On Some Statistical Properties of Double Stars in Space. II. by Luyten W. J.

By Luyten W. J.

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Replace X in C(X, U ) by its estimate and minimise the resulting quantity with respect to all currently unmade decisions: {uτ ; τ ≥ t}. Then the value of ut determined in this way is optimal. This rather complicated-sounding procedure has a simple recursive realisation in the state-structured case; see the next section. 7 that the CEP has a version for processes with the so-called LEQG structure – more general than LQG structure. State structure turns out to have an added significance in this more general context.

37) in principle determine the posterior distribution in a form stripped of asymptotic irrelevancies. Hijab (1984) developed a relation in a particular case (that in which the plant equation is a differential equation driven by low-power white noise) which he termed the ‘wave equation of nonlinear filtering’. 37) would seem much more deserving of this distinction. However, the reduction they achieve cannot solve the fundamental problem: that very seldom will the distribution have a finite parameterisation.

G. Harvey (1989), West and Harrison 1997 and Durbin and Koopman (2001)). g. Rabiner (1989a)), the family of possible models that one would like to use is far bigger than those that permit analytic solutions. An introduction to particle filters 45 One can approximate the models as linear and Gaussian in locality of estimates and then use a Kalman filter with these approximating models (BarShalom and Li 1995). This results in the extended Kalman filter, or EKF. 1 Throughout this and subsequent sections, we will refer to a concrete example.

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