More commonly used in civil GNSS applications are “1-sigma” and “2- sigma” error limits. In the case of position errors that follow Gaussian Solutions: distributions, these limits express the 63rd and 95th percentiles of navigation errors, respectively, for a one- Quantifying the What are the dimensional parameter (e.g., altitude). differences between For higher-dimension parameters, performance such as 2-D horizontal position, the accuracy, integrity, one- and two-sigma limits represent of navigation lower percentiles than in the one- continuity, and dimensional case and can be computed systems and availability, and from a chi-squared distribution if the underlying range-domain errors are standards for how are they Gaussian. computed? Because the Gaussian distribution assisted-GNSS describes most navigation system hese four words describe param- error distributions fairly well out to eters that quantify the perfor- the 95th percentile, many accuracy “GNSS Solutions” is a mance of navigation systems. descriptions use “95%” and “2-sigma” regular column featuring T The terms are not unique to numbers interchangeably. However, questions and answers satellite navigation, as they have been this convention should not be taken about technical aspects of used for many years with respect to to mean that the underlying error other navigation systems and, with distribution is actually Gaussian, GNSS. Readers are invited to broader definitions, throughout the particularly in the “tails” beyond 2- send their questions to the practice of engineering. This column sigma, where the norm is for variations columnist, Dr. Mark Petovello, will describe the use of these terms for from the Gaussian distribution to exist. Department of Geomatics navigation and focus on their applica- Accuracy is obviously a value of bility to GNSS. paramount importance when selecting Engineering, University of Accuracy is the navigation among candidate navigation systems Calgary, who will find experts performance parameter that is most and deciding what use can be made of to answer them. commonly used and is the easiest their measurements. Because accuracy to understand. It is a measure of the defines errors under typical conditions, error, or the deviation of the estimated it expresses what users will experience position from the unknown true in normal, everyday use. position, of a given navigation tool or system. More precisely, accuracy is a Beyond Accuracy statistical quantity associated with the To varying extents, the other three probabilistic distribution of navigation parameters described next express Mark Petovello is an Assistant error. relatively rare phenomena that may not Professor in the Department of Geomatics Engineering at Depending on the system and its be noticed by typical users (unless sys- the University of Calgary. He intended application, this quantity can tem performance is far short of what has been actively involved in be expressed in somewhat different is required) and thus are mostly evalu- many aspects of positioning and ways. For example, many military ated by offline analysis and simulation. navigation since 1997 including systems express accuracy in terms Integrity relates to the level of trust GNSS algorithm development, of “circular error probable” (CEP) in that can be placed in a navigation inertial navigation, sensor two dimensions or “spherical error system. Here, “trust” refers to reliance integration, and software probable” (SEP) in three dimensions. that gross errors (errors much larger development. This represents the median position than the accuracy of the system) can be Email: mark.petovello@ error — it exceeds 50 percent of all avoided. ucalgary.ca position errors and falls below the In practice, this concept is other 50 percent. expressed quantitatively using three

20 InsideGNSS september/october 2008 www.insidegnss sub-parameters. The first isintegrity bounds, such as a horizontal alert limit position error to exceed its alert limit risk, which denotes the probability (HAL) and a vertical alert limit (VAL), under “nominal” conditions without (per operation or per unit of time) that often exist depending on the intended any particular system fault or anomaly the system generates an unacceptable application. taking place. The probability of this is error without also providing a timely The third sub-parameter istime typically extremely low given the gap warning that the system’s outputs to alert (TTA), which is defined as between typical system accuracy and cannot be trusted. Such an event is the time between the occurrence of errors large enough to be unsafe, but it called “loss of integrity” (LOI) in some potential misleading information (i.e., cannot be ruled out. contexts and “misleading information” one or more alert limits are violated) Because no failure or anomaly (MI) in others. Depending on the and the time at which an alert or is involved in this form of integrity potential consequence of “misleading correction (i.e., exclusion of the failed loss, there is nothing to detect. Thus, information,” a word expressing the measurements) is issued to the system in such cases, integrity monitoring severity of the consequence may user to protect him or her from the in general and the time-to-alert be added, such as “hazardously underlying problem. metric in particular do not apply, at misleading information” or HMI. Note that the TTA “clock” begins least in theory. In practice, because The second sub-parameter is ticking not when a failure takes place many degrees of “off-nominal” the alert limit, which defines the but when this failure causes navigation circumstances exist between magnitude of error that, if exceeded, errors to grow to the extent that one or “nominal” and “faulted” conditions, is unacceptable from a safety more alert limits might be exceeded. detection is possible, but this standpoint. Alert limits generally possibility is normally not considered come from requirements for particular Losing Integrity in analysis. applications and are expressed in terms Loss of integrity generally occurs in The second and more likely of position error bounds. Multiple two ways. The first of these is for a possibility for loss of integrity is a fault

www.insidegnss.com september/october 2008 InsideGNSS 21 GNSS SOLUTIONS

defined meet the requirements of a particular application. The most common definition of availability is the long-term average probability (subject to certain conditions) that the accuracy, integrity, and continuity requirements are simultaneously met. This does not always apply in practice, however. For example, some applications do not require that continuity be assured at the time the operation is conducted. Also, many

Copyright iStockphoto.com/Mark Evans common applications only have accuracy requirements. Therefore, or anomaly occurring that leads to loss because of the actions of one or more when availability is mentioned, the of integrity if detection and exclusion integrity monitors in detecting a real or requirements that must be met for a do not occur within the time to alert. imaginary fault, and then either failing given operation (at a given moment in In this case, the prior probability of to exclude the affected measurements time) to be declared “available” should the fault occurring is an important (leading to complete loss of navigation) be clear or commonly understood. contributor to integrity risk, as is the or implementing an exclusion that probability of missed detection, or leaves the remaining measurements All Together Now the probability that the fault will not incapable of meeting the required To compute a long-term average prob- be detected before the time to alert performance. ability of a GNSS system meeting all expires. For applications that cannot be of its requirements simultaneously, Although detailed analysis of interrupted without some level of simulations of satellite orbits and vis- these scenarios must be done offline, danger, such as aircraft precision ibility at one or more user locations are the results of these analyses can be approach and landing under Category conducted. These simulations normally encapsulated into real-time user III weather minima, loss of continuity include the possibility that one or more calculations of protection levels, which poses its own safety hazards. satellites are unhealthy for one reason express the position-error bounds Two additional parameters or another, including planned mainte- that can be protected to the required are useful in analyzing continuity nance, unplanned failures that are still probability level of integrity risk. performance. Theprobability of false being corrected, and “end-of-life” out- By ensuring that these protection alert (or false detection or fault-free ages of a satellite that has not yet been levels are no greater than the alert) is the probability that one or replaced with a new one. corresponding alert limits (i.e., more integrity monitors issue an alert Because GNSS satellite ground confirming that, in the vertical (leading to measurement exclusion tracks typically repeat (e.g., every position axis, the vertical protection and possibly continuity loss) when no 24 hours for today’s GPS satellites), level or VPL ≤ VAL), integrity can be underlying fault is present. simulations need only cover the period verified in real-time for the set of GNSS A critical satellite for GNSS before the ground tracks (and thus user satellites available to the user. applications refers to one whose loss satellite geometry) begin to repeat. Continuity concerns the due to sudden failure or exclusion by For a given constellation state and reliability of the position outputs of the integrity monitor (whether needed time epoch, the relevant performance a navigation system. Continuity risk to protect integrity or not) would metrics are checked, and either a is the probability that the system will cause loss of continuity. Because, “1” (available) or “0” (unavailable) stop providing navigation outputs of in most cases, accuracy predictions is stored. The result of each epoch is the specified quality during a given and integrity protection levels can then multiplied by its probability of operation or time interval, assuming be computed in advance of a given occurrence (based on published or that the outputs were present and of operation, we can usually determine estimated satellite-outage probabilities) specified quality at the beginning. which satellites (and how many) of to calculate a long-term average Loss of continuity can occur when the set in view are critical and if the probability. a navigation system (or an individual resulting implied continuity risk is Other definitions of availability, GNSS satellite) simply stops working or acceptable. different from a long-term average broadcasting signals. In these cases, it Finally, availability expresses probability, are sometimes used. is obvious that something went wrong. the likelihood that the other three One example is sometimes called In other cases, continuity is lost performance parameters previously “operational availability” and

22 InsideGNSS september/october 2008 www.insidegnss refers to the maximum duration of knowing that, for all scenarios where how the results would differ if key unavailability given some worst-case no more than three satellites in the assumptions were changed. system state. This is a useful additional nominal 24 primary orbit slots in the Sam Pullen quantity to know for systems with very GPS constellation are unhealthy, the Dr. Sam Pullen is a senior research engineer at high availability requirements. maximum consecutive duration of Stanford University, where he is the manager For example, for GNSS systems unavailability is 75 minutes. of the local area augmentation system designed to aid in landing airplanes in When assessing availability, one (LAAS) research effort. He has supported bad weather, knowing that the long- should always remember that the the FAA in developing LAAS and wide area term availability of the system is, for resulting numbers are only as good as augmentation system (WAAS) concepts, example, approximately 0.999 would the assumptions (error models, satellite technical requirements, integrity algorithms, be important — suggesting an average constellations, worst-case outages and performance models since he received period of unavailability of about 86 and probabilities, etc.) that go into his Ph.D. in Aeronautics and Astronautics from seconds per day, 44 minutes per month, them. For this reason, all results from Stanford in 1996. His research involves optimal or 8.76 hours per year. But users would availability analyses must make clear aerospace system design and verification under also derive an important benefit from all relevant assumptions and, ideally, uncertainty.

What is assisted GNSS? What changes are straightforward due to the multi-GNSS framework already in place in the assis- needed in assistance service standards to tance data specifications from earlier releases. support the new near-future GNSSs such as One of the most promising activi- GLONASS and QZSS? ties is the work towards OMA SUPL 2.1 that promises to bring convergence ssisted GNSS (AGNSS) is a positioning and data bit assistance for to the currently very messy situation technology that enables faster high sensitivity. in application layer–based AGNSS position determination in an When the assistance data is deliv- solutions. The current OMA SUPL 2.0 AAGNSS-enabled handset than ered over a telecom system architec- specification is largely a collection of could be achieved using the broadcast ture’s application layer connection cellular network–specific protocols GNSS satellite data only. (usually a TCP/IP connection), the typ- applied to the application layer that When a handset positions itself, ical position fix times are in the order offer very different levels of perfor- it requests assistance data from the of 10–20 seconds compared to 40–60 mance from each other, none of which network. This assistance data includes, seconds using autonomous methods is optimally suited for the application among other things: navigation models or even longer fix times in weak signal layer. for ephemerides and clock corrections, conditions. In the best case, the hand- The OMA SUPL2.1 solution also reference location, ionosphere models, set already has the assistance data in its offers a unique opportunity to enable reference time, and optionally differ- memory — for example, in the form of hybrid use of GNSS-based methods ential corrections for high-accuracy extended ephemeris — and, as a result, with non-cellular and non-GNSS posi- the position fix time can be as short as tioning solutions, such as Wi-Fi posi- Acronyms few seconds. tioning because the key principle in the AGNSS Assisted GNSS Currently the multi-GNSS cellular design is its independence of cellular EDGE Enhanced Data rates for Global standards in 3GPP GERAN (GSM), network specific protocols and their Evolution 3GPP RAN (UMTS) and OMA SUPL limitations. GERAN GSM EDGE Radio Access Network 2.0 (Application Layer) support only GNSS Global Navigation Satellite System GPS L1 C/A-code–based Standard Other Performance GSM Global System for Mobile Positioning Service and all Galileo Improvements Communications Open Service signals. The work to The new GNSSs obviously address the OMA Open Mobile Alliance include other GPS signals such as L5, issue of low signal availability in urban PPP Precise Point Positioning L2C, and L1C signals and those from canyons. Accuracy improvements QZSS Quasi-Zenith Satellite System other GNSSs, such as GLONASS, can be achieved, first of all, by the RAN Radio Access Network satellite-based augmentation systems introduction of carrier-phase position- SBAS Satellite Based Augmentation System (SBASs) and Japan’s regional Quasi ing–based methods to the assistance SUPL Secure User Plane Location Zenith Satellite System (QZSS) is service standards. For example, RTK- UMTS Universal Mobile Telecommunications starting in 3GPP and OMA forums based carrier phase services are already System this autumn. Adding new systems is GNSS Solutions continued on page 50

www.insidegnss.com september/october 2008 InsideGNSS 23 in place in a plethora of countries and, hence, the mass market applications could now also start exploiting the full advantage of this technology and exist- ing services. The OMA SUPL 2.1 solu- tion is intended to support streaming of assistance data between the handset and the assistance data server enabling, amongst other things, continuous transfer of carrier-phase assistance from the server to the handset. The new assistance standards also improve positioning availability in terms of novel types of navigation models. For example, the multi-GNSS assistance standards support long-term navigation models that may be valid several days in the future. Moreover, the multi-GNSS assistance standards support non-native formats, result- ing in the performance harmoniza- tion across different GNSSs. This is achieved by presenting the orbit models for all the GNSSs in the same format. Over the longer term, AGNSS stan- dards are open for the addition of even more advanced assistance data. To name a few, these could include real- time or predicted ionosphere and tro- posphere maps enabling precise point positioning (PPP) in handsets.

Jari Syrjärinne and Lauri Wirola Jari Syrjärinne received his M.Sc. and Ph.D. from Tampere University of Technology, Finland, majoring in digital signal processing and applied mathematics. Since 1999 he has been at Nokia Inc. working with various positioning technologies from wireless network–based positioning methods to GNSS positioning. He is currently involved in work on assisted GNSS and algorithms for hybrid positioning, running multiple R&D projects in these areas. Lauri Wirola, received his Master of Science degree from Tampere University of Technology, Finland, majoring in electrophysics. In 2005 he joined the positioning group at Nokia. His present research interests include multi-GNSS positioning, RTK, and PPP as well as AGNSS. He is also involved in the location service standardization in the Open Mobile Alliance. Moreover, he is currently undertaking postgraduate studies in modern electromagnetism and mathematics.

24 InsideGNSS september/october 2008 www.insidegnss