**2. System Model**

The system model of the echo signal detection and reception system based on data fusion of multiple GPS satellites is shown in Figure 1, where *Rt* is the distance from the satellite to a target, *L* is the distance from a satellite to a receiver, *θ* is the arrival angle of the echo, *ϕ* is the arrival angle of the direct wave, and *Rr* is the distance from a target to a receiver.

**Figure 1.** Passive detection based on multiple collaborative GPS satellites.

As shown in Figure 2, a standard GPS receiver exists in the reference channel, which is vertically pointed to the zenith in order to receive the reference signals. Then, the received reference signals will be used for the DPI and MPI suppression in the monitoring channel. Through the monitoring channel, the receiver is able to realize the self-positioning of the detection system, the baseline measurement, and the tracking of the current satellite, obtaining the ephemeris position information of the zenith at the current moment. These measurements will facilitate subsequent offline signal processing.

**Figure 2.** The diagram of the receiving signal channels.

The monitoring channel for reflected echo receptions is mainly composed of a GPS receiving antenna, an amplifier, a filter, a down conversion circuit, and a digital storage oscilloscope. In the GPS receiving antenna, a left-handed circularly polarized receiving antenna is deployed, which is tilted towards the target. The amplifier amplifies the GPS echo signal to achieve a 20 dB to 30 dB amplification. The filter is employed for interference cancellation of clutter signals outside the GPS *L*-band, reducing the influence of out-of-band clutter on subsequent detection processes. The down-conversion module is applied to down-convert the GPS signal from the *L*-band to the intermediate frequency to reduce the complexity of the processing. The digital storage oscilloscope is used for the rapid sampling and storage of data to enable following offline processing.

In the monitoring channel, it is assumed that there are *M* GPS satellites as the radiation source. In addition to the reflected echoes received by the plurality of GPS satellite signals from the target, on the monitoring channel, direct wave signals and multipath interference can be received, which are

produced by the reflection of GPS direct wave signals from close ground objects. Accordingly, the received signals of the monitoring channel can be expressed as

$$\begin{array}{ll} \mathbf{x}\_{s}(t) = a\_{1}\mathbf{x}\_{1}(t-\tau\_{1})\exp(j2\pi f\_{d\_{1}}) + a\_{2}\mathbf{x}\_{2}(t-\tau\_{2})\exp(j2\pi f\_{d\_{2}}) + \dots + a\_{M}\mathbf{x}\_{M}(t-\tau\_{m})\exp(j2\pi f\_{d\_{M}}) \\ \mathbf{w}\_{1} \\ \qquad + \sum\_{i=0}^{W\_{1}}\omega\_{1}\mathbf{x}\_{1}(t-\tau\_{1}) + \sum\_{i=0}^{\tau}\omega\_{2}\mathbf{x}\_{2}(t-\tau\_{2}) + \dots + \dots + \sum\_{i=0}^{\tau}\omega\_{M\_{i}}\mathbf{x}\_{M}(t-\tau\_{M\_{i}}) + n\_{i}(t), \end{array} \tag{1}$$

where *<sup>α</sup>MxM*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup>m*) exp *j*2*π fdM* ! represents the echo signal of the *M*th GPS satellite, *α<sup>M</sup>* represents the amplitude of the echo signal, and *xM*(*t*) is the *M*th GPS satellite signal. In addition, *τ<sup>M</sup>* and *fdM* are the delay and frequency offset of that signal, respectively, *ns*(*t*) is the noise of the monitoring channel, *WM* ∑ *i*=0 *ωMi xM t* − *τMi* ! stands for the multipath of the *M*th GPS satellite affected by multipath interference, *i* represents the subscript of the *i*th path in the multipath, W*<sup>M</sup>* is the number of multipath components of the *M*th GPS signal, *ωMi* is the gain of the *i*th path in the *M*th GPS satellite signal, and *τMi* is the delay of the *i*th path in the *M*th GPS satellite signal.

In the reference channel, GPS satellites share and reuse the same frequency band due to the characteristics of GPS satellite system distribution and Code Division Multiple Access (CDMA) modulation. Thus, the ground receiver is likely to receive more than four frequency-overlapped GPS signals. The received signal by the GPS receiver could be given by

$$\mathbf{x}\_r(t) = \sum\_{k=1}^{M} \mathbf{x}\_k \left(t - \tau\_k\right) + \boldsymbol{n}\_r(t), \tag{2}$$

where *xk* (*t* − *τk*) is the direct wave signal of the *k*th GPS satellite, and *nr*(*t*) represents the noise of the reference channel.

## **3. Interference Suppression**

Since GPS signals may be transmitted on the same frequency bands and the zenith can simultaneously have multiple GPS satellites, a near-earth orbit target can be simultaneously illuminated by multiple satellite beams. Therefore, multiple different GPS signals may be received on the reference channel, contaminating desired reference signals and degrading the suppression of DPI and MPI.
