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The updated formula for the METT can be described as [8] D k | k x = L Z k x D k | k - 1 x (2).

Shape sensitivity analysis is used to find a descent direction for the cost functional which leads to an update formula for the contour in the level-set framework.

In the SAP, the derived weight updating formula for the subband adaptive filter has a simple form as ever compared with the normalized least-mean-square (NLMS) algorithm.

That is, the updating formula for (x_{1}) does not incorporate the relaxation factor α explicitly.

The updating formula for the Hessian matrix H in each major iteration is given by, (17).

Our new contribution is to show rigorously that the singularity is removable and derive the updating formulae for mass and energy at the center.

The Jacobian updating formulae for the conventional Newton Raphson methods are described in Eqs.

The transformation of the particle updating formulas For solving the GTSP formula, (7) and (8) of PSO have to be transformed using swap sequences and swap operations as follows: begin{aligned} V_i(t+1)= & V_i(t)oplus r_1 odot (X_{mathrm{pbesti}}(t) - X_i(t)), nonumber &oplus ;r_2 odot (X_{mathrm{gbest}}(t) - X_i(t)) end{aligned} (9) begin{aligned} X_i(t+1)= & X_i(t)oplus V_i(t+1).

Looking at the update formula for the trajectory of a jump Markov process [ 29], (5) X n + 1 = X n + ∑ j = 1 M ν j P ∫ t n t n + τ a j (X (t ) ) dt, it is clear that the quantity we must calculate is ∫ t n t n + τ a (X (t ) ) dt, in order to then take a Poisson sample for the update (the τ-leap method approximates this as a(X(t n )) τ).

The main difference between these adaptive algorithms consists in the calculation of the step size matrix (constrained vs. unconstrained, block-structured vs. diagonal) used in the update formula for the multichannel adaptive filter.

Therefore, the resulting update formula for the sequential LR test affords the development of track-before-detect algorithms for PMHT.

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