$$\left [\left \{x^{i}_{n},\, L_{n}^{i},\,w_{n}^{i}\right \}_{i=1}^{M}\right ]$$ = TS$$\left [\left \{ x^{i}_{n-1},\,L^{i}_{n-1},\,w_{n-1}^{i} \right \}^{M}_{i=1},\,y_{n}\right ]$$ –Initialize $$x_{0}^{i} \sim p_{0}$$ and $$w_{0}^{i} = 1/M$$ for i=1,2,⋯,M. –DO for n=1,2,⋯,T: –DO for each particle i, i=1,2,⋯,M: – STEP 1: Construct the EnKF importance sampling density and sample – from it: 1. Construct: $$[\hat {x}^{i}_{n},\, \hat {P}_{n}^{i}]$$ = EnKF$$\left [x^{i}_{n-1},\, L^{i}_{n-1},\,y_{n}\right ]$$. 2. Sample: Draw $$x^{*i}_{n} \sim \phi _{d}\left (x\,|\,\hat {x}_{n}^{i},\,\hat {P}_{n}^{i}\right)$$ as in (18). 3. Calculate weights $${w}^{*i}_{n} = { w_{n-1}^{i}\frac {p\left (y_{n}|x^{*i}_{n}\right)p\left (x^{*i}_{n}|x^{i}_{n-1}\right)}{q\left (x^{*i}_{n}\,|\,\hat {x}_{n}^{i},\,\hat {P}_{n}^{i}\right)}}$$. – STEP 2: Learn p(x n | y1:n): 1. Find its estimate, $$\hat {f}_{n}(x)$$, based on GMMs and data $$\left \{\,x_{n}^{*i},\,w_{n}^{*i}\,\right \}_{i=1}^{M}$$ – from STEP 1. 2. Sample: Draw $$(x_{n}^{j},\,L_{n}^{j}) \sim \hat {f}_{n}(x)$$ 3. Compute weights $$w_{n}^{j} = \frac {1}{M}\sum _{i=1}^{M}\,\frac {w_{n-1}^{i}\,p\left (y_{n}\,|\,x_{n}^{j}\right)\,p\left (x_{n}^{j}\,|\,x_{n-1}^{i}\right)}{\hat {f}_{n}\left (x_{n}^{j}\right)}$$ – Propagate: $$\left \{x^{j}_{n},\, L^{j}_{n},\,w_{n}^{j}\right \}^{M}_{j=1}$$