# Interference Monitoring from Low Earth Orbit: The OPS-SAT Experiment +
## 4 Single Satellite Two-Step Geolocation of the On-Ground Emitter  
This work assumes a two-step approach for localization, hence time or frequency shift observation obtained from the received signal processing can then be converted into a time series of measurements to feed the emitter geolocation algorithm. A key technique in single-satellite localization of emitters is the FDOA method [7], which locates the interference  
Figure 4: Spectrogram computed on the I/Q samples collected from OPS-SAT with active chirp jammer (Acquisition window 2, i.e., the one collecting more jammer energy). by calculating the finite variation \(\Delta\)FOA of the frequency of arrival (FOA) [8]. Therefore, the first step of the emitter localization is based on the generation of FDOA observables, obtained by means of the computation of the Complex Ambiguity Function (CAF), whose theoretical expected accuracies and computational complexity is addressed in [9]. The calculation of the CAF can be considered as the basis for joint estimation of the differential delay and differential frequency offset between two waveforms that contain a common component plus additive noise. This could be the case of two waveforms acquired by two different sensors [3] or two chunks of signal acquired by a unique sensor at different time instants, as for our OPS-SAT case. The FDOA measurements can be obtained by detecting the pair \(\left(\hat{t}_{i,j},\hat{\Delta f}_{i,j}\right)\) in correspondence of the CAF peak, i.e.,  
\[\left(\hat{\tau}_{i,j},\hat{\Delta f}_{i,j}\right)=arg\max_{\tau_{i,j}\Delta f _{i,j}}\left\{\int_{o}^{T}s_{i}(t)s_{j}^{*}(t+\tau_{i,j})\text{exp}\left(-j2 \pi\Delta f_{i,j}t\right)dt\right\}, \tag{1}\]  
where \(s_{i}(t)\) and \(s_{j}(t)\) are the complex envelopes of two waveforms that contain a common component, while \(\tau_{i,j}\) and \(\Delta f_{i,j}\) are the time lag and the frequency offset to be searched. It is worth observing that the integration time for the CAF computation has been set equal to 1 ms, whereas the frequency shift domain has been dimensioned by observing the Doppler shift curve for OPS-SAT. In fact, by observing this curve, we can compute the maximum Doppler shift between two time instants separated by 25 s. The example of CAF is reported in Figure 5.  
Now let us observe that the FDOA approach, which relies on the computation of CAF, generates observables affected by a noise greater than the one embedded in the single acquisition window. However, this is the most viable approach for our experiment, considering the imprecise time and frequency tag of each acquisition window, which may lead to biased observables. Instead, by using a differential approach (based on the CAF), these biases can be mitigated. Now let us focus on the estimation of the SNR for each acquisition window, where with the expression \"signal\" we refer to the signal from the jammer. The jammer power has been computed by integrating the filtered PSD over the jammer bandwidth, whereas the noise power has been computed by integrating the  
Figure 5: Example of CAF computed between window 2 and window 3.  
noise floor over the digital filter bandwidth. The obtained SNR estimations are reported in Table 1.  
By using the approach proposed in [9], it is possible to compute the effective input SNR and effective output SNR, basing on the SNR estimated from the acquisition windows collected by OPS-SAT. It is worth noticing that [9] suggests, as rule of thumb, that the effective output SNR should always exceed 10 dB. Considering the effective output SNRs measured for our experiment (see Table 1), which are few dBs above the minimum value of 10 dB, we can figure out that FDOA observables will be noisy, impacting the jammer geolocation accuracy. The second step is based on mapping FDOA observables at that measurement epoch \(t_{k}\) in the geometric domain in order to localize the emitter.