# The Local Integrity Approach for Urban Contexts:
## 2 Local GNSS Integrity Approach
### Exploitation of Pseudorange Residual Measurements  
A useful raw source of information for assessing the GNSS signal quality can be identified in the _pseudorange residual measurements_ or a function of them [10; 11].  
Such residuals are conventionally defined as the differences between observations and estimated observations of pseudorange measurements [14]. They can be computed starting from the measured pseudoranges for each satellite and the geometrical ranges between the satellites and the user. The measured pseudoranges can be possibly corrected (e.g., applying SBAS corrections), whereas the geometrical ranges are a-posteriori computed knowing the satellite position and the estimated position of the receiver (linearization point).  
In case of a simple Least Squares (LS) solution, the _vector of pseudorange residuals_\(\mathbf{w}_{n}=\left(w_{1,n}w_{2,n}...w_{N_{sat},n}\right)^{\mathsf{T}}\), referred to a specific discrete time instant (\(n\)) and a set of \(N_{sat}\) satellite-user pseudoranges, can be computed as [14]:  
\[\mathbf{w}_{n}=\delta\mathbf{y}_{n}-\mathbf{H}\delta\mathbf{x}_{\text{LS},n} \tag{1}\]  
where:  
* \(\delta\mathbf{y}_{n}=\left(\delta y_{1,n}\delta y_{2,n}...\delta y_{N_{sat},n} \right)^{\mathsf{T}}\) is the vector \(R^{N_{sat}\times\ 1}\) containing the differences between nominal (geometrical) ranges and pseudoranges (observations) measured at the \(n\)-th time instant for each \(i\)-th satellite (with \(i\) ranging from 1 to \(N_{sat}\));
* \(\mathbf{H}\) is the linear connection matrix \(R^{N_{sat}\times\ 4}\), derived from the linearization of the PVT solution problem about the selected linearization point;
* \(\delta\mathbf{x}_{\text{LS},n}=\left(\delta x_{n}\delta y_{n}\delta z_{n}- \delta t_{n}\right)^{\mathsf{T}}\) is a vector \(R^{4\times\ 1}\) containing the position-time deviation obtained after the LS solution at the \(n\)-th time instant [15].  
As noticed in [10; 11], various consumer-grade receivers (e.g., uBlox-6T [16]) can directly output the residuals by means of a specific sentence (SGPGRS) defined in the common standard output format NMEA 0183, from the National Marine Electronics Association [17]. For this reason, it is possible to assume that vehicles in a VANET can time-stamp and share their respective residuals together with their estimated positions. All these data can be combined by a central processing facility, thus building a data base in the form of a digital map, with a reasonable granularity. Notably, it is possible to combine GNSS observations taken at the same place over multiple days due to the repeatability of satellite/receiver geometrical conditions, depending on the satellite orbits [10]. In fact, every sidereal day (23 h and 56 min) a GPS satellite passes over the same place on Earth with the same azimuth and elevation and then with comparable signal degradations due to multipath effect. This concept can be extended to GNSS signals other than GPS (e.g., Galileo satellite orbit repeat period is equal to 10 d [18]). In case of a decommissioned (or replaced) satellite, its related data can be reset in the data base.