Abstract
This paper considers the problem of estimating the parameters of continuous-time stationary Gaussian processes with rational spectra, from uniformly sampled measurements. The sampled process is shown to be an autoregressive moving-average process, and explicit relationships between the parameters of the continuous-time and the sampled processes are derived. These relationships are then used to derive a lower bound on the variances of biased estimates of the continuous-time parameters, and on the generalized variance of such estimates. It is shown by some examples that the bound on the generalized variance depends on the sampling interval in a nonmonotonic manner. In particular, for each specific set of parameters there exists a sampling interval for which the lower bound is minimized.
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References
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This work was supported by the Army Research Office under Contract Number DAAG29-83-C-0027.
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Porat, B., Friedlander, B. Parameter estimation of continuous-time stationary Gaussian processes with rational spectra. Circuits Systems and Signal Process 6, 107–119 (1987). https://doi.org/10.1007/BF01599009
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DOI: https://doi.org/10.1007/BF01599009