## 3 Positioning Based on DVB-T
### Initialization Phase for DVB Ranging  
We assume here that in the future, a PD is likely to be equipped with a GNSS sensor as a primary tool and with other sensors able to exploit the nearby signals-of-opportunity. This means that the architecture of a PD will include a hybrid receiver, which computes its position with GNSS and resorts to SoSs only when the GNSS satellites are not visible. Moreover, in the case of DVB-T towers, it is realistic that the PD has a map of their locations (they are indeed available and easy to find also on the web).  
In this scenario, we can suppose that the trilateration with DVB-T-based measurements is generally preceded by a phase of position computation based on GNSS, performed when the PD is in open sky with complete visibility of GNSS satellites. This phase is the standard mode of operation and, at the same time, represents the initialization phase for the position computation based on DVB-T. During this phase, the PD continuously evaluates the ranges, \(r_{i}\), between each emitter and the PD, by using its own position, provided by GNSS, and the location of the nearby DVB-T emitters, whose map is stored in the PD memory. Therefore, in this phase, the PD can also associate the estimated ranges with the emitter locations, solving the problem of emitter identification, as shown in Figure 3.  
Each range can be written at each discrete-time instant, \(n\), as:  
\[r_{i,G}[n]=N_{i,G}[n]r_{s}+\delta_{i,G}[n] \tag{3}\]  
where \(N_{i,G}[n]\) is an integer, \(r_{s}\) is the distance traveled by the DVB-T signal during an OFDM symbol time, \(\delta_{i,G}[n]\) is a fractional range with respect to \(r_{s}\) and the subscript, \(G\), stands for GNSS. Notice that \(N_{i,G}[n]\) could be also zero, depending on the coverage area of the DVB-T towers. At the same time, the PD can estimate the ranges from the DVB-T emitters by using the SoOs. This can be obtained  
Figure 3: Initialization pahse.  
by measuring the fractional range, \(\delta_{i,D}[n]\), as shown in Section 3.2, and by evaluating \(N_{i,G}[n]\) from Equation (3), as:  
\[N_{i,G}[n]=\left\lfloor\frac{r_{i,G}[n]}{r_{s}}\right\rfloor \tag{4}\]  
where \(\lfloor\cdot\rfloor\) stands for the integer part. Therefore, the PD knows at each instant, \(n\), both \(r_{i,G}[n]\) and the range provided by the DVB-T SoOs, which can be written as:  
\[r_{i,D}[n]=N_{i,G}[n]r_{s}+\delta_{i,D}[n] \tag{5}\]  
and can keep these values aligned. At this point, if the PD enters a GNSS-blocked area at the time instant, \(n_{0}\), it can start the position computation in DVB-mode by using the range measured at the time instant, \(n_{0}-1\), that is, the range measured during the initialization phase. This represents a hot start for the PD, similar to the one encountered in a PD only working in GNSS-mode.  
Another benefit of the initialization phase is that the out bound peaks can be discarded, as shown in Figure 4. The red peak is a multipath of emitter 1, close to the peaks of emitter 2 and stronger than them. However, since it is out of the bound defined by the receiver position, this peak can be recognized as a multipath and, then, discarded.