Algorithm 1.

RB-CPF-AS

Input: ${\stackrel{\sim }{\mathbf{z}}}_{1:T}^{\prime }={\stackrel{\sim }{\mathbf{z}}}_{1:T}[k-1]$, θ = θk−1
Output: z̃1:T [k] ~ ℳθk−1 (·|z̃1:T [k − 1])
Compute ${\{{\mathbf{\Omega }}_t,{\mathit{\lambda }}_t\}}_{t=1}^T$ according to (19a)–(19g)
Draw ${\stackrel{\sim }{\mathbf{z}}}_1^i$ with ${\stackrel{\sim }{\mathbf{z}}}_1^i~p_{\theta }({\stackrel{\sim }{\mathbf{z}}}_1)$ for i = 1, …, N
Compute ${\mathit{\mu }}_1^i,{\mathbf{\sum }}_1^i$, and $w_1^i$ for i = 1, …, N
for t=2 to T do
	Draw $a_t^i$ with $P(a_t^i=j)\propto w_{t-1}^j$ for i = 1, …, N
	// Resampling and ancestor sampling
	Draw ${\stackrel{\sim }{\mathbf{z}}}_t^i$ with ${\stackrel{\sim }{\mathbf{z}}}_t^i~p_{\theta }({\stackrel{\sim }{\mathbf{z}}}_t)$ for i = 1, …, N
	Compute $\{{\mathbf{M}}_{t-1}^i,{\eta }_{t-1}^i\}$ according to (18a) and (18b)
	Draw $a_N^i$ according to (15) for i = 1, …, N
	// Particle propagation
	Set ${\stackrel{\sim }{\mathbf{z}}}_{1:t}^i=\{{\stackrel{\sim }{\mathbf{z}}}_{1:t-1}^{a_t^i},{\stackrel{\sim }{\mathbf{z}}}_t^i\}$ for i = 1, …, N
	Set ${\hat{\mathit{\mu }}}_{f,1:t-1}^i={\hat{\mathit{\mu }}}_{f,1:t-1}^{a_t^i},{\hat{\mathit{\mu }}}_{p,1:t-1}^i={\hat{\mathit{\mu }}}_{p,1:t-1}^{a_t^i}$,
	${\hat{\mathbf{\sum }}}_{f,1:t-1}^i={\hat{\mathbf{\sum }}}_{f,t-1}^{a_t^i},{\hat{\mathbf{\sum }}}_{p,1:t-1}^i={\hat{\mathbf{\sum }}}_{p,1:t-1}^{a_t^i}$
	// Weighting
	Compute ${\hat{\mathit{\mu }}}_{f,t}^i,{\hat{\mathit{\mu }}}_{p,t}^i,{\hat{\mathbf{\sum }}}_{f,t}^i$, and ${\hat{\mathbf{\sum }}}_{p,t}^i$
	Compute weights $w_t^i$ according to (20)
Draw J with $P(J=j)\propto W_T^j$ and set ${\stackrel{\sim }{\mathbf{z}}}_{1:T}[k]={\stackrel{\sim }{\mathbf{z}}}_{1:T}^J$.