Signal Estimation in Continuous Time

Abstract

In Chapter VI we treated the problem of signal detection with continuous-time observations. In this chapter we consider the problem of signal estimation in continuous time. We treat three basic problems: parameter estimation for signals of known form (up to a set of unknown parameters) observed in additive Gaussian noise; linear/Gaussian estimation in which either we assume that the signals and noise of interest are Gaussian processes or we restrict attention to linear estimators; and nonlinear filtering, in which we derive estimators for non-Gaussian random signals generated by nonlinear differential equations when observed in additive Gaussian noise. In all cases, we consider primarily the case of white Gaussian noise, although as we have seen in Chapter VI, other Gaussian noise models can be transformed to this model, so that these results are more general.