## 3 Prediction-Driven Measurement Sub-Partitioning
### Notations

\(m_{k+1|k}^{(j),d}\)

The first \(d\) components of the prediction mean of \(j\)th GIW component

\(\mathbb{X}_{k+1|k}^{(j)}\)

The extension estimate of \(j\)th GIW component

\(z_{k}^{(i)}\)

The \(i\)th measurement

\(\Delta_{d}(p)\)

A value calculated by the inverse \(\chi^{2}\) distribution

\(K\)

The target number

\(J_{k-1}\)

The number of targets at time step \(k-1\)

\(J_{\gamma,k}\)

The number of newborn targets

\(J_{\beta,k}\)

The number of spawned targets

\(N_{p}\)

The partition number

\(P_{1}\)

The initial partition

\(W^{(i)}\)

The \(i\)th subset

\(\left|W^{(i)}\right|\)

The number of measurements in subset \(W^{(i)}\)

\(x_{k|k-1}^{(i)}\)

The prediction corresponding to \(i\)th unreasonable subset \(W^{(i)}\)

The expected number of measurements generated from one target

\((p_{j,x},p_{j,y})\)

The position of alternative point

\(p_{1}\)

The first alternative point

\(TH\)

The distance between \(x_{k|k-1}^{(i)}\) and \(p_{1}\)

\(X_{\beta,k|k-1}=\left\{x_{k|k-1}^{(i)}\right\}_{i=1}^{k-1}\)

The set of predictions of existing targets

\(Z_{k}\)

The set of measurements observed at time step \(k\)

\(N_{x,k}

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