Think of measuring the temperature of a liquid in a breaker heated by a burner. Suppose that we use a thermometer immersed in the liquid and periodically observe the temperature and record it.
(a) Construct a measurement model assuming that the thermometer is linearly related to the temperature, that is, y(t) = kΔT (t). Also model the uncertainty of the visual measurement as a random sequence v(t) with variance Rvv .
(b) Suppose that we model the heat transferred to the liquid from the burner as
Q(t) = C A ΔT (t)
where C is the coefficient of thermal conductivity, A is the cross-sectional area, and ΔT (t) is the temperature gradient with assumed random uncertainty w(t) and variance Rww . Using this process model and the models developed above, identify the model-based processor representation.
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