3.2.4. Wavelet Coefficient *L*

Wavelet transform is a multi-resolution signal analysis method. It assumes that the measurement sequence is a non-stationary sequence *x*(*n*) with polynomial trend. After a wavelet transformation, *x*(*n*) can be reconstructed as

$$\mathbf{x}(n) = \sum\_{k} h(2n - k)\mathbf{x}(k) + \sum\_{k} \mathbf{g}(2n - k)\mathbf{x}(k) \tag{27}$$

where *h* is the high frequency coefficient reflecting the overall situation of the track and *g* is the low frequency coefficient reflecting the change of the target movement. In the frequency domain, the trend of the signal is represented by the low frequency part of the signal, which is represented by the low frequency coefficient in a wavelet analysis. The low frequency coefficient of a two-scale wavelet transformation based on the Haar function is taken as a track feature, which can represent the trend of the track segment.
