(1) Detection statistics based on CAF

The signal *<sup>x</sup>i*(*t*) of the reconstructed reference signal *<sup>x</sup>*ˆ1(*t*), *<sup>x</sup>*ˆ2(*t*)... *<sup>x</sup>*ˆ*M*(*t*) is selected, and the carrier frequency information *fi* of the locally known reference signal *<sup>x</sup>i*(*t*) is used for down-conversion processing to obtain the down-converted reference signal *x*ˆ*IF <sup>i</sup>* (*t*). Then, the same down-conversion process is performed on the monitoring channel signal *x <sup>s</sup>*(*t*) after DPI and MPI suppression, and the down-converted reference signal *xIF <sup>s</sup>* (*t*) is obtained. In addition, calculate the CAF of *x*ˆ*IF <sup>i</sup>* (*t*) and *<sup>x</sup>IF <sup>s</sup>* (*t*) to obtain the Doppler-time delay spectrum of the i-th GPS satellite, which is expressed as

$$S\_i(\mathbf{r}, f) = \int\_{-T/2}^{T/2} \hat{\mathbf{x}}\_i^{IF}(t) \mathbf{x}\_s^{IF}(t-\mathbf{r}) e^{j2\pi ft} dt. \tag{13}$$

The discretization of Equation (13) is expressed as

$$S\_i(\mathbf{r}\_\prime f) = \sum\_{n=0}^{N-1} \pounds\_i^{IF} \left( nT\_\mathbf{s} \right) \mathbf{x}\_\mathbf{s}^{IF} \left( nT\_\mathbf{s} - \mathbf{r} \right) \mathbf{e}^{j2\pi fnT\_\mathbf{s}} \,, \tag{14}$$

where *τ* is the delay, *f* is the Doppler shift, *T* represents the accumulation time, *Ts* stands for the sampling period, and *N* is the number of sampling points.
