Algorithm 1. Trivariate empirical mode decomposition via convex optimization

Perform the low-rank matrix approximation via convex optimization framework to a trivariate signal $\mathit{Y}(t)$ and the new observed signal $\mathit{X}(t)$ can be obtained. The projection $p^k(t)$($k=1,2,\dots ,K$) can be calculated of the input low-rank trivariate signal $\mathit{X}(t)$ along the direction vector $\left\{e_1{}^k,e_2{}^k,e_3{}^k\right\}$. It should also be noted that $K$ is the number of the directional vector sets. The time instants $t_m^k$ corresponding to the maxima of the set of projected signals $p^k(t)$ is determined. Interpolate [$t_m^k$, $\mathit{X}(t_m^k)$] to obtain multivariate envelope curves $E^k(t)$. Then, the envelop mean can be calculated $\mathit{M}(t)=\frac{1}{K}{\displaystyle \sum _{k=1}^K{E}^k(t)}$. Calculate the residual by $\mathit{R}(t)=\mathit{X}(t)-\mathit{M}(t)$. If the stopping criterion condition of iteration can be satisfied, then $\mathit{R}(t)$ is set as one IMF and repeat the above steps to $\mathit{X}(t)-\mathit{R}(t)$ until the next IMF is isolated. If it does not satisfy the stopping criterion, then repeat the above steps to $\mathit{R}(t)$ until it meets the criterion.