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There exists a (C^{infty} -smooth interval map (f:Ito I) such that (1) f is Li-Yorke chaotic,   (2) (I_{f} -smoothftarrow}{f,interval not contain an indecomapsable subcontinuum.  .

The first scan of each smoothing interval is discarded, and a new scan is appended for the next smoothing interval, except the last smoothing interval.

The procedure continues for each subsequent smoothing interval.

The smoothing interval [ k,N] consists of N−k+1 scans.

The backward multi-track state predictions at each scan in the smoothing interval are obtained recursively by utilizing the sensor measurements starting from the end of the smoothing interval to the beginning of the smoothing interval.

(1) Target exists at all scans k τ in the smoothing interval, where 1≤r≤N.

Both FLIPDA-S and sIPDA have the same smoothing interval, for a fair comparison.

fIPDA tracks and bIPDA tracks are initialized for each smoothing interval.

In this technique, a relatively small window of scans is defined in each smoothing interval.

(3) Target does not exist at any scan k τ in the smoothing interval.

Therefore, there are no backward tracks in the last two scans of each smoothing interval.