ConjGrad:
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Solves the least squares problem for
J = 0.5 rho'*W*rho + 0.5*(x-xA)'*S0*(x-xA)
rho = y - h(x)
�h/�x = H(x)
�J/�x = g = -H'*W*rho + S0*(x-xA)
Uses the conjugate gradient method to solve the least squares
problem
The next step is
x(k+1) - x(k) = alpha*d(k)
where
d(k) = -g(k) + [(g(k)'(g(k)-g(k-1))/g(k-1)'g(k-1)]d(k-1)
alpha is found by minimizing J with respect to alpha at
each step
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Form:
[x, k, P, wmr, sr, J, sig, nz] = ConjGrad( F, CF, S0, xA, kX, tol, prog, sd )
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Inputs
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F [rho,H,W,jL] = F(xA)
CF [J] = CF( alpha, x0, d, S0, xA )
S0 A priori state covariance matrix
xA A priori state
kX States to be found
tol Cost tolerance
prog If not = 0 give progress reports
sd Use steepest descent
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Outputs
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x Matrix of state vectors
k Number of iterations
P Covariance matrix: inv[S0 + G'WG]
wmr Weighted mean of the residuals
sr Weighted rms deviation of the residuals
J Loss estimate
sig Uncertainty in the estimates
nz Number of measurements used
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References: Strang, G., Introduction to Applied Mathematics, Wellesley-
Cambridge Press, 1986, pp. 378-379.
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