[1] |
Stratonovich, R. L., On the theory of optimal nonlinear filtration of random functions, Theory Prob. Appl., 4, 223-225 (1959) |
[2] |
Stratonovich, R. L., Conditional Markov processes, Theory Prob. Appl., 5, 2, 156-178 (1960) · Zbl 0106.12401 |
[3] |
Masani, P.; Wiener, N., Nonlinear prediction, (Proc. 4th Berkeley Symp. Math. Stat. Problems, 2 (1961)), 403-419 |
[4] |
Kushner, H. J., On the differential equations satisfied by conditional probability densities of Markov processes with applications, SIAM J. Control, 2, 1, 106-119 (1962) · Zbl 0131.16602 |
[5] |
Kushner, H. J., On the dynamical equations of conditional probability density functions with applications to optimal control theory, J. Math. Anal. Appl., 8, 322-344 (1964) · Zbl 0126.33304 |
[6] |
Ho, Y. C.; Lee, R. C.K., A bayeskn approach to problems in stochastic estimation and control, IEEE Trans. Auto. Control, 9, 333-339 (1964) |
[7] |
Wonham, W. M., Some applications of stochastic differential equations to optimal nonlinear filtering, SIAM J. Control, 2, 347-369 (1965) · Zbl 0143.19004 |
[8] |
Bucy, R. S., Nonlinear filtering, IEEE Trans. Auto. Control, AC10, 2, 198 (April 1965) |
[9] |
Magill, D. T., Optimal adaptive estimation of sampled stochastic processes, IEEE Trans. Auto. Control, AC10, 434-439 (October 1965) |
[10] |
Shiryaev, A. N., On stochastic equations in the theory of conditional Markov processes, Theory Prob. Appl., 11, 179-184 (1966) |
[11] |
Mortensen, R. E., Optimal control of continuous-time stochastic systems, (Technical Report No. ERL-66-1 (August 19, 1966), Electronics Research Laboratory, Univ. of California: Electronics Research Laboratory, Univ. of California Berkeley) · Zbl 0201.48403 |
[12] |
Detchmendy, D. M.; Sridhar, R., Sequential estimation of states and parameters in noisy nonlinear dynamical systems, Trans. ASME, J. Basic Eng., D88, 362-368 (1966) |
[13] |
Kushner, H. J., Dynamical equations for optimal nonlinear filtering, J. Differential Equations, 3, 2, 179-190 (April 1967) · Zbl 0158.16801 |
[14] |
Duncan, T. E., Probability densities for diffusion processes with applications to nonlinear filtering theory and detection theory, (Technical Report TR No. 7001-4 (May 1967), Stanford Electronics Laboratory, Stanford University) |
[15] |
Aoki, M., Optimization of Stochastic Systems (1967), Academic Press: Academic Press New York · Zbl 0168.15802 |
[16] |
Kushner, H. J., Approximations to optimal nonlinear filters, IEEE Trans. Auto. Control, 12, 5, 546-556 (October 1967) |
[17] |
Fisher, J. R.; Stear, E. B., Optimal nonlinear filtering for independent increment processes, 3, 4, 558-578 (October 1967), Part I, II · Zbl 0168.40401 |
[18] |
Lainiotis, D. G.; Hilborn, C. G., Learning systems for minimum risk adaptive pattern classification and optimal adaptive estimation, (CSRG Technical Report No. 9 (November 1967), Department of Electrical Engineering, University of Texas: Department of Electrical Engineering, University of Texas Austin) · Zbl 0184.22002 |
[19] |
Frost, P. A., Nonlinear estimation in continuous time systems, (Ph.D. Dissertation (1968), Department of Electrical Engineering, Stanford University) |
[20] |
Schwartz, L.; Stear, E. B., A valid mathematical model for approximate nonlinear minimal-variance filtering, J. Math. Anal. Appl., 21, 1, 1-6 (January 1968) · Zbl 0155.27805 |
[21] |
Sorenson, H. W.; Stubberud, A. R., Nonlinear filtering by approximation of the a-posteriori density, Int. J. Control, 8, 1, 35-51 (1968) · Zbl 0176.08302 |
[22] |
Lainiotis, D. G., A nonlinear adaptive estimation recursive algorithm, IEEE Trans. Auto. Control, AC13, 2 (April 1968) |
[23] |
Lainiotis, D. G., Adaptive mixture decomposition: A unifying approach, (Proc. Nat. Electron. Conf., 24 (1968)) · Zbl 0257.68090 |
[24] |
Mortensen, R. E., Maximum likelihood recursive nonlinear filtering, J. Optimization Theory Appl., 2, 6, 386-394 (1968) · Zbl 0177.36004 |
[25] |
Hilborn, C. G.; Lainiotis, D. G., Optimal estimation in the presence of unknown parameters, IEEE Trans. System Sci. Cybernet., SSC5, 1 (January 1969) · Zbl 0184.22002 |
[26] |
Kailath, T., A general likelihood-ratio formula for random signals in gaussian noise, IEEE Trans. Inform. Theory, IT15, 2, 350-361 (March 1969) · Zbl 0172.42805 |
[27] |
Sengbush, R. L.; Lainiotis, D. G., Simplified parameter quantization procedure for adaptive estimation, IEEE Trans. Auto. Control, AC14, 4, 424-425 (August 1969) |
[28] |
Lo, J. T., Finite dimensional sensor orbits and optimal nonlinear filtering, (Ph.D. Dissertation (August 1969), Department of Aerospace Engineering, University of Southern California: Department of Aerospace Engineering, University of Southern California Los Angeles) · Zbl 0246.93042 |
[29] |
Bucy, R. S., Bayes theorem and digital realizations for nonlinear filters, J. Astronaut. Sci., 17, 2, 80-94 (September-October 1969) |
[30] |
Lainiotis, D. G., (Technical Report No. 74 (September 1969), Electronics Research Center, University of Texas), also published as · Zbl 0199.54603 |
[31] |
Hilborn, C. G.; Lainiotis, D. G., Optimal adaptive filter realizations for sampled stochastic processes with an unknown parameter, IEEE Trans. Auto. Control, AC14, 6 (December 1969) |
[32] |
Leondes, C. T.; Peller, J. B.; Stear, E. B., Nonlinear smoothing theory, IEEE Trans. Systems Sci. Cybernet., SSC6, 1, 63-71 (January 1970) · Zbl 0201.21102 |
[33] |
Licht, B. W., Approximations in optimal nonlinear filtering, (Technical Report No. SRC 70-1 (April, 1970), Systems Research Center, Case Western Reserve Univ) |
[34] |
Lainiotis, D. G.; Sims, F. L., Performance measures for adaptive kalman estimators, IEEE Trans. Auto. Control, AC15, 2 (April 1970) |
[35] |
Jazwinski, A. H., Stochastic Processes and Filtering Theory (1970), Academic Press: Academic Press New York · Zbl 0203.50101 |
[36] |
Fisher, J. R.; Stear, E. B., Near-optimal nonlinear filtering using quasimoment functions, Int. J. Control, 12, 4, 685-697 (1970) · Zbl 0199.49203 |
[37] |
Meditch, J. S., Formal algorithms for continuous-time nonlinear filtering and smoothing, Int. J. Control, 11, 1061-1068 (1970) · Zbl 0223.93037 |
[38] |
Lainiotis, D. G., Sequential structure and parameter adaptive pattern recognition, part I: Supervised learning, IEEE Trans. Inform. Theory, IT16, 5, 548-556 (September 1970) · Zbl 0199.54603 |
[39] |
Kallianpur, G.; Striebel, C., Estimation of stochastic systems: arbitrary system process with additive white observation errors, Ann. Math. Stat., 39, 785-801 (1969) · Zbl 0174.22102 |
[40] |
Lainiotis, D. G., Optimal adaptive estimation: Structure and parameter adaptation, IEEE Trans. Auto. Control, AC16, 2, 160-170 (April 1971) |
[41] |
Lainiotis, D. G.; Park, S. K.; Krishnaiah, R., Optimal state-vector estimation for non-gaussian initial state-vector, IEEE Trans. Auto. Control, AC16, 2, 197-198 (April 1971) |
[42] |
Frost, P. A.; Kailath, T., An innovations approach to least-squares estimation, part III: Nonlinear estimation in white gaussian noise, IEEE Trans. Auto. Control, AC16, 3, 217-226 (1971) |
[43] |
Lainiotis, D. G., Optimal nonlinear estimation, Int. J. Control, 14, 6, 1137-1148 (1971) · Zbl 0225.93034 |
[44] |
Center, J. L., Practical nonlinear filtering of discrete observations by generalized leastsquares approximation of the conditional probability distribution, (Proc. Nonlinear Estimation Symp., 2 (1971)), 88-99 · Zbl 0314.93031 |
[45] |
Sorenson, H. W.; Alspach, D. L., Recursive bayesian estimation using gaussian sums, Automatica, 7, 4 (1971) · Zbl 0219.93020 |
[46] |
Lainiotis, D. G., Joint detection, estimation, and system identification, Inform. Control J., 19, 8, 75-92 (August 1971) · Zbl 0231.62109 |
[47] |
de Figuerido, R. J.D.; Jan, Y. O., Spline filters, (Proc. Nonlinear Estimation Symp. (September 1971)) · Zbl 0314.93037 |
[48] |
Sage, A. P.; Melsa, J. L., Estimation Theory with Applications to Communications and Control (1971), McGraw-Hill: McGraw-Hill New York · Zbl 0255.62005 |
[49] |
Lo, J. T., On optimal nonlinear estimation, part I: Continuous observations, Inform. Sci., 6, 1, 19-32 (1973) · Zbl 0255.93024 |
[50] |
Lainiotis, D. G., Adaptive pattern recognition: A state-variable approach, (Watanabe, M., Frontiers of Pattern Recognition (May 1972), Academic Press: Academic Press New York) · Zbl 0257.68090 |
[51] |
Lainiotis, D. G.; Deshpande, J. G.; Upadhyay, T. N., Optimal adaptive control: A nonlinear separation theorem, Int. J. Control, 15, 5, 877-888 (May 1972) · Zbl 0234.93031 |
[52] |
Park, S. K.; Lainiotis, D. G., Monte-Carlo study of the optimal nonlinear estimator: Linear systems with non-gaussian initial state, Int. J. Control, 16, 6, 1029-1040 (1972) · Zbl 0246.93035 |
[53] |
Alspach, D. L.; Sorenson, H. W., Nonlinear bayesian estimation using gaussian sum approximations, IEEE Trans. Auto. Control, AC17, 4, 439-448 (August 1972) · Zbl 0264.93023 |
[54] |
Lo, J. T., Finite-dimensional sensor orbits and optimal nonlinear filtering, IEEE Trans. Inform. Theory, IT18, 5, 583-588 (September 1972) · Zbl 0246.93042 |
[55] |
Lainiotis, D. G.; Park, S. K., On joint detection, estimation and system identification: Discrete data case, Int. J. Control, 17, 3, 609-633 (March 1973) · Zbl 0249.93046 |
[56] |
Lainiotis, D. G., Optimal linear smoothing: Continuous data case, Int. J. Control, 17, 5, 921-930 (May 1973) · Zbl 0256.93056 |
[57] |
Deshpande, J. G.; Lainiotis, D. G., Identification and control of linear stochastic systems using spline functions, (Technical Report No. 146 (May 1973), Electronics Research Center, University of Texas: Electronics Research Center, University of Texas Austin) · Zbl 0264.93038 |
[58] |
Dunn, K. P.; Rhodes, I. B., A measure-transformation approach to estimation and detection, (Proc. 1973 Allerton Conf. System Sci. (October 1973)) |
[59] |
Sorenson, H. W., On the development of practical nonlinear filters, Inform. Sci., 7, 3/4 (1974), this issue. · Zbl 0291.93052 |
[60] |
Lainiotis, D. G.; Deshpande, J. G., Parameter estimation using splines, Inform. Sci., 7, 3/4 (1974), this issue. · Zbl 0309.62072 |
[61] |
Alspach, D. G., The use of gaussian sum approximations in nonlinear filtering, Inform. Sci., 7, 3/4 (1974), this issue. |
[62] |
Lainiotis, D. G., Partitioned estimation algorithms, II: Linear estimation, Inform. Sci., 7, 3/4 (1974), this issue. · Zbl 0301.62051 |
[63] |
Richardson, J. M., The implicit conditioning method in statistical mechanics, Inform. Sci., 7, 3/4 (1974), this issue. · Zbl 0308.62070 |
[64] |
D. G. Lainiotis, Approximate nonlinear filters: Partitioned realizations, submitted for publication to Int. J. Control; D. G. Lainiotis, Approximate nonlinear filters: Partitioned realizations, submitted for publication to Int. J. Control |
[65] |
Bucy, R. S.; Senne, K. D., Digital synthesis of nonlinear filters, Automatica, 7, 3, 287-298 (May 1971) · Zbl 0269.93070 |
[66] |
Park, S. K.; Lainiotis, D. G., A unified approach to detection, estimation, and system identification, (Technical Report No. 136 (August 1972), Electronics Research Center, University of Texas: Electronics Research Center, University of Texas Austin, Texas) · Zbl 0249.93046 |
[67] |
Cameron, A. V., Control and estimation of linear systems with non-gaussian a-priori distributions, (Proc. 2nd Allerton Conf. Systems Sci. University of Illinois (October 1968)), 426-431 |
[68] |
Sorenson, H. W.; Alspach, D. L., Gaussian sum approximations for nonlinear filtering, (Proc. 1970 IEEE Symp. Adaptive Processes (December 1970)), 19.3.1-19.3.9 · Zbl 0313.93044 |
[69] |
Lo, J. T., On optimal nonlinear estimation, (Proc. 1970 IEEE Symp. Adaptive Processes (December 1970)), 19.2.1-19.2.4, Part II |
[70] |
Kailath, T., Some new algorithms for recursive estimation in constant linear systems, IEEE Trans. Inform. Theory, IT19, 6, 750-760 (November 1973) · Zbl 0342.93053 |
[71] |
Morf, M.; Sidhu, G. S.; Kailath, T., Some new algorithms for recursive estimation in constant, linear, discrete-time systems, IEEE Trans. Auto. Control, AC-19, 4 (November 1973) |
[72] |
Sidhu, G. S.; Kailath, T., Development of new estimation algorithms by innovations analysis and shift-invariance properties, IEEE Trans. Inform. Theory (1975), to appear in · Zbl 0303.93062 |
[73] |
Levinson, N., The Wiener rms error criterion in filter design and prediction, J. Math. Phys., 24, 4, 261-278 (January 1974) |
[74] |
Mayne, D. Q., A solution of the smoothing problem for linear dynamic systems, Automatica, 4, 73-92 (1966) · Zbl 0146.37801 |
[75] |
Fraser, D. C., A new technique for optimal smoothing of data, (Sc. D. Dissertation (January 1967), MIT) |
[76] |
Kailath, T.; Frost, P., An innovations approach to least-squares estimation-part II: Linear smoothing in additive white noise, IEEE Trans. Auto. Control, AC13, 6, 655-660 (December 1968) |
[77] |
Wiggins, R. A.; Robinson, E. A., Recursive solution to the multichannel filtering problem, J. Geophys. Res., 70, 8, 1885-1891 (April 1965) |
[78] |
Lindquist, A., A new algorithm for optimal filtering of discrete-time stationary processes, SIAM J. Control (1974), to appear in · Zbl 0296.93037 |
[79] |
Lainiotis, D. G., Partitioned linear estimation algorithms: Discrete case, submitted for publication to IEEE Trans. Auto. Control; Lainiotis, D. G., Partitioned linear estimation algorithms: Discrete case, submitted for publication to IEEE Trans. Auto. Control |
[80] |
Lainiotis, D. G., Riccati equations: Partitioned solutions, submitted for publication to IEEE Trans. Auto. Control; Lainiotis, D. G., Riccati equations: Partitioned solutions, submitted for publication to IEEE Trans. Auto. Control |
[81] |
Sawaragi, Y.; Katayama, T.; Fujishige, S., State-estimation for continuous-time systems with interrupted observations, IEEE Trans. Auto. Control, AC-19, 4 (1974) · Zbl 0281.93015 |