Abstract
A new suboptimum estimation scheme is proposed for nonlinear discrete dynamic systems with aKth-order memory. These systems are first represented by trellis diagrams, and then states are estimated by the Viterbi algorithm of information theory. The state and observation models of the proposed scheme can be nonlinear functions of the disturbance noise, observation noise, and present and past discrete values of the state, whereas the models of the classical estimation algorithms, such as the extended Kaiman filter, must be linear functions of the disturbance noise and observation noise. States are estimated in blocks, which results in an estimation scheme whose implementation requries a constant memory.
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References
Demirbas, K., 1982,New Smoothing Algorithms for Dynamic Systems with or without Interference, The NATO AGARDograph Advances in the Techniques and Technology of Application of Nonlinear Filters and Kaiman Filters, No. 256, AGARD, pp. 19–166.
Demirbas, K., and Leondes, C. T., 1986, A Suboptimum Decoding-based Smoothing Algorithm for Dynamic Systems with or without Interference,The International Journal of Systems Science, Vol. 17, No. 3, pp. 499–511.
Demirbas, K., 1988. Maneuvering Target Tracking with Hypothesis Testing,IEEE Transactions on Aerospace and Electronic Systems, Vol. 23, No. 6, pp. 757–766.
Forney Jr., G. D., 1974, Convolution Codes II. Maximum Likelihood Decoding,Information and Control, Vol. 25, pp. 222–266.
Hutchinson, C. E., 1984, The Kaiman Filter Applied to Aerospace and Electronic Systems,IEEE Transactions on Aerospace and Electronic Systems, Vol. 20, No. 4, pp. 500–504.
Kailath, T., 1974, A View of Three Decades in Linear Filtering Theory,IEEE Transactions on Information Theory, Vol. 20, No. 2, pp. 146–181.
Kaiman, R. E., 1960, A New Approach to Linear Filtering and Prediction Problems,Transactions of the ASME, Series D, Journal of Basic Engineering, Vol. 82, pp. 35–45.
Makhoul, J., 1975, Linear Prediction: A Tutorial Review,Proceedings of the IEEE, Vol. 63, pp. 561–580.
Medich, J. S., 1973, A Survey of Data Smoothing for Linear and Nonlinear Dynamic Systems,Automatica, Vol. 9, pp. 151–162.
Miller, K. S., and Leskiw, D. M., Nonlinear Estimation with Radar Observation,IEEE Transactions on Aerospace and Electronic Systems, Vol. 18, No. 2, pp. 192–200.
Sage, A. P., and Melsa, J. L., 1971,Estimation Theory with Applications to Communications and Control, McGraw-Hill, New York.
Van Trees, H. L., 1968,Detection, Estimation and Modulation Theory, Wiley, New York.
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Demirbaş, K. Use of trellis diagrams in state estimation in blocks for nonlinear discrete dynamic systems with aKth-order memory. Circuits Systems and Signal Process 10, 3–14 (1991). https://doi.org/10.1007/BF01183237
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DOI: https://doi.org/10.1007/BF01183237