## 1 Introduction  
Satellite visibility is of the greatest importance for high accuracy surveying. Although four satellites are the minimum number mathematically required for a 3D positional fix [1], most receivers require a minimum of five satellites to operate in Real Time Kinematic (RTK) mode. There is, therefore, a strong motivation for surveyors to ensure that an adequate number of satellites are visible at the required location, as it may provide savings in terms of financial cost, where having to resurvey an area if the accuracy requirements set down in the survey specification are not met or time when a low number of visible satellites will cause the receiver to lose the Global Navigation Satellite System (GNSS) signal resulting in delays as the surveyor waits for signal to be reacquired. Predicting how many satellites will be visible to the receiver at a particular location is relatively easy for surveys in unobstructed areas thanks to existing desktop GNSS planning packages like Trimble Planning [2] or similar online GNSS planning tools [3]. These tools are capable of predicting satellite visibility at any location of the globe, at any time of day. Each package is equipped with almanacs containing orbital ephemeris data for all satellites and can be configured to include satellites from the GPS, GLONASS, COMPASS or GALILEO constellations in the prediction results. One shortcoming of the existing methods is that they have a limited capability for modelling satellite visibility when there are obstructions on the horizon. This limits their applicability in many survey scenarios as it is quite common for topographic surveys to be carried out in confined areas, and, therefore, GNSS shadows are almost certain to be present. For example, in Figure 1a, a GNSS topographic survey is underway in a confined area where the GNSS signal could potentially be obstructed by buildings, earthen embankments and vegetation. Trimble Planning provides added prediction functionality by allowing portions of the horizon to be manually specified and excluded from the visibility calculation. This functionality simulates buildings or other vertical structures which may obstruct GNSS signal, as illustrated in Figure 1b. However, this method assumes a stationary GNSS reference point, whereas, in the majority of situations, the surveyor is mobile unless using static GNSS for establishing permanent survey ground control. Additionally, manually specifying the portions of the horizon that will obstruct satellite signals on a 2D plot requires experience to do so accurately, and the elevation of the target must be estimated unless previously surveyed. It is possible to save the settings for a survey and repeatedly apply these obstructions for subsequent prediction tests; however, this is not a suitable solution for a mobile receiver. Although severe GNSS shadows will be unavoidable in areas such as narrow urban canyons, GNSS prediction methodologies provide useful information when planning a survey by helping to optimise satellite visibility in less problematic urban areas. The need to improve survey planning to assist with mobile GNSS receivers is increasing with the advent of mobile mapping systems (MMSs). An example of an MMS, designed and developed at the National Centre for Geocomputation (NCG), Maynooth University, is displayed in Figure 2a. MMSs are mobile survey platforms that survey an area at speeds comparable with the surrounding vehicular-traffic and therefore a measure of GNSS visibility at a single area is clearly of limited use for a mobile survey platform. GNSS prediction methodologies can also be used to identify problematic areas prior to a survey so MMSs can be routed to minimise GNSS outages. Figure 2b displays a 2D plot of the track of a MMS over an area approximately 2 km\({}^{2}\). Breaks in the greenline correspond to areas of low GNSS visibility, something that is common in built-up residential areas, near tall vegetation or in urban canyons.