Richard S. Bucy

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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation" completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian(More)
Since the appearance of [6] and [7], the theory of linear filtering has experienced a renaissance. This theory, although evidently well known to statisticians in terms of "least squares estimates," has found many applications in the early sixties, largely because of the realization and synthesis methods provided in [6] and [7]. For an indication ofsome of(More)