UKFSUnited Kingdom Forestry Standard (Forestry Commission; UK)
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The idea of the UKF is to approximate the posterior PDF in recursive Bayesian estimation by a Gaussian PDF.
The CKF differs from the UKF only in the choice of the sigma points.
The Appendix summarizes the equations for the prediction and update steps of the UKF. If the state transition model in (1) or the measurement model in (2) are linear or if Gaussian noise is assumed in the state transition or measurement model, methods from [46] can be applied to decrease the computational complexity of the UKF.
The posterior PDF of each of the NUKF Gaussian components in a Gaussian mixture is estimated by a UKF. The structure of the resulting RBGSPF representation is shown in Figure 4.
Both [x.sup.<i,j,l>.sub.TX,k|k] and [P.sup.<i,j,l>.sub.k|k] are obtained from the update step of the corresponding UKF. Similarly, the likelihood for the measurement of the jth transmitter of the ith user particle is
The results were compared to those obtained using an EKF and a UKF and showed that the DDF was more accurate than estimators based on a Taylor approximation like the EKF.
Hong, "Design of UKF with correlative noises based on minimum mean square error estimation," Control and Decision, vol.
Therefore, using the state and parameter estimates from the joint UKF, both state and parameter estimates can be refined by running a series of linear Kalman filters.
It should be noted that the UKF approximates the posterior distribution of the state estimates with Gaussian distributions because we do not know the true distribution of the states.
To avoid complications in making model selection and diagnostic decisions across three sets of prediction errors, we ran another UKF using the refined parameter estimates and analyzed the prediction errors from that estimation.
To deal with this problem, we introduce an UC-inspired approach that decomposes the observed transaction price into buyers' and sellers' reservation prices and a time-varying bargaining-power parameter through the combined use of a nonlinear Kalman filter, the UKF, and a series of linear Kalman filters.
(14.) The UKF creates a total of 2L + 1 sampling points for each iteration, where L is the length of the state vector.