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Separation block

In this paper, in order to reduce the computational cost for estimating Ck,R(t) and Dk,R(t), we assumes that Ck,R(t) is a linear (R=1) polynomial ( dAk(t)/dt=Ck,1(t)) and Dk,R(t) is zero ( $d\theta_{1k}(t)/dt=D_{k,0}=0$) in constraint (i). In this assumption, Ak(t) which can be allowed to undergo a temporal change in region, constrains the second-order polynomial ( $A_k(t)=\int C_{k,1}(t)dt+C_{k,0}$). Moreover, $\theta_{1k}(t)$, which is constrained (i.e. $\theta_{1k}(t)=D_{k,0}$), cannot be allowed to temporarily change. Here, if the number of channels K is very large, each frequency of the signal component that passed through the channel approximately coincides with the center frequency of each channel. Even if the above condition is false, its frequency difference can be represented by Dk,0.

In the segment Th-Th-1, Ck,1(t) and Dk,0 are determined by the following steps. First, let Dk,0 be any value within $-\pi/2 \leq D_{k,0} \leq \pi/2$. Next, using the Kalman filter, determine the estimated region, $\hat{C}_{k,0}(t)-P_k(t) \leq C_{k,1}(t) \leq \hat{C}_{k,0}(t)+P_k(t)$, where $\hat{C}_{k,0}(t)$ is the estimated value and Pk(t) is the estimated error. Then select candidates of Ck,1(t) using the spline interpolation in the estimated error region. Next, determine Ck,1(t) using

 \begin{displaymath}\hat{C}_{k,1}=\mathop{\arg\max}_{\hat{C}_{k,0}-P_k\leq C_{k,1...
...\vert\hat{A}_k\vert\vert \vert\vert\hat{\hat{A}}_k\vert\vert},
\end{displaymath} (18)

where $\hat{A}_k(t)$ is obtained by the spline interpolation and $\hat{\hat{A}}_k(t)$ is determined in across-channel which is satisfied constraint (iii). Finally, determine Dk,0 using

 \begin{displaymath}\hat{D}_{k,0}=\mathop{\arg\max}_{-\pi/2 \leq D_{k,0} \leq \pi...
...\vert\hat{A}_k\vert\vert \vert\vert\hat{\hat{A}}_k\vert\vert}.
\end{displaymath} (19)

Then, determining $\theta_{1k}(t)=\hat{D}_{k,0}$ and $\theta_{2k}(t)=\theta_k(t)+\theta_{1k}(t)$, we can determine Ak(t) and Bk(t) from Eqs. ([*]) and ([*]).


next up previous
Next: SIMULATIONS Up: IMPROVEMENTS TO PREVIOUS MODEL Previous: F(t) estimation block
Masashi Unoki
2000-10-26