ivp2ekf0¶

probnum.diffeq.
ivp2ekf0
(ivp, prior, evlvar)[source]¶ Computes measurement model and initial distribution for KF based on IVP and prior.
Initialdistribution:
Conditions the initial distribution of the Gaussian filter onto the initial values.
If preconditioning is set to
False
, it conditions the initial distribution \(\mathcal{N}(0, I)\) on the initial values \((x_0, f(t_0, x_0), ...)\) using as many available deri vatives as possible.If preconditioning is set to
True
, it conditions the initial distribution \(\mathcal{N}(0, P P^\top)\) on the initial values \((x_0, f(t_0, x_0), ...)\) using as many available derivatives as possible. Note that the projection matrices \(H_0\) and \(H_1\) become \(H_0 P^{1}\) and \(H_1 P^{1}\) which has to be taken into account during the preconditioning.
Measurement model:
Returns a measurement model \(\mathcal{N}(g(m), R)\) involving computing the discrepancy
\[g(m) = H_1 m(t)  f(t, H_0 m(t)).\]Then it returns either type of Gaussian filter, each with a different interpretation of the Jacobian \(J_g\):
EKF0 thinks \(J_g(m) = H_1\)
EKF1 thinks \(J_g(m) = H_1  J_f(t, H_0 m(t)) H_0^\top\)
UKF thinks: ‘’What is a Jacobian?’‘
Note that, again, in the case of a preconditioned state space model, \(H_0\) and \(H_1\) become \(H_0 P^{1}\) and \(H_1 P^{1}\) which has to be taken into account. In this case,
EKF0 thinks \(J_g(m) = H_1 P^{1}\)
EKF1 thinks \(J_g(m) = H_1 P^{1}  J_f(t, H_0 P^{1} m(t)) (H_0 P^{1})^\top\)
UKF again thinks: ‘’What is a Jacobian?’‘
Note: The choice between \(H_i\) and \(H_i P^{1}\) is taken care of within the Prior.
Returns ExtendedKalmanFilter object that is compatible with the GaussianIVPFilter.
 evlvarfloat,
measurement variance; in the literature, this is “R”