]
[17] Yu X, Wang H Q, Yang E H 2010 IEEE Trans. Inform. Theory 56 5796
[18] Bianchi P, Jakubowicz J 2013 IEEE Trans. Signal Process. 61 3119
[19] Cui S, Xiao J J, Goldsmith A J, Luo Z Q, Poor H V 2007 IEEE Trans. Signal Process. 55 4683
[20] Chen H B, Feng J C, Fang Y 2008 Chin.Phys.Lett. 25 405
[21] Yu S M, Yu Z D 2008 Acta Phys. Sin. 57 6859 (in Chinese) [禹思敏, 禹之鼎 2008 57 6859]
[22] Gao G R, Liu Y P, Pan Q 2012 Acta Phys. Sin. 61 139701 (in Chinese) [高国荣, 刘艳萍, 潘琼 2012 61 139701]
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