Algorithm 1 Particle filter for rotor temperature estimation

Initialization  Initialize posterior distribution: $p\left(T_{net,k-1}/d_{1:k-1}\right)\leftarrow p_0$  Generate $N_p$ particles with initial distribution $p_0$ and place them in a set called $T_{post}$.  Run  Compute  $T_{\alpha }\left[k\right]$  $T_{\alpha }\left[k\right]=\frac{h}{(h+\tau )}\left[\frac{h}{\tau }{T}_{\alpha }[k-1]-\frac{{\alpha }_1}{h}{T}_s[k-1]+\frac{({\alpha }_1+h{\alpha }_2)}{h}{T}_s\left[k\right]\right]$  while $i\le N_p$ do   $\mathbf{Predict}$   $T_{net}\left[i\right]=narx(i_r\left[k\right],i_s\left[k\right],\eta \left[k\right],T_s\left[k\right],T_{post}\left[i\right])$   $\mathbf{Update}$   Calculate the weight associated with each projected state:   $w\left(i\right)=1/\sqrt{2\pi R_m}exp[-{(T_{\alpha }\left[k\right]-T_{net}\left(i\right))}^2/\left(2R_m\right)];$   i = i + 1  end while  $\mathit{Normalize\; weights}:$ $w\left(i\right)=w\left(i\right){\sum }_{i=1}^{N_p}w\left(i\right)$  $\mathbf{Re}-\mathbf{sample}$  Sample the discrete distribution w to generate $N_p$ random samples which will represent the posterior $T_{post}$:  $X=rand(N_p,1)$; fetch $N_p$ values from a uniform distribution $X\in [0,1]$;  for j = 1: $N_p$ do   $csw\left(j\right)={\sum }_{L=1}^{j}w\left(L\right)$; Cumulative Sum of W; $csw\in [0,1]$  end for  for j = 1: $N_p$ do   $i_p\left(j\right)=argmi{n}_i|X\left(i\right)-csw\left(j\right)|$; $i_p$ will be the index of the posterior after re-sampling  end for  for j = 1: $N_p$ do   $T_{post}\left(j\right)=T_{net}\left[i_p\left(j\right)\right]$  end for  ${\widehat{T}}_r\left(k\right)=\frac{1}{N_p}{\sum }_{i=1}^{N_p}{T}_{post}\left(i\right)$