User`s guide

Algorithms for Recursive Estimation
The Kalman filter is used to obtain Q(t).
Thisformulationalsoassumesthatthetrueparameters
θ
0
t
()
are described
by a random walk:
θθ
00
1ttwt
()
=−
()
+
()
w(t) is Gaussian white noise with the following covariance matrix, or dri ft
matrix R
1
:
Ew t w t R
T
() ()
=
1
R
2
is the v ariance of the inno vations e(t) in the following equation:
yt t t et
T
()
=
() ()
+
()
ψθ
0
The Kalman filter algorithm is entirely specified by the sequence of data y(t),
the gradient
ψ t
()
, R
1
, R
2
, and the initial conditions
θ t =
()
0
(initial guess of
the p arameters) and
Pt=
()
0
(covariance matrix that indicates parameters
errors).
Note To simplify the inputs, yo u can scale R
1
, R
2
,and
Pt=
()
0
of the
original problem by the same value s uch that R
2
is equal to 1. This scaling
does not affect the parameters estimates.
Using the Kalman Filter Algorithm
The general syntax for the command described in “Algorithms for Recursive
Estimation” on page 7-6 is the following:
[params,y_hat]=command(data,nn,adm,ad g)
7-9