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Table 1 Hyperparameters tuned by the GA for each recursive estimator

From: Root tracking using time-varying autoregressive moving average models and sigma-point Kalman filters

ModelRecursive estimatorCandidate solution form
TV-ARMA direct-formKF-RPLS\( \left[p,q,{R}_1,{R}_2,{P}_0,{\hat{\boldsymbol{c}}}^T(0)\right] \)
TV-ARMA cascade-formKF-RPEM\( \left[{p}_r,{p}_c,{q}_r,{q}_c,{R}_1,{R}_2,{P}_0,{\hat{\boldsymbol{c}}}^T(0)\right] \)
RB-UKF\( \left[{p}_r,{p}_c,{q}_r,{q}_c,\alpha, \beta, \kappa, {R}_1,{R}_2,{P}_0,{\hat{\boldsymbol{c}}}^T(0)\right] \)
RB-CDKF\( \left[{p}_r,{p}_c,{q}_r,{q}_c,\gamma, {R}_1,{R}_2,{P}_0,{\hat{\boldsymbol{c}}}^T(0)\right] \)
  1. The upper and lower bounds ([LB, UB]) were set to [0,1] for R1, R2, and P0 [1, 10]; for p and q [1, 5]; for pc and qc; [0, 2] for pr and qr [1, 2]; for γ; [0, 1] for α; [0, 3] for β; [0, 3] for κ; and [− 1, 1] for each element of \( {\hat{\boldsymbol{c}}}^T(0) \)