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I have a simple Kalman problem: how does one estimate the following local level univariate state-space model, but with some driving factor:

y(t) = m(t) + e,                Observation equation
m(t) = m(t-1)+ F(t) + d         State equation

e~iid N(0,V)
d~iid N(0,W)

where F(t) is the observed independent factor at time t.

What are the relevant recursive equations for estimating m(t)?

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I believe everything you need is in here, or you can see the tutorial here.

Hope this helps.

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