Abstract

The problem of estimating the return power in a laser integrated radar (lidar) system in the presence of multiplicative noise and partially unmodeled dynamics is explored. Several nonlinear methodologies are reviewed and compared to develop a systematic approach to signal model identification and estimation. The situations considered operate in mode-switching environments, that is, the desired unknown parameters are allowed to vary according to sudden jumps exhibiting discontinuous behavior at random times. Partitioning-based, parallel-structured techniques are shown to be significantly superior to the usual extended Kalman filter algorithm.

© 1996 Optical Society of America

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    [CrossRef]
  2. B. J. Rye, R. M. Hardesty, “Time series identification and Kalman filtering techniques for doppler LIDAR velocity estimation,” Appl. Opt. 28, 879–891 (1989).
    [CrossRef] [PubMed]
  3. B. J. Rye, R. M. Hardesty, “Nonlinear Kalman filtering techniques for incoherent backscatter LIDAR: return power and log power estimation,” Appl. Opt. 28, 3908–3917 (1989).
    [CrossRef] [PubMed]
  4. B. J. Rye, “A wavelength switching algorithm for single laser differential absorption LIDAR systems,” in Laser Applications in Meteorology and Earth Atmospheric Remote Sensing, M. M. Sokoloski, ed., Proc. SPIE 1062, 267–273 (1989).
  5. B. J. Rye, “Kalman filtering in LIDAR,” in Proceedings of the Fifth Conference on Coherent Laser Radar, Munich, 1989.
  6. B. J. Rye, R. M. Hardesty, “Power estimator bias in filtered incoherent backscatter heterodyne LIDAR returns,” in Coherent Laser Radar, 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Poster paper.
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  9. D. S. Zrnic, “Mean power estimation with a recursive filter,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 281–289 (1977).
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    [CrossRef]
  12. J. V. Candy, Signal Processing: The Model-Based Approach (McGraw-Hill, New York, 1986).
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    [CrossRef] [PubMed]
  15. J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
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  17. G. A. Ackerson, K. S. Fu, “On state estimation in switching environments,” IEEE Trans. Autom. Control AC-15, 10–17 (1970).
    [CrossRef]
  18. L. S. Segal, D. G. Lainiotis, “Partitioned adaptive estimation of time-varying random parameters with applications to economic forecasting,” in Proceedings of the Joint Automatic Control Conference, Denver, Colo. (1979), pp. 527–531.
  19. D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—I. Identification of persistent rhythms,” IEEE Trans. Biomed. Eng. BME-25, 344–353 (1978).
    [CrossRef]
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    [CrossRef]
  21. H. Akashi, H. Kumamoto, “Random sampling approach to state estimation in switching environments,” Automatica 13, 429–434 (1977).
    [CrossRef]
  22. J. K. Tugnait, A. H. Haddad, “A detection estimation scheme for state estimation in switching environments,” Automatica 15, 477–481 (1979).
    [CrossRef]
  23. B. Jeyendran, V. U. Reddy, “Recursive system identification in the presence of burst disturbance,” Signal Process. 20, 227–245 (1990).
    [CrossRef]
  24. B. S. Rao, H. F. Durrant-Whyte, “A decentralized Bayesian algorithm for identification of tracked targets,” IEEE Trans. Syst. Man Cybern. 23, 1683–1698 (1993).
    [CrossRef]
  25. J. K. Tugnait, “Detection and estimation for abruptly changing systems,” Automatica 18, 607–615 (1982).
    [CrossRef]
  26. D. G. Lainiotis, “Sequential structure and parameter adaptive pattern recognition, part I: supervised learning,” IEEE Trans. Inf. Theory IT-16, 548–556 (1970).
    [CrossRef]
  27. D. G. Lainiotis, “Joint detection, estimation, and system identification,” Inf. Control J. 19, 75–92 (1971).
    [CrossRef]
  28. D. G. Lainiotis, “Adaptive pattern recognition: a state variable approach,” in Advances in Pattern Recognition, M. Watanabe, ed. (Academic, New York, 1972).
  29. D. G. Lainiotis, S. K. Park, “On joint detection, estimation and system identification: discrete data case,” Int. J. Control 17, 609–633 (1973).
    [CrossRef]
  30. D. Andrisani, F. P. Kuhl, D. Gleason, “A nonlinear tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. AES-22, 533–539 (1986).
    [CrossRef]
  31. D. Andrisani, E. T. Kim, J. Schierman, “A nonlinear helicopter tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. 27, 40–47 (1991).
    [CrossRef]
  32. H. W. Sorenson, A. R. Stubberud, “Nonlinear filtering by approximation of the A-posteriori density,” Int. J. Control 18, 33–51 (1968).
    [CrossRef]
  33. H. W. Sorenson, D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica 7, 465–479 (1971).
    [CrossRef]
  34. D. G. Lainiotis, “Optimal adaptive estimation: structure and parameter adaptation,” IEEE Trans. Autom. Control AC-16, 160–170 (1971).
    [CrossRef]
  35. D. G. Lainiotis, “Optimal nonlinear estimation,” Int. J. Control 14, 1137–1148 (1971).
    [CrossRef]
  36. D. G. Lainiotis, “Partitioned estimation algorithms II: nonlinear estimation,” J. Inf. Sci. 7, 202–235 (1974).
  37. D. G. Lainiotis, “Partitioning: a unifying framework for adaptive systems, I: estimation,” Proc. IEEE 64, 1126–1143 (1976).
    [CrossRef]

1993 (1)

B. S. Rao, H. F. Durrant-Whyte, “A decentralized Bayesian algorithm for identification of tracked targets,” IEEE Trans. Syst. Man Cybern. 23, 1683–1698 (1993).
[CrossRef]

1992 (1)

1991 (1)

D. Andrisani, E. T. Kim, J. Schierman, “A nonlinear helicopter tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. 27, 40–47 (1991).
[CrossRef]

1990 (1)

B. Jeyendran, V. U. Reddy, “Recursive system identification in the presence of burst disturbance,” Signal Process. 20, 227–245 (1990).
[CrossRef]

1989 (2)

1988 (1)

1987 (2)

1986 (1)

D. Andrisani, F. P. Kuhl, D. Gleason, “A nonlinear tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. AES-22, 533–539 (1986).
[CrossRef]

1983 (1)

B. J. Rye, “Power ratio estimation in incoherent backscatter LIDAR: heterodyne receiver with square law detection,” J. Climate Appl. Meteorol. 22, 1899–1913 (1983).
[CrossRef]

1982 (2)

1979 (1)

J. K. Tugnait, A. H. Haddad, “A detection estimation scheme for state estimation in switching environments,” Automatica 15, 477–481 (1979).
[CrossRef]

1978 (2)

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—I. Identification of persistent rhythms,” IEEE Trans. Biomed. Eng. BME-25, 344–353 (1978).
[CrossRef]

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—II. Identification of transient rhythms,” IEEE Trans. Biomed. Eng. BME-25, 353–361 (1978).
[CrossRef]

1977 (2)

H. Akashi, H. Kumamoto, “Random sampling approach to state estimation in switching environments,” Automatica 13, 429–434 (1977).
[CrossRef]

D. S. Zrnic, “Mean power estimation with a recursive filter,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 281–289 (1977).
[CrossRef]

1976 (1)

D. G. Lainiotis, “Partitioning: a unifying framework for adaptive systems, I: estimation,” Proc. IEEE 64, 1126–1143 (1976).
[CrossRef]

1974 (1)

D. G. Lainiotis, “Partitioned estimation algorithms II: nonlinear estimation,” J. Inf. Sci. 7, 202–235 (1974).

1973 (1)

D. G. Lainiotis, S. K. Park, “On joint detection, estimation and system identification: discrete data case,” Int. J. Control 17, 609–633 (1973).
[CrossRef]

1971 (4)

D. G. Lainiotis, “Joint detection, estimation, and system identification,” Inf. Control J. 19, 75–92 (1971).
[CrossRef]

H. W. Sorenson, D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica 7, 465–479 (1971).
[CrossRef]

D. G. Lainiotis, “Optimal adaptive estimation: structure and parameter adaptation,” IEEE Trans. Autom. Control AC-16, 160–170 (1971).
[CrossRef]

D. G. Lainiotis, “Optimal nonlinear estimation,” Int. J. Control 14, 1137–1148 (1971).
[CrossRef]

1970 (2)

G. A. Ackerson, K. S. Fu, “On state estimation in switching environments,” IEEE Trans. Autom. Control AC-15, 10–17 (1970).
[CrossRef]

D. G. Lainiotis, “Sequential structure and parameter adaptive pattern recognition, part I: supervised learning,” IEEE Trans. Inf. Theory IT-16, 548–556 (1970).
[CrossRef]

1968 (1)

H. W. Sorenson, A. R. Stubberud, “Nonlinear filtering by approximation of the A-posteriori density,” Int. J. Control 18, 33–51 (1968).
[CrossRef]

1965 (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

1960 (1)

R. E. Kalman, “A new approach to linear filtering and prediction problems,” J. Basic Eng. 82, 35–45 (1960).
[CrossRef]

Ackerson, G. A.

G. A. Ackerson, K. S. Fu, “On state estimation in switching environments,” IEEE Trans. Autom. Control AC-15, 10–17 (1970).
[CrossRef]

Akashi, H.

H. Akashi, H. Kumamoto, “Random sampling approach to state estimation in switching environments,” Automatica 13, 429–434 (1977).
[CrossRef]

Alspach, D. L.

H. W. Sorenson, D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica 7, 465–479 (1971).
[CrossRef]

Andrisani, D.

D. Andrisani, E. T. Kim, J. Schierman, “A nonlinear helicopter tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. 27, 40–47 (1991).
[CrossRef]

D. Andrisani, F. P. Kuhl, D. Gleason, “A nonlinear tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. AES-22, 533–539 (1986).
[CrossRef]

Bogan, J. R.

Brothers, A. M.

Candy, J. V.

J. V. Candy, Signal Processing: The Model-Based Approach (McGraw-Hill, New York, 1986).

Durrant-Whyte, H. F.

B. S. Rao, H. F. Durrant-Whyte, “A decentralized Bayesian algorithm for identification of tracked targets,” IEEE Trans. Syst. Man Cybern. 23, 1683–1698 (1993).
[CrossRef]

Fu, K. S.

G. A. Ackerson, K. S. Fu, “On state estimation in switching environments,” IEEE Trans. Autom. Control AC-15, 10–17 (1970).
[CrossRef]

Gleason, D.

D. Andrisani, F. P. Kuhl, D. Gleason, “A nonlinear tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. AES-22, 533–539 (1986).
[CrossRef]

Grant, W. B.

Gustafson, D. E.

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—I. Identification of persistent rhythms,” IEEE Trans. Biomed. Eng. BME-25, 344–353 (1978).
[CrossRef]

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—II. Identification of transient rhythms,” IEEE Trans. Biomed. Eng. BME-25, 353–361 (1978).
[CrossRef]

Haddad, A. H.

J. K. Tugnait, A. H. Haddad, “A detection estimation scheme for state estimation in switching environments,” Automatica 15, 477–481 (1979).
[CrossRef]

Hardesty, R. M.

Jeyendran, B.

B. Jeyendran, V. U. Reddy, “Recursive system identification in the presence of burst disturbance,” Signal Process. 20, 227–245 (1990).
[CrossRef]

Kalman, R. E.

R. E. Kalman, “A new approach to linear filtering and prediction problems,” J. Basic Eng. 82, 35–45 (1960).
[CrossRef]

Killinger, D. K.

Kim, E. T.

D. Andrisani, E. T. Kim, J. Schierman, “A nonlinear helicopter tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. 27, 40–47 (1991).
[CrossRef]

Kuhl, F. P.

D. Andrisani, F. P. Kuhl, D. Gleason, “A nonlinear tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. AES-22, 533–539 (1986).
[CrossRef]

Kumamoto, H.

H. Akashi, H. Kumamoto, “Random sampling approach to state estimation in switching environments,” Automatica 13, 429–434 (1977).
[CrossRef]

Lainiotis, D. G.

D. G. Lainiotis, “Partitioning: a unifying framework for adaptive systems, I: estimation,” Proc. IEEE 64, 1126–1143 (1976).
[CrossRef]

D. G. Lainiotis, “Partitioned estimation algorithms II: nonlinear estimation,” J. Inf. Sci. 7, 202–235 (1974).

D. G. Lainiotis, S. K. Park, “On joint detection, estimation and system identification: discrete data case,” Int. J. Control 17, 609–633 (1973).
[CrossRef]

D. G. Lainiotis, “Optimal adaptive estimation: structure and parameter adaptation,” IEEE Trans. Autom. Control AC-16, 160–170 (1971).
[CrossRef]

D. G. Lainiotis, “Optimal nonlinear estimation,” Int. J. Control 14, 1137–1148 (1971).
[CrossRef]

D. G. Lainiotis, “Joint detection, estimation, and system identification,” Inf. Control J. 19, 75–92 (1971).
[CrossRef]

D. G. Lainiotis, “Sequential structure and parameter adaptive pattern recognition, part I: supervised learning,” IEEE Trans. Inf. Theory IT-16, 548–556 (1970).
[CrossRef]

D. G. Lainiotis, “Adaptive pattern recognition: a state variable approach,” in Advances in Pattern Recognition, M. Watanabe, ed. (Academic, New York, 1972).

L. S. Segal, D. G. Lainiotis, “Partitioned adaptive estimation of time-varying random parameters with applications to economic forecasting,” in Proceedings of the Joint Automatic Control Conference, Denver, Colo. (1979), pp. 527–531.

Lancaster, M. C.

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—I. Identification of persistent rhythms,” IEEE Trans. Biomed. Eng. BME-25, 344–353 (1978).
[CrossRef]

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—II. Identification of transient rhythms,” IEEE Trans. Biomed. Eng. BME-25, 353–361 (1978).
[CrossRef]

Letalick, D.

Mead, R.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Menyuk, C. R.

Menyuk, N.

Millnert, M.

Milton, M. J. T.

Nelder, J. A.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Park, S. K.

D. G. Lainiotis, S. K. Park, “On joint detection, estimation and system identification: discrete data case,” Int. J. Control 17, 609–633 (1973).
[CrossRef]

Rao, B. S.

B. S. Rao, H. F. Durrant-Whyte, “A decentralized Bayesian algorithm for identification of tracked targets,” IEEE Trans. Syst. Man Cybern. 23, 1683–1698 (1993).
[CrossRef]

Reddy, V. U.

B. Jeyendran, V. U. Reddy, “Recursive system identification in the presence of burst disturbance,” Signal Process. 20, 227–245 (1990).
[CrossRef]

Renhorn, I.

Rye, B. J.

B. J. Rye, R. M. Hardesty, “Nonlinear Kalman filtering techniques for incoherent backscatter LIDAR: return power and log power estimation,” Appl. Opt. 28, 3908–3917 (1989).
[CrossRef] [PubMed]

B. J. Rye, R. M. Hardesty, “Time series identification and Kalman filtering techniques for doppler LIDAR velocity estimation,” Appl. Opt. 28, 879–891 (1989).
[CrossRef] [PubMed]

B. J. Rye, “Power ratio estimation in incoherent backscatter LIDAR: heterodyne receiver with square law detection,” J. Climate Appl. Meteorol. 22, 1899–1913 (1983).
[CrossRef]

B. J. Rye, “A wavelength switching algorithm for single laser differential absorption LIDAR systems,” in Laser Applications in Meteorology and Earth Atmospheric Remote Sensing, M. M. Sokoloski, ed., Proc. SPIE 1062, 267–273 (1989).

B. J. Rye, “Kalman filtering in LIDAR,” in Proceedings of the Fifth Conference on Coherent Laser Radar, Munich, 1989.

B. J. Rye, R. M. Hardesty, “Power estimator bias in filtered incoherent backscatter heterodyne LIDAR returns,” in Coherent Laser Radar, 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), Poster paper.

Schierman, J.

D. Andrisani, E. T. Kim, J. Schierman, “A nonlinear helicopter tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. 27, 40–47 (1991).
[CrossRef]

Segal, L. S.

L. S. Segal, D. G. Lainiotis, “Partitioned adaptive estimation of time-varying random parameters with applications to economic forecasting,” in Proceedings of the Joint Automatic Control Conference, Denver, Colo. (1979), pp. 527–531.

Sorenson, H. W.

H. W. Sorenson, D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica 7, 465–479 (1971).
[CrossRef]

H. W. Sorenson, A. R. Stubberud, “Nonlinear filtering by approximation of the A-posteriori density,” Int. J. Control 18, 33–51 (1968).
[CrossRef]

Stubberud, A. R.

H. W. Sorenson, A. R. Stubberud, “Nonlinear filtering by approximation of the A-posteriori density,” Int. J. Control 18, 33–51 (1968).
[CrossRef]

Triebwasser, J. H.

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—II. Identification of transient rhythms,” IEEE Trans. Biomed. Eng. BME-25, 353–361 (1978).
[CrossRef]

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—I. Identification of persistent rhythms,” IEEE Trans. Biomed. Eng. BME-25, 344–353 (1978).
[CrossRef]

Tugnait, J. K.

J. K. Tugnait, “Detection and estimation for abruptly changing systems,” Automatica 18, 607–615 (1982).
[CrossRef]

J. K. Tugnait, A. H. Haddad, “A detection estimation scheme for state estimation in switching environments,” Automatica 15, 477–481 (1979).
[CrossRef]

Wang, J. Y.

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—I. Identification of persistent rhythms,” IEEE Trans. Biomed. Eng. BME-25, 344–353 (1978).
[CrossRef]

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—II. Identification of transient rhythms,” IEEE Trans. Biomed. Eng. BME-25, 353–361 (1978).
[CrossRef]

Warren, R. E.

Willsky, A. S.

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—I. Identification of persistent rhythms,” IEEE Trans. Biomed. Eng. BME-25, 344–353 (1978).
[CrossRef]

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—II. Identification of transient rhythms,” IEEE Trans. Biomed. Eng. BME-25, 353–361 (1978).
[CrossRef]

Woods, P. T.

Zrnic, D. S.

D. S. Zrnic, “Mean power estimation with a recursive filter,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 281–289 (1977).
[CrossRef]

Appl. Opt. (7)

Automatica (4)

H. Akashi, H. Kumamoto, “Random sampling approach to state estimation in switching environments,” Automatica 13, 429–434 (1977).
[CrossRef]

J. K. Tugnait, A. H. Haddad, “A detection estimation scheme for state estimation in switching environments,” Automatica 15, 477–481 (1979).
[CrossRef]

J. K. Tugnait, “Detection and estimation for abruptly changing systems,” Automatica 18, 607–615 (1982).
[CrossRef]

H. W. Sorenson, D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica 7, 465–479 (1971).
[CrossRef]

Comput. J. (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

IEEE Trans. Aerosp. Electron. Syst. (3)

D. S. Zrnic, “Mean power estimation with a recursive filter,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 281–289 (1977).
[CrossRef]

D. Andrisani, F. P. Kuhl, D. Gleason, “A nonlinear tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. AES-22, 533–539 (1986).
[CrossRef]

D. Andrisani, E. T. Kim, J. Schierman, “A nonlinear helicopter tracker using attitude measurements,” IEEE Trans. Aerosp. Electron. Syst. 27, 40–47 (1991).
[CrossRef]

IEEE Trans. Autom. Control (2)

D. G. Lainiotis, “Optimal adaptive estimation: structure and parameter adaptation,” IEEE Trans. Autom. Control AC-16, 160–170 (1971).
[CrossRef]

G. A. Ackerson, K. S. Fu, “On state estimation in switching environments,” IEEE Trans. Autom. Control AC-15, 10–17 (1970).
[CrossRef]

IEEE Trans. Biomed. Eng. (2)

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—I. Identification of persistent rhythms,” IEEE Trans. Biomed. Eng. BME-25, 344–353 (1978).
[CrossRef]

D. E. Gustafson, A. S. Willsky, J. Y. Wang, M. C. Lancaster, J. H. Triebwasser, “ECG/VCG rhythm diagnosis using statistical signal analysis—II. Identification of transient rhythms,” IEEE Trans. Biomed. Eng. BME-25, 353–361 (1978).
[CrossRef]

IEEE Trans. Inf. Theory (1)

D. G. Lainiotis, “Sequential structure and parameter adaptive pattern recognition, part I: supervised learning,” IEEE Trans. Inf. Theory IT-16, 548–556 (1970).
[CrossRef]

IEEE Trans. Syst. Man Cybern. (1)

B. S. Rao, H. F. Durrant-Whyte, “A decentralized Bayesian algorithm for identification of tracked targets,” IEEE Trans. Syst. Man Cybern. 23, 1683–1698 (1993).
[CrossRef]

Inf. Control J. (1)

D. G. Lainiotis, “Joint detection, estimation, and system identification,” Inf. Control J. 19, 75–92 (1971).
[CrossRef]

Int. J. Control (3)

D. G. Lainiotis, “Optimal nonlinear estimation,” Int. J. Control 14, 1137–1148 (1971).
[CrossRef]

H. W. Sorenson, A. R. Stubberud, “Nonlinear filtering by approximation of the A-posteriori density,” Int. J. Control 18, 33–51 (1968).
[CrossRef]

D. G. Lainiotis, S. K. Park, “On joint detection, estimation and system identification: discrete data case,” Int. J. Control 17, 609–633 (1973).
[CrossRef]

J. Basic Eng. (1)

R. E. Kalman, “A new approach to linear filtering and prediction problems,” J. Basic Eng. 82, 35–45 (1960).
[CrossRef]

J. Climate Appl. Meteorol. (1)

B. J. Rye, “Power ratio estimation in incoherent backscatter LIDAR: heterodyne receiver with square law detection,” J. Climate Appl. Meteorol. 22, 1899–1913 (1983).
[CrossRef]

J. Inf. Sci. (1)

D. G. Lainiotis, “Partitioned estimation algorithms II: nonlinear estimation,” J. Inf. Sci. 7, 202–235 (1974).

Proc. IEEE (1)

D. G. Lainiotis, “Partitioning: a unifying framework for adaptive systems, I: estimation,” Proc. IEEE 64, 1126–1143 (1976).
[CrossRef]

Signal Process. (1)

B. Jeyendran, V. U. Reddy, “Recursive system identification in the presence of burst disturbance,” Signal Process. 20, 227–245 (1990).
[CrossRef]

Other (7)

D. G. Lainiotis, “Adaptive pattern recognition: a state variable approach,” in Advances in Pattern Recognition, M. Watanabe, ed. (Academic, New York, 1972).

J. V. Candy, Signal Processing: The Model-Based Approach (McGraw-Hill, New York, 1986).

A. Gelb, ed., Applied Optimal Estimation (MIT, Cambridge, 1974).

B. J. Rye, “A wavelength switching algorithm for single laser differential absorption LIDAR systems,” in Laser Applications in Meteorology and Earth Atmospheric Remote Sensing, M. M. Sokoloski, ed., Proc. SPIE 1062, 267–273 (1989).

B. J. Rye, “Kalman filtering in LIDAR,” in Proceedings of the Fifth Conference on Coherent Laser Radar, Munich, 1989.

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Figures (16)

Fig. 1
Fig. 1

Unknown plant dynamics: a posteriori probability convergence for ALEF (solid curve) and IALEF (solid curve with open circles).

Fig. 2
Fig. 2

Unknown plant dynamics: ALEF probability evolution versus time (three levels, two switches; high bound of 0.1). Dashed and solid curves are the first and second active models, respectively.

Fig. 3
Fig. 3

Unknown plant dynamics: ALEF probability evolution versus time (three levels, two switches; low bound of 0.01). Curves are the same as in Fig. 2.

Fig. 4
Fig. 4

Unknown plant dynamics: parameter identification for ALEF and IALEF (three levels, 20 switches; high bound of 0.05).

Fig. 5
Fig. 5

Unknown plant dynamics: histogram of the mismatched EKF speckle return estimates (15 levels, no switches).

Fig. 6
Fig. 6

Unknown plant dynamics: histogram of the ALEF speckle return estimates (15 levels, no switches).

Fig. 7
Fig. 7

Unknown plant dynamics: log power estimation for mismatched EKF (solid curve with crosses), ALEF (dotted curve), and IALEF (dashed–dotted curve; 15 levels, no switches). Actual data shown by solid curve.

Fig. 8
Fig. 8

Unknown plant dynamics: error performance comparison for mismatched EKF (solid curve with asterisks), ALEF (dotted curve), and IALEF (solid curve; three levels, three switches).

Fig. 9
Fig. 9

Unknown plant dynamics: average mean-square error as a function of mode variability. Dotted, solid, and dashed–dotted curves represent mismatched EKF, ALEF, and IALEF, respectively.

Fig. 10
Fig. 10

Unknown measurement dynamics: ALEF a posteriori probabilities (three levels, two switches; high bound of 0.05).

Fig. 11
Fig. 11

Unknown measurement dynamics: IALEF probability evolution versus time (three levels, 20 switches; high bound of 0.05).

Fig. 12
Fig. 12

Unknown measurement dynamics: parameter identification for AEKF, (dotted curve), ALEF (solid curve with asterisks), and IALEF (solid curve with open circles; three levels, 20 switches; high bound of 0.05). Actual data shown by solid curve.

Fig. 13
Fig. 13

Unknown measurement dynamics: log power estimation for AEKF (solid curve with crosses) and ALEF (solid curve with open circles; three levels, nine switches). Actual state shown by solid curve.

Fig. 14
Fig. 14

Unknown measurement dynamics: log power estimation for IALEF (dotted curve; three levels, nine switches). Actual state shown by solid curve.

Fig. 15
Fig. 15

Unknown measurement dynamics: error performance comparison for AEKF, ALEF, and IALEF (three levels, nine switches).

Fig. 16
Fig. 16

Unknown measurement dynamics: error performance as a function of parameter variability for AEKF, ALEF, and IALEF.

Tables (1)

Tables Icon

Table 1 Partitioned Identifier Implementation Guidelines

Equations (40)

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x ( k + 1 ) = f ( x ( k ) , k ; Θ ( k ) ) + Γ ( k ; Θ ( k ) ) w ( k ) ,
z ( k ) = h ( x ( k ) , k ; Θ ( k ) ) x ( k ) + v ( k ) ,
Θ ( k ) = Θ ( k - 1 ) + γ ( k - 1 ) .
x a ( k + 1 ) = { f [ x ( k ) , k ; Θ ( k ) ] Θ ( k ) } + { Γ [ k ; Θ ( k ) ] w ( k ) γ ( k ) } ,
x a ( k + 1 ) [ x ( k + 1 ) Θ ( k + 1 ) ] .
x ^ ( k k ) = i μ i ( k ) x ^ i ( k k ) ,
P ( k k ) = i μ i ( k ) { P i ( k k ) + [ x ^ i ( k k ) - x ^ ( k k ) ] [ ] T } ,
μ i ( k ) = c μ i ( k - 1 ) F i ( k ) - 1 / 2 exp [ - 0.5 ϑ i T ( k ) F i - 1 ( k ) ϑ i ( k ) ] ,
F i ( k ) = H i ( k ) P i ( k k - 1 ) H i ( k ) + R i ( k ) ,
H i ( k ) x ( k ) h ( x ( k ) , k ) x ( k ) = x ^ i ( k / k - 1 ) ,
c = 1 i { μ i ( k - 1 ) F i ( k ) - 1 / 2 exp [ - 0.5 ϑ i T ( k ) F i - 1 ( k ) ϑ i ( k ) ] } .
ϑ i ( k ) = z ( k ) - h [ x ^ i ( k k - 1 ) ] .
x ^ i ( k + 1 k ) = f ( x ^ i ( k k ) , k ) .
P i ( k + 1 k ) = F i ( k ) P i ( k k ) F i T ( k ) + Q i ( k ) .
K i ( k + 1 ) = P i ( k + 1 k ) H i T ( k + 1 ) [ H i ( k + 1 ) P i × ( k + 1 k ) H i T ( k + 1 ) + R i ( k + 1 ) ] - 1 .
x ^ i ( k + 1 k + 1 ) = x ^ i ( k + 1 k ) + K i ( k + 1 ) [ z ( k + 1 ) - h ( x ^ i ( k + 1 k ) , k + 1 ) ] .
P i ( k + 1 k + 1 ) = [ I - K i ( k + 1 ) H i ( k + 1 ) ] P i ( k + 1 k ) .
x i ( 0 ) ~ N ( x ^ i ( 0 0 ) , P i ( 0 0 ) ) ,
x ^ i ( k - 1 k - 1 ) x ^ ( k - 1 k - 1 ) ,
P i ( k - 1 k - 1 ) P ( k - 1 k - 1 ) .
z ( k ) = Θ z ( k ) x 1 ( k ) + v ( k ) ,
z ( k ) = Θ z ( k ) exp [ x 1 ( k ) ] + v ( k ) ,
z ( k ) = Θ z ( k ) W ( k ) exp [ x 1 ( k ) ] + v ( k ) ,
W ( k ) = 1 + w ( k ) ,
x 1 ( k + 1 ) = x 1 ( k ) + Θ w ( k ) w 1 ( k ) ,
x 2 ( k + 1 ) = 1 + w 2 ( k ) ,
z ( k + 1 ) = Θ z ( k + 1 ) x 2 ( k + 1 ) exp [ x 1 ( k + 1 ) ] + v ( k + 1 ) .
x 1 ( k + 1 ) = x 1 ( k ) + w 1 ( k ) ,
x 2 ( k + 1 ) = 1 + w 2 ( k ) ,
z ( k + 1 ) = x 2 ( k + 1 ) exp [ x 1 ( k + 1 ) ] + v ( k + 1 ) ,
p [ x ( 0 ) ] = N { [ 8.1 1 ] , [ 0.09 0 0 0 ] } .
Q 2 ( k ) = 0.15 ,
R = 300.
x 1 ( k + 1 ) = x 1 ( k ) + w 1 ( k ) ,
x 2 ( k + 1 ) = 1 + w 2 ( k ) ,
z ( k + 1 ) = Θ z ( k + 1 ) x 2 ( k + 1 ) exp [ x 1 ( k + 1 ) ] + v ( k + 1 ) ,
p ( x ( 0 ) ) = N { [ 8.1 1 ] , [ 0.09 0 0 0 ] } .
Q 1 ( k ) = 0.05 ( constant mode ) , Q 1 ( k ) = 0.001 ( varying mode ) ,
Q 2 ( k ) = 0.15 ,
R = 300.

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