The purpose of this monograph is to develop a general theory of the estimation of a random process that has been nonlinearly transformed and also corrupted by noise, the effects of wich need not to be simply additive. The estimation procedures are developed within the formalism of state-variable modeling techniques and continous-time, continuous-state Markov processes. The theory assumes that the observations from which the original random rpocess is to be estimated are taken continuously in time and that the entire past history of the observations in available for generating an estimate at each point in time, but that future observations will not be used to update or improve previous estimates. The theory is applicable to numerous practical systems involvinv message transmission and estimation, such as radio communication, radar, sonar, radio, astronomy, and automatic control.
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