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The filtering problem for a class of non-uniform sampling discrete stochastic systems is studied, where the state is<br>updated at a fast uniform sampling rate and the measurement is sampled at a slow non-uniform sampling rate. The state update rate is a multiple of the measurement sampling rate. The non-augmented state model at the measurement sampling points is established. Optimal state filters at the measurement sampling points are presented in the linear minimum variance sense by projecti
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ϔ㉏䴲ഛࣔ䞛ḋ㋏㒳ⱘⒸ⊶఼䆒䅵
܃
2
ē৴ࡁ
1,2
ēൄೠ
1
1. 咥啭∳ᄺ ⬉ᄤᎹᄺ䰶, જᇨⒼ 150080
E-mail: sunsl@hlju.edu.cn
2. 咥啭∳ᄺ ᭄ᄺ⾥ᄺᄺ䰶, જᇨⒼ 150080
E-mail: majing427@gmail.com
ᨬ 㽕: ⷨおњϔ㉏䴲ഛࣔ䞛ḋ⾏ᬷ䱣ᴎ㋏㒳ⱘⒸ⊶䯂乬ˈ݊Ё⢊ᗕҹᖿ䗳⥛ഛࣔ䖯㸠ᮄˈ㾖⌟ҹ᜶䗳⥛䴲ഛࣔ䖯㸠
䞛ḋˈϨ⢊ᗕᮄ⥛Ў㾖⌟䞛ḋ⥛ⱘᭈ᭄סDŽᓎゟњ㾖⌟䞛ḋ⚍Ϟⱘ䴲ᑓⱘ⢊ᗕൟDŽ߽⫼ᇘᕅ⧚䆎ᦤߎњ㾖
⌟䞛ḋ⚍Ϟⱘ㒓ᗻ᳔ᇣᮍᏂ᳔Ӭ⢊ᗕⒸ⊶఼DŽ䖯㗠ˈѢ㾖⌟䞛ḋ⚍Ϟⱘ⢊ᗕԄؐˈᦤߎњ⢊ᗕᮄ⚍Ϟⱘ⢊ᗕⒸ
⊶఼DŽ᳔ৢߚᵤњ᠔ᦤߎⱘⒸ⊶఼ⱘ⏤䖥〇ᅮᗻDŽӓⳳⷨお偠䆕њㅫ⊩ⱘ᳝ᬜᗻDŽ
݇䬂䆡: 䴲ഛࣔ䞛ḋ, Ⓒ⊶఼, ⢊ᗕぎ䯈ൟ, ᇘᕅ⧚䆎
Design of Filters for a Class of Non-uniform Sampling Systems
Hong-Lei Lin
2
, Jing Ma
1, 2
, Shu-Li Sun
1
1. School of Electronics Engineering, Heilongjiang University, Harbin 150080, China
E-mail: sunsl@hlju.edu.cn
2. School of Mathematics Science, Heilongjiang University, Harbin 150080, China
E-mail: majing427@gmail.com
Abstract: The filtering problem for a class of non-uniform sampling discrete stochastic systems is studied, where the state is
updated at a fast uniform sampling rate and the measurement is sampled at a slow non-uniform sampling rate. The state update
rate is a multiple of the measurement sampling rate. The non-augmented state model at the measurement sampling points is
established. Optimal state filters at the measurement sampling points are presented in the linear minimum variance sense by
projection theory. Further, the state filters at the state update points are presented based on the estimates at the measurement
sampling points. At last, the asymptotic stability of the proposed filters is analyzed. The simulation research verifies the
effectiveness of the proposed algorithm.
Key Words: Non-uniform sampling, Filter, State space model, Projection theory
1 ᓩ㿔
䖥ᑈᴹˈ䱣ⴔࠊ㋏㒳ⱘ㾘ᠽˈᴖᑺⱘ
ϡᮁᦤ催ˈᭈϾ㋏㒳ϡৃ㛑ҹϔⱘ䞛ḋ⥛䞛ḋ᠔᳝
ⱘ⠽⧚ֵোDŽℸˈ䗳⥛㋏㒳ⱘ⢊ᗕԄ䅵䯂乬ᓩ䍋
њ䆌ᄺ㗙ᎹҎⱘᑓ⊯݇⊼
[1-8]
DŽ
ᇍѢ䗳⥛Ӵᛳ఼ഛࣔ䞛ḋ⾏ᬷ䱣ᴎ㋏㒳ˈ᭛
⤂
[1]䞛⫼⢊ᗕᑓᮍ⊩ᦤߎњ㒓ᗻ᳔ᇣᮍᏂ᳔Ӭ⢊
ᗕԄ఼ؐˈԚ⢊ᗕᑓᇐ㟈Ⓒ⊶఼ⱘ䅵ㅫ᳝ᕜⱘ
䋳ᢙDŽᇍ䗳⥛Ӵᛳ఼ഛࣔ䞛ḋ⾏ᬷ䱣ᴎ㋏㒳ˈ᭛
⤂
[2]䗮䖛ᓎゟ↣ϾӴᛳ఼㾖⌟䞛ḋ⚍Ϟⱘ⢊ᗕぎ䯈
ൟˈ㒭ߎњ㾖⌟䞛ḋ⚍Ϟ⢊ᗕԄ䅵ؐˈ䖯㗠㒭ߎњ
ߚᏗᓣ㵡ড়Ⓒ⊶఼DŽԚᇍѢӴᛳ఼ˈা㛑㦋ᕫ↣Ͼ
㾖⌟䞛ḋ⚍Ϟⱘ⢊ᗕԄ䅵ؐˈᑊ≵᳝㒭ߎ݊Ҫ᮴㾖⌟
䞛ḋ⚍Ϟ⢊ᗕԄ఼ؐⱘ䆒䅵ᮍ⊩DŽᇍѢ䗳⥛Ӵᛳ
఼䴲ഛࣔ䞛ḋ㋏㒳ˈ᭛⤂
[3-5]䗮䖛ᓎゟ↣Ͼ㾖⌟䞛ḋ
*
ℸ乍Ꮉᕫࠄᆊ㞾✊⾥ᄺ䞥(61174139); ᬭ㚆䚼ᮄϪ㑾Ӭ⾔Ҏ
ᠡᬃᣕ䅵ߦ(NCET-10-0133); 咥啭∳ᄺ催ሖҎᠡ߯ᮄಶ䯳
(Hdtd2010-03); 咥啭∳ⳕ催䞡⚍ᅲ偠ᅸ䌘ࡽ.
⚍Ϟⱘ⢊ᗕぎ䯈ൟˈ㒭ߎњߚᏗᓣֵᙃ㵡ড়Ⓒ⊶
఼DŽԚ᭛⤂
[3]䞛⫼⢊ᗕᑓᮍ⊩ˈҹ᭄ഫЎԡᓎ
ˈℸ᠔䆒䅵ⱘⒸ⊶఼᳝䕗ⱘ䅵ㅫ䋳ᢙDŽ㱑✊
᭛⤂
[4-5]ᓎᯊ䙓ܡњ⢊ᗕᑓˈԚ⬅Ѣᓎᯊᗑ⬹
њ㋏㒳ాໄˈҢ㗠ᇐ㟈䕗ⱘᓎ䇃Ꮒˈ䰡ԢњԄ䅵
㊒ᑺDŽ᭛⤂
[6]ᇍѢ䖲㓁㋏㒳ˈѢֵᙃⒸ⊶఼㒭ߎњ
ܼሔ᳔Ӭ䲚ЁᓣߚᏗᓣԄ఼ؐDŽ᭛⤂
[5,7,8]ߚ߿໘
⧚њ䗳⥛䴲ഛࣔഛࣔ䞛ḋ㔥㒰㋏㒳ⱘⒸ⊶䯂乬DŽ
ѢҹϞߚᵤˈᴀ᭛㗗㰥њϔ㉏⢊ᗕ㾖⌟᳝
ϡৠ䞛ḋ⥛ǃϨ㾖⌟䴲ഛࣔ䞛ḋⱘ⾏ᬷ䱣ᴎ㒓ᗻ㋏㒳
ⱘⒸ⊶఼䆒䅵䯂乬DŽ佪ܜˈপ⢊ᗕᮄ⚍Ϟⱘ⢊ᗕᑇ
ഛؐЎ㾖⌟䞛ḋ⚍Ϟⱘ⢊ᗕؐᓎゟ㾖⌟䞛ḋ⚍Ϟ
ⱘ⢊ᗕൟDŽѢ᠔ᓎゟⱘ⢊ᗕぎ䯈ൟˈᑨ⫼ᇘᕅ
⧚䆎䆒䅵њ⢊ᗕᮄ⚍Ϟⱘ⢊ᗕԄ఼ؐDŽ⬅Ѣ≵᳝䖯
㸠⢊ᗕᑓˈℸϢ᭛⤂[3]Ⳍ↨ˈৃᯢᰒޣᇣ䅵ㅫ䋳
ᢙ˗⬅Ѣᓎゟ㋏㒳ൟᯊ㗗㰥њ㋏㒳ాໄˈℸϢ᭛
⤂[4-5]Ⳍ↨ˈ᳝ᬜഄޣᇣњᓎゟ⢊ᗕൟⱘ䇃ᏂˈҢ
㗠ᦤ催њԄ䅵㊒ᑺDŽ
3URFHHGLQJVRIWKHVW&KLQHVH&RQWURO&RQIHUHQFH
-XO\+HIHL&KLQD
1995
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