Table 2 The CPSF framework

Initialization:

Set \(\alpha\),\({{\varvec{\uptau}}}\)

Calculate \({{\mathbb{C}}}_{{p\left( {{\mathbf{x}}_{0} } \right)}}^{\alpha }\)

Obtain the weighted grid samples according to PST

\(\left\{ {{\hat{\mathbf{X}}}_{0} ,{{\varvec{\upomega}}}_{0} } \right\}_{{N_{0} }} \leftarrow PST\left( {p\left( {{\mathbf{x}}_{0} } \right),{{\mathbb{C}}}_{{p\left( {{\mathbf{x}}_{0} } \right)}}^{\alpha } ,{{\varvec{\uptau}}}} \right)\)

//Overall time steps:

For \(k \leftarrow 1\) to \(K\) do

1): Get the expression of the posterior PDF at time step k (see Eq. 15);

2): Obtain the posterior CPS at time step k according to Definition 1 and Eq. (15);

3): Obtain the weighted grid samples according to PST

\(\left\{ {{\hat{\mathbf{X}}}_{k} ,{{\varvec{\upomega}}}_{k} } \right\}_{{N_{k} }} \leftarrow PST\left( {p\left( {{\mathbf{x}}_{k} \left| {{\mathbf{y}}_{1:k} } \right.} \right),{{\mathbb{C}}}_{{p\left( {{\mathbf{x}}_{k} \left| {{\mathbf{y}}_{1:k} } \right.} \right)}}^{\alpha } ,{{\varvec{\uptau}}}} \right)\)

4): State estimation (see Eq. 17)

End