I have a problem in understanding the concept of trianguline representation. Maybe someone can enlighten me.

Let $K$ be a finite extension of $\mathbb{Q}_p$ and $V$ be a $p$-adic representation of $G_K$ (absolute Galois group of $K$) of dimension $n$. By $p$-adic Hodge theory $V$ corresponds to some étale $(\varphi,\Gamma)$-module $M$ over the Robba ring $\mathcal{R}_K$. Lets call $M$ trianguline if there exists a filtration $$ 0=M_0 \subset M_1 \subset \cdots \subset M_n=M,$$ of sub-$(\varphi,\Gamma)$-modules of $M$ such that the successive quotients $M_i/M_{i-1}$ are of rank $1$. Since rank $1$ $(\varphi,\Gamma)$-moduels over $\mathcal{R}_K$ are of the form $\mathcal{R}_K(\delta)$ for some unique continuous character $\delta: \mathbb{Q}_p^{\times} \rightarrow K^{\times}$ we can describe a triangulation by a sequence of such characters $(\delta_i)_{1 \leq i \leq n}$.

So lets us say that $M$ is trianguline, is there a unique triangulation? What confuses me is that in such a case the generalized Hodge-Tate weights of $V$ correspond to the weights of the $\delta_i$ defined as $$ w(\delta_i):= \log_p \delta_i(u) / \log_p u $$ for some $u \in 1 +p \mathbb{Z}_p$ doesn't this make the triangulation unique? Where is my mistake here...