×

zbMATH — the first resource for mathematics

Nonlinear dynamical system identification from uncertain and indirect measurements. (English) Zbl 1129.93545

MSC:
93E12 Identification in stochastic control theory
37M10 Time series analysis of dynamical systems
62F10 Point estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
93E10 Estimation and detection in stochastic control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1103/RevModPhys.65.1331
[2] DOI: 10.1007/978-1-4612-0763-4
[3] DOI: 10.1142/S0218127495000363 · Zbl 0886.58100
[4] DOI: 10.1103/PhysRevA.38.3017
[5] DOI: 10.1007/978-3-642-59281-2
[6] Anderson B. D. O., Optimal Filtering (1979)
[7] DOI: 10.1111/j.1467-9892.1984.tb00374.x · Zbl 0536.93064
[8] DOI: 10.1103/PhysRevLett.88.234302
[9] DOI: 10.1007/978-3-642-75883-6
[10] Arulampalam S., IEEE Trans. Sign. Process
[11] DOI: 10.1103/PhysRevA.45.5524
[12] DOI: 10.1007/BF02460663 · Zbl 0757.92006
[13] Bar-Shalom Y., Tracking and Data Association (1988) · Zbl 0634.93001
[14] DOI: 10.1002/0471221279
[15] Barnett S., Polynomials and Linear Control Systems (1983) · Zbl 0528.93003
[16] Bellman R. E., Quasiliniearization and Boundary Value Problems (1965)
[17] DOI: 10.1080/17442508108833174 · Zbl 0458.60030
[18] DOI: 10.2307/3318679 · Zbl 0830.62075
[19] DOI: 10.1007/978-3-642-68220-9_8
[20] H. G. Bock, Progress in Scientific Computing 2, eds. P. Deuflhard and E. Hairer (Birkhäuser, Boston, 1983) pp. 95–121.
[21] DOI: 10.1137/0908085 · Zbl 0637.65150
[22] DOI: 10.1103/PhysRevA.42.5817
[23] DOI: 10.1080/01621459.1985.10478157
[24] DOI: 10.1016/S0167-2789(01)00323-2 · Zbl 1001.37087
[25] DOI: 10.1063/1.1357454 · Zbl 1080.37598
[26] Bryson A. E., Applied Optimal Control (1969)
[27] DOI: 10.1214/aos/1176347739 · Zbl 0721.62068
[28] DOI: 10.1080/01621459.1992.10475231
[29] DOI: 10.1007/978-1-4899-4477-1
[30] DOI: 10.1007/978-3-642-61312-8 · Zbl 0666.93053
[31] Conti R., Linear Differential Equations and Control (1976) · Zbl 0356.34007
[32] Cremers J., Z. Naturforsch. 42 pp 797–
[33] Crutchfield J. P., Compl. Syst. 1 pp 417–
[34] Csaki P., Magyar Tud. Akad. Mat. Kutato Int. Kozl. 8 pp 27–
[35] DOI: 10.1080/17442508608833428 · Zbl 0626.62085
[36] DOI: 10.1109/TAC.1986.1104344 · Zbl 0621.93067
[37] DOI: 10.1142/S0218127493000076 · Zbl 0875.62414
[38] DOI: 10.1063/1.166363 · Zbl 1039.62502
[39] Dempster A. P., J. Roy. Stat. Soc. B 39 pp 1–
[40] DOI: 10.1080/10556789508805633
[41] DOI: 10.1016/0167-2789(91)90037-A · Zbl 0729.65501
[42] DOI: 10.1016/S0006-3495(61)86902-6
[43] DOI: 10.1093/comjnl/7.2.149 · Zbl 0132.11701
[44] Florens-Zmirou D., Statistics 4 pp 547– · Zbl 0673.62072
[45] DOI: 10.1016/0169-7439(88)80029-7
[46] Fraser D. C., IEEE Trans. Automat. Contr. 7 pp 387–
[47] DOI: 10.1111/j.1467-9892.1994.tb00184.x · Zbl 0815.62065
[48] DOI: 10.1002/9780470316665
[49] DOI: 10.1002/zamm.19410210604 · Zbl 0026.33402
[50] Gelb A., Applied Optimal Estimation (1974)
[51] Gershenfeld N., The Nature of Mathematical Modeling (1999) · Zbl 0905.00015
[52] Ghahramani Z., Advances in Neural Information Processing Systems 11 (1999)
[53] Gill P. E., Practical Optimization (1981) · Zbl 0503.90062
[54] DOI: 10.1049/ip-f-2.1993.0015
[55] DOI: 10.1103/PhysRevA.44.6264
[56] DOI: 10.1103/PhysRevA.43.5321
[57] DOI: 10.1103/PhysRevA.46.1784
[58] DOI: 10.1103/PhysRevLett.50.346
[59] DOI: 10.1016/0167-2789(83)90298-1 · Zbl 0593.58024
[60] DOI: 10.1142/S0218127491000403 · Zbl 0874.58029
[61] Grewal M. S., Kalman Filtering: Theory and Practice Using MATLAB (2001)
[62] Hamilton J. D., Time Series Analysis (1994) · Zbl 0831.62061
[63] DOI: 10.1090/S0273-0979-1988-15701-1 · Zbl 0689.58026
[64] DOI: 10.1016/0375-9601(90)90493-8
[65] DOI: 10.1145/356004.356010 · Zbl 0486.65040
[66] DOI: 10.1017/CCOL0521382483
[67] DOI: 10.1016/0167-6911(83)90074-9 · Zbl 0539.93077
[68] DOI: 10.1063/1.166356 · Zbl 0971.37039
[69] DOI: 10.1103/PhysRevE.60.4970
[70] DOI: 10.1063/1.166424 · Zbl 0990.37522
[71] DOI: 10.1017/S0305004100013517 · JFM 61.1304.01
[72] DOI: 10.1113/jphysiol.1952.sp004764
[73] DOI: 10.1007/BF02459643 · Zbl 0553.92005
[74] DOI: 10.1007/978-3-662-04763-7
[75] DOI: 10.1007/3-540-39949-6_19
[76] DOI: 10.1103/PhysRevE.64.016222
[77] DOI: 10.1016/S0375-9601(02)00748-X · Zbl 0996.37077
[78] DOI: 10.1063/1.166196
[79] Jazwinski A. H., Stochastic Processes and Filtering Theory (1970) · Zbl 0203.50101
[80] DOI: 10.1086/112659
[81] DOI: 10.1086/114727
[82] DOI: 10.1109/9.847726 · Zbl 0973.93053
[83] DOI: 10.1142/S0218127493000507 · Zbl 0875.58025
[84] Kalman R., Trans. ASME J. Basic. Eng. Series 82 pp 35–
[85] Kalman R. E., Trans. ASME J. Basic. Eng. Series 83 pp 95–
[86] DOI: 10.1063/1.166096
[87] Kantz H., Nonlinear Time Series Analysis (1997) · Zbl 0873.62085
[88] DOI: 10.1103/PhysRevA.45.3403
[89] Kitagawa G., J. Comput. Graph. Stat. 5 pp 1–
[90] Kloeden P., Numerical Solution of Stochastic Differential Equations (1995) · Zbl 0858.65148
[91] DOI: 10.1016/0167-2789(92)90105-V · Zbl 1194.37134
[92] DOI: 10.1103/PhysRevE.64.016213
[93] Ljung L., Theory and Practice of Recursive Identification (1983) · Zbl 0548.93075
[94] DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · Zbl 1417.37129
[95] DOI: 10.1109/9.704992 · Zbl 0957.93085
[96] DOI: 10.1109/ICCV.1999.791275
[97] DOI: 10.1080/01621459.1959.10501505
[98] DOI: 10.1080/00207177108932073 · Zbl 0224.93043
[99] DOI: 10.1103/PhysRevE.59.284
[100] DOI: 10.1103/PhysRevLett.83.4285
[101] Meinhold R. J., Amer. Statist. 37 pp 123–
[102] Mendel J. M., Lessons in Estimation Theory for Signal Processing, Communications and Control (1995) · Zbl 0886.62101
[103] DOI: 10.1175/1520-0469(1994)051<1037:ADAISN>2.0.CO;2
[104] DOI: 10.1090/conm/115/1117054
[105] DOI: 10.1016/S0167-2789(02)00546-8 · Zbl 1009.65062
[106] DOI: 10.1017/CBO9781139170802
[107] DOI: 10.1016/S0167-2789(01)00251-2 · Zbl 0981.34053
[108] DOI: 10.1016/S0005-1098(00)00089-3 · Zbl 0973.93050
[109] DOI: 10.1007/BF01242136 · Zbl 0697.58036
[110] Ott E., Wiley Series in Nonlinear Science, in: Coping with Chaos (1994)
[111] DOI: 10.1103/PhysRevLett.45.712
[112] DOI: 10.1016/0005-1098(67)90001-5
[113] Peifer M., J. Sound Vibr.
[114] DOI: 10.1007/978-1-4612-1594-3
[115] Press W. H., Numerical Recipes in C (1997)
[116] Radons G., IEEE Sign. Process. Lett. 6 pp 213–
[117] DOI: 10.1007/BF02024507 · Zbl 0091.14403
[118] DOI: 10.1214/aoms/1177729586 · Zbl 0054.05901
[119] Sakaguchi H., Phys. Rev. E 65 pp 1–
[120] Sayed A. H., Total Least Squares and Errors-in-Variables Modeling, III: Analysis, Algorithms and Applications (2002)
[121] DOI: 10.1002/9781118150658
[122] DOI: 10.1007/s002110050052 · Zbl 0809.65067
[123] DOI: 10.1142/9789812798862_0023
[124] DOI: 10.2514/3.21012 · Zbl 0775.93283
[125] DOI: 10.1002/0471725315
[126] DOI: 10.1093/biomet/81.1.115 · Zbl 0796.62079
[127] DOI: 10.1111/j.1467-9892.1982.tb00349.x · Zbl 0502.62085
[128] DOI: 10.1007/978-1-4757-3261-0
[129] DOI: 10.1016/S0375-9601(98)00283-7 · Zbl 0940.82047
[130] DOI: 10.1007/978-94-011-3558-0
[131] DOI: 10.1103/PhysRevE.66.016210
[132] DOI: 10.1103/PhysRevE.68.016202
[133] DOI: 10.1016/S0165-1684(02)00252-9 · Zbl 0994.93065
[134] DOI: 10.1137/0708038 · Zbl 0219.90039
[135] DOI: 10.1007/978-1-4757-2272-7
[136] DOI: 10.1142/S0218127496001715 · Zbl 1298.94105
[137] DOI: 10.1007/978-3-642-80149-5_27
[138] Strang G., Linear Algebra and Its Applications (1988) · Zbl 0338.15001
[139] Sunahara Y., Joint Automatic Control Conf. (1969)
[140] DOI: 10.1007/BFb0091924
[141] DOI: 10.1007/978-3-662-22237-9
[142] DOI: 10.1103/PhysRevA.41.3038
[143] DOI: 10.1103/PhysRevE.51.3738
[144] DOI: 10.1142/S0218127498001157 · Zbl 0937.92006
[145] DOI: 10.1016/S0960-0779(00)00015-1 · Zbl 0956.62070
[146] DOI: 10.1016/S0375-9601(00)00548-X · Zbl 1055.37586
[147] DOI: 10.1137/1.9781611971002
[148] DOI: 10.1016/S0375-9601(97)00598-7 · Zbl 1044.34510
[149] DOI: 10.1103/PhysRevE.57.2820
[150] Voss H. U., Phys. Rev. Lett. 83
[151] DOI: 10.1016/S0375-9601(99)00219-4
[152] DOI: 10.1007/978-1-4615-0931-8_7
[153] E. A. Wan, R. Merwe and A. T. Nelson, Advances in Neural Information Processing Systems 12, eds. S. Solla, T. Leen and K.R. Müller (The MIT Press, 2000) pp. 666–672.
[154] DOI: 10.1007/978-1-4757-4067-7
[155] Xie L., IEEE Trans. Autom. Contr. 39 pp 1310– · Zbl 0812.93069
[156] DOI: 10.1016/0005-1098(81)90082-0 · Zbl 0451.93052
[157] P. Young, Nonlinear and Nonstationary Signal Processing, eds. W. J. Fitzgerald (Cambridge University Press, Cambridge, 2000) pp. 74–114.
[158] DOI: 10.1016/0005-1098(70)90098-1
[159] DOI: 10.1007/978-3-642-82336-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.