# GNSS Performance Modelling and Augmentation for Urban Air Mobility +
## 3 GNSS Performance Characterization
### Error Modelling
#### 3.1.4 Multipath Errors  
In general, GNSS error components are assumed to be zero-mean and normally distributed. However, this assumption does not hold for multipath. A comprehensive investigation of terrestrial multipath based on several measurement campaigns was performed in [25; 26]. The results are instructive from the perspective of urban environments. Echoes are classified either as near echoes caused by reflections in the foreground, with delays within 600 ns relative to the direct path, or as far echoes, with delays exceeding 600 ns. The multipath echoes distort the ideal correlation function of the code-tracking loop in the receiver, potentially leading to multipath pseudorange errors that are difficult to model. The magnitude of the multipath pseudorange errors depends upon not only the echo delays but also on the strength and phase of the echoes relative to the direct path, and the type of code-tracking loop employed in the receiver. The relative strength is characterized by the ratio of amplitudes of the multipath and direct rays - the Multipath to Direct Ratio (MDR), which in turn depends on the angle of incidence of the signal on the reflector, and the material properties of the reflector itself. The pseudorange error is directly proportional to the MDR value, with higher MDR values denoting a tendency to 'overpower' the direct ray. A distinction is made here between multipath and Non-Line of Sight (NLOS) instances. The'multipath' instance refers to conditions in which the receiver has a direct line of sight to the satellite in addition to receiving one or more multipath echoes. As shown in Figure 5, in the NLOS condition, a direct line of sight does not exist.  
If the NLOS ray is not significantly attenuated by interactions with objects in the local environment (reflection/diffraction), the receiver will be unable to reject the subsequently contaminated pseudorange from the navigation solution. NLOS conditions, therefore, can result in hazardously misleading information being provided to the vehicle guidance and control loops (when operating autonomously). The following signal reflection parameters directly impact pseudorange error:  
* Relative delay: Additional distance (typically converted to time-delay) of the reflected signal relative to the direct signal;  
Figure 5: Satellite visibility and NLOS/multipath conditions in a typical urban environment.  
* Relative amplitude: Amplitude of the reflected signal relative to the direct signal. This is typically in the range [0,1];
* Relative polarization: Reflection of the Right-Hand Circularly Polarized (RHCP) L1 wave from a perfect conductor results in a polarization reversal to Left-Hand Circularly Polarization (LHCP). RHCP receiver antennas can therefore partially mitigate multipath. However, since the urban environment has an unpredictable distribution of conductors and dielectrics, reflected signals will typically be a mix of right- and left-handed polarization, resulting in partial attenuation of the reflected signal.  
The relative phase of the reflected signal impacts the fading characteristic of the overall received signal, but does not directly impact code-ranging error, and is therefore, not the primary focus of this paper. NLOS/multipath modelling approaches include numerical methods such as the traditional Method of Moments and parabolic methods, asymptotic methods such as ray-tracing, and hybrid stochastic-deterministic methods [17]. Driven by the need for accurate and precise positioning in urban road transport, a number of NLOS modelling methods based on ray-tracing and urban models have been published over the last two decades [13; 27; 28; 29]. A more comprehensive survey of ray-tracing methods can be found in [30]. The approach in this paper is to model overall NLOS/multipath error as a function of three components: ground reflection, building facade reflection and UAV airframe reflection. Each of these components are addressed in turn.