1.3 GNSS performance parameters

The performance of any navigation system is characterized by several factors. Some of the primary factors consists of accuracy, precision, availability, continuity, reliability and integrity (IMO 2001; Grimes 2007; Porretta et al. 2016). The priority given to these different factors are application specific. For applications such as, geodetic control surveying, accuracy is the core requirement (Donahue et al. 2013). Whereas, for safety of life applications, such as automotive, aeronautical and marine navigation integrity and reliability is given the highest priority (RTCA DO-181 1983; IMO 2001; European GNSS Agency 2015). Presented is a review of some of the definitions which have been utilized within the research presented.

Accuracy and Precision: The accuracy of an estimated or measured position of a navigation system at a given time is the degree of conformance of that position with respect to a reference position, velocity and/or time (RTCA DO-181 1983; Pullen 2011). Accuracy is represented as an averaged root mean square (rms) error with respect to the reference position. Whereas precision represents the standard deviation with respect to the averaged error or mean. Where error represents the difference between the estimated position and reference position and mean represents the average of the time period positions were provided by the navigation system (Anderson et al. 1998).

Availability: The availability of a navigation system is the percentage of time that the services of the system are usable by the navigator. Availability is an indication of the ability of the system to provide usable service within the specified coverage area (IMO 2001; U.S. Coast Guard Navigation Center 2008; Pullen 2011). Non-availability can be caused by schedule and/or unscheduled interruptions (IMO 2001). The description of availability can be broken into different components, such as, operational, service, system and signal availability (Pullen 2011). Where operational availability for e.g. is defined as the typical or maximum periods of time over which the service is unavailable and service availability is the fraction of time (expressed as a probability over all satellite geometries and conditions) that the navigation service is unavailable (Pullen 2011). Renfro et al. (2018) states there will an operational satellite count availability of ≥ 95% probability that the constellation will have at least 24 operational satellites. The IGS (2013) states that the operational availability of their real time products has a 95% availability for their rapid, ultra-rapid products and real-time products. Presented in Figure 1.7 is an overview of the availability of each of the contributing analysis centres towards IGS’s Multi-GNSS Experiment (MGEX). Figure 1.7 highlights the importance of redundancy within a network ensure product availability. Additional information about each of the contributing analysis centres can be found at IGS (2018a).

Figure 1.7 Multi-GNSS Experiment (MGEX) product availability (IGS 2018a)

Continuity: The continuity of a system is the ability of the total system (comprising all elements necessary to maintain position navigation system within the defined area) to perform its function without interruption during the intended operation. More specifically, continuity is the probability that the specified system performance will be maintained for the duration of a phase of operation, presuming that the system was available at the beginning of that phase of operation (U.S. Coast Guard Navigation Center 2008). Presented by U.S. Coast Guard Navigation Center (2008), the most stringent requirement for the location determination system to support the Positive Train Control (PTC) system is the ability to determine which of two tracks a given train is occupying with a probability of 99.999%. The minimum centre-to-centre spacing of parallel tracks is 3.5 m. While GPS alone cannot meet the specified continuity of service and accuracy, Nationwide Differential Global Positioning Systems NDGPS (previously called United States Coast Guard DGPS) in combination with map matching, inertial navigation systems, accelerometers, and other devices and techniques will provide both the continuity of service and accuracy required to meet the stringent requirements set forth for PTC (U.S. Coast Guard Navigation Center 2017). The IGS (2013) describes the continuity of their ultra-rapid products as 4x daily, at 03, 09, 15 and 21 UTC, daily at 17 UTC for their rapid and continuous for their real time.

Reliability: The probability of success or the probability that the system will perform its intended function under specified design limits. More specifically, reliability is the probability that a product will operate within their specifications for a period of time (design life) under the design operating conditions (such as temperature, volt, etc.) without failure. In other words, reliability may be used as a measure of the system’s success in providing its function properly (RTCA DO-181 1983; Pham 2006). Reliability of a system can be decomposed into failure prevention (robustness and redundancy) and failure response (resilience). For e.g. the Wide Area Augmentation System (WAAS) focuses on failure prevention by providing reliability and redundancy to meet the overall National Airspace System (NAS) requirements with no single point of failure. The overall reliability of the WAAS signal- in-space approaches 100% (U.S. Coast Guard Navigation Center 2008). Where redundancy is the existence of multiple equipment or means for accomplishing a given function in order to increase the reliability of the total system (IMO 2001).

A system is considered reliable in terms of robustness if it is resilient with respect to input and failure uncertainties, and consequently it has low reliability when even the small amounts of uncertainty entail the possibility of failure (RTCA DO-181 1983). The IGS also focuses on failure prevention by improving reliability and robustness primarily through redundancy. IGS products consist of a combination from multiple analysis centres (IGS 2007). As of writing there are 12 analysis centres which contribute towards the combination of the IGS products (IGS 2018b). By combining multiple products, the navigation system is less vulnerable to network outages and can maintain availability and continuity of the service. Integrity: Integrity is the measure of the trust that can be placed in the correctness of the information supplied by a navigation system. Integrity includes the ability of the system to provide timely warnings to users when the system should not be used for navigation (Ochieng et al. 2003; U.S. Coast Guard Navigation Center 2008; Pullen 2011). Where integrity risk is the probability of an undetected, threatening navigation system problem (Parkinson and Axelrad 1988; Ober 1999; Pullen 2011). Overall GNSS system integrity is described by three parameters: the threshold value or alert limit, the time to alarm and the integrity risk. The output of integrity monitoring is that individual (erroneous) observations or the overall GNSS system cannot be used for navigation (IMO 2001). Other definitions of integrity combine the concepts of reliability and integrity under the title Integrity Monitoring (Parkinson and Axelrad 1988; Sturza 1988; Feng et al. 2012; Seepersad and Bisnath 2013; Jokinen et al. 2013a).