A precise observation should have GNSS a higher weight and thus contribute more to the computed parameters than an imprecise one. Proper observation weighting is only possible if the vari- Solutions: ance-covariance matrix (VCM) of the observations is known, and in fact LS Weighting How important is estimation and Kalman filtering yield GNSS observation the most precise results only if the cor- GNSS rect VCM is used (advanced approach- weighting? es with less stringent requirements are beyond the scope of this column). Observations Knowledge of the VCM is even n the early days of GPS, most more important in view of statistical and Variations receivers tracked only as many failure detection and identification; of GNSS/INS satellites as were required to com- inappropriate weights may cause outli- Ipute a position. This meant that ers to remain undetected and truly observation weighting was not needed accurate observations to be rejected, Integration and not even possible when process- thus inverting the desired benefit of ing on the epoch-by-epoch level. quality control into a considerable loss “GNSS Solutions” is a Soon, though, receivers were capable of accuracy. Both redundant observa- regular column featuring of tracking all satellites “in view,” and tions and proper observation weighting questions and answers instead of the four minimum pseu- are essential for obtaining a precise and dorange observations required for a reliable estimate. about technical aspects of three-dimensional position, five, six, Proper observation weighting, as GNSS. Readers are invited or more pseudoranges could be avail- it turns out, is not a trivial task with to send questions to the able at each epoch. GNSS observation GNSS observations. The reason is columnists, Professor redundancy will increase further as that the variance must incorporate all GLONASS and Galileo approach their unmodeled effects and thus depends Gérard Lachapelle and Dr. full constellations. on factors such as tracking loop char- Mark Petovello, Department Inevitably, redundant observations acteristics, receiver and antenna hard- of Geomatics Engineering, are inconsistent. At first sight, this ware, signal strength, receiver dynam- University of Calgary, might seem a nuisance best avoided ics, multipath effects, atmospheric by selecting a suitable non-redundant propagation effects, and so forth, most who will find experts to subset of the observations to compute of which can hardly be controlled or answer them. Their e-mail position and receiver clock bias — for determined accurately. The practical addresses can be found with example, the one yielding minimum solution is to use a simple variance their biographies at the GDOP. In reality, however, GDOP model that comes close enough to real- tells nothing about the actual errors ity so that LS estimation or Kalman conclusion of the column of the observations, and the chosen filtering yield nearly optimum results subset may produce a larger position and reliability checking works well. error than other subsets would. It is The simplest variance model far better to exploit the inconsisten- assigns identical variance to all observ- cies using statistical methodsGPS | GALILEO such as | GLONASSables of the same type produced by least-squares (LS) estimation, Kal- the same receiver, for example, 1m2 for man filtering, and hypothesis testing. C/A pseudorange, 1 Hz2 for L1 Dop- This increases the positioning preci- pler, and 0.012 cyc2 for L1 carrier phase. sion, allows checking for failures, and Several studies have shown that this is reduces the probability of undetected not a suitable variance model, unless gross errors. the receiver is operated only in clear- However, exploiting the inconsis- sky environment under line-of-sight tencies requires that the relative preci- conditions, and only high elevation sat-
sion of each observation with respect ellites are used. Elevation or C/N0 (car- to the other observations be known. rier-to-noise-density ratio) dependent
26 InsideGNSS january/february 2007 www.insidegnss FIGURE 1 Normal probability plot of standardized pseudorange errors from low-multipath dataset (left) and high-multipath data set (right)
FIGURE 2 Error of estimated receiver positions in a low-multipath environment (left) and high-multipath environment (right; note different scale of axes). Percentages of solutions with more than four satellites are shown in brackets in the legend. variance models usually perform sig- high-multipath data set collected in a receiver and antenna types, and were nificantly better, with the C/N -based dense urban environment (right). determined in advance. 0 GPS | GALILEO | GLONASS models being more widely applicable. The coordinates of both locations If the observations are normally This can be shown both in the observa- were precisely known beforehand; so, distributed and their variance is tion domain (Figure 1) and in the coor- ‘pseudorange errors’ could be esti- matched by any of the variance mod- dinate domain (Figure 2). mated. These errors were then stan- els, the corresponding standardized Figure 1 presents a so-called nor- dardized using three different variance errors should lie exactly on the blue mal probability plot of pseudorange models: (i) identical variances σ2 (ID), straight line in Figure 1. Actually, all 2 errors obtained from two different (ii) elevation dependent variances σ 0 three models represent the majority of static GPS data sets: a three-hour /sin2 E (ELV), and (iii) SIGMA-ε vari- the low-multipath data set well (left), low-multipath data set collected on a ances C2 • 10-C/N0/10 (EPS). The model with a slight advantage shown for EPS mountain slope (left) and a five-hour parameters σ, σ0, and C depend on the (see vertical axis range over which the
www.insidegnss.com january/february 2007 InsideGNSS 27 GNSS SOLUTIONS
plotted data coincide approximately ance model is also crucial for success- Wieser, A., and M. Gaggl and H. Hartinger, with the straight line). However, both ful ambiguity resolution. “Improved positioning accuracy with high-sen- ID and ELV fail completely in the high- The above examples highlight the sitivity GNSS receivers and SNR aided integrity monitoring of pseudo-range observations,” in multipath environment (right), while fact that proper GNSS observation Proceedings ION GNSS 2005, 18th Int. Technical EPS still represents more than 90 per- weighting is in fact very important in Meeting of the Satellite Division, Sept. 13–16, cent of the data. order to obtain the most precise and Long Beach, CA: 1545 – 1554, (2005) Figure 2 shows that, indeed, the reliable position, velocity, and time Wieser, A., “Robust and fuzzy techniques precision of the computed coordinates solutions that can be computed from a for parameter estimation and quality assess- depends on the chosen variance model. given set of redundant observations. ment in GPS,” Ph.D. dissertation, Graz University of Technology, Shaker Verlag, Aachen, ISBN The plot on the left contains the epoch- andreas wieser by-epoch results obtained from the 3826598075 (2002) low-multipath data set at the mountain Dr. Andreas Wieser is a university assistant slope. The identical raw observations with the Institut für Ingenieurgeodäsie und were processed separately using each of Messsysteme at the Graz University of Technol- the three variance models. Obviously, ogy. He has worked on GNSS weight models and “What is the EPS yields the highest precision and quality control as part of his Ph.D. dissertation, the fewest large errors. and he has been actively involved in parameter difference between estimation and GNSS research since 1998. The plot on the right contains the corresponding position solutions Editor’s Note For details of observation ‘loose’, ‘tight’, obtained for the high-multipath site, weighting models, see the following references: ‘ultra-tight’ and and again EPS yields the best results: Collins, J.P., and R.B Langley, “Possible Weighting Schemes for GPS Carrier Phase Obser- 95% of the position errors are within ‘deep’ integration vations in the Presence of Multipath,” Geodetic 38 meters, as opposed to 60 meters Research Laboratory, University of New Bruns- strategies for INS when using the other variance models. wick, Canada, Report to the United States Army Furthermore, fewer observations are Corps of Engineers Topographic Engineering and GNSS?” rejected as potential outliers by the Center,
GPS | GALILEO | GLONASS
28 InsideGNSS january/february 2007 www.insidegnss Greenspan in his seminal work on INS/GPS integration (see citation in Further Readings section at the end of this Solu- tion.) described the “loose” and “tight” integration architec- tures in the way they were understood at the time. Over the years, however, a slight departure from these definitions has occurred. Unfortunately, this has led to some confusion especially because — as a review of recent literature on the subject indicates — an alternate consensus has emerged regarding the terms used to describe the vari- ous INS/GNSS architectures. Another source of confusion is the fact that some INS/GNSS architectures contain ele- ments of the various fusion schemes such that they cannot be described simply as loose, tight, or deep. In the following discussion, we present a synopsis of the various INS/GNSS fusion architectures and point out where some of the confusion lies. (This discussion isnot meant to be a tutorial on the details of INS/GNSS integration. The reader interested in a more detailed treatment of the subject is urged to consult the papers and texts listed in the “Further Reading” section at the end of this article.) Before we discuss the definitions of these terms and architectures, however, it would be beneficial to define some terminology and review the overall objectives of INS/GNSS fusion. Overview of INS/GNSS Fusion. An INS is a self-contained navigator that generates an attitude (orientation), position, and velocity solution at rates higher than those normally available from a GNSS receiver. The sensors used in an INS are a triad of gyros (for measuring rotation or rotation rate) and accelerometers (for measuring accelerations or specific force). An INS is the combination of these sensors, navigation algorithms, and the computer which hosts the algorithms. The INS algorithms for generating attitude, position, and velocity involve, in part, performing the mathematical operation of integration on the outputs of these sensors. Thus, any error on the output of the sensors leads to cor- related attitude, position, and velocity errors that are poten- tially unbounded. A GNSS receiver, on the other hand, generates position and velocity estimates with bounded errors. Although GNSS can be used to provide an attitude solution, this is normally avoided in practice because it involves using a complex, and potentially costly, system with multiple receivers and anten- nas. GPS | GALILEO | GLONASS The error characteristics of an INS and GNSS are comple- mentary. When the information from INS and GNSS are fused, the high-fidelity GNSS position and velocity estimates are used to calibrate the INS sensor errors. The INS, in turn, provides the high bandwidth attitude, position, and velocity estimates needed for vehicle guidance and control. The INS estimates also allow coasting through momen- tary drop-outs of the GNSS solution, which can result from signal blockage caused by obstructions between the GNSS antennas and the satellites. Yet another way the INS informa-
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integration architecture. In the loose r GNSS Navigation Signal n architecture, the INS and GNSS receiv- Solution Preprocessing Correlators Navigation ers operate as independent navigation and Sampling Processor and Tracking r systems. The information from them is Loop #1 1 GNSS Receiver blended using an estimator to form a third navigation solution. Normally, an extended kalman filter (EKF) is used to accomplish the blending even though Blending Software currently some interest in using other Blended Navigation Inertial Sensor Navigation Solution non-linear estimators such as the Measurement and Filtering unscented kalman filter or particle fil- Pre-processing Algorithms ters has arisen. The purpose of the loose archi- tecture is to extract the desirable attributes from INS and GNSS while Accelerometers suppressing the undesirable attributes Inertial Navigation of each. That is, the blended solution Solution Inerital Navigation generated by loose integration of INS Algoirthms and GNSS features the high band- width information from the INS Gyros INS and the bounded errors from the GNSS. There are many variants of the FIGURE 1 INS/GNSS Loose Integration loose integration, and we will briefly describe a couple of examples here — what are sometimes referred to as feedback or feed-forward configura- Signal tions. In the feedback configuration, Preprocessing Correlators inertial sensor errors estimated by the and Sampling and Tracking EKF are fed back to correct the rate Loop #1 GNSS Receiver gyro and accelerometer measurements. When the feedback path is absent, the r r1 n configuration is said to be a feed-for- ward configuration. Blending Software Blended Navigation The feedback path is shown by a Inertial Sensor Navigation Solution dashed line in Figure 1 to indicate that Measurement and it is not always required. When low Pre-processing Filtering quality inertial sensors (which have Algorithms large output errors) are used, a feedback path is almost always required. In these instances, if the feedback path is absent, Accelerometers the linearization assumption inherent in estimators such as the EKF can be INS violated, leading to filter divergence. GPS | GALILEO | GLONASS The feed-forward configuration is normally used with high-grade Gyros inertial navigation systems, such as those found on commercial transport aircraft. FIGURE 2 INS/GNSS Tight Integration (Classic Definition) In summary, note that the key fea- ture of loose integration is that both tion can be used is to help increase the mation to aid the signal processing the INS and GNSS receiver are inde- robustness of GNSS receivers to jam- algorithms inside a GNSS receiver. pendent navigators. The information ming or radio frequency interference Loose INS/GNSS Integration. Figure 1 from the two navigators is blended to (RFI). This involves using INS infor- shows a schematic of a loose INS/GNSS form a third navigation solution.
30 InsideGNSS january/february 2007 www.insidegnss Tight INS/GNSS Integration: Classic the tight integration architecture cur- The performance enhancements Definition. Tight INS/GNSS architec- rently in use is shown schematically in offered by this alternative comes at a ture, as defined by Greenspan (i.e., the Figure 3. In addition to the fact that the price. Compared to a loose or a clas- classic definition), is illustrated inF ig- INS and GNSS receivers are reduced to sic tight integration architecture, this ure 2. In this architecture, the INS and their basic sensor functions, informa- version of tight integration is more GNSS are reduced to their basic sensor tion from the blending filter is fed back complex in that it requires incorporat- functions. That is, pseudorange, pseu- to the GNSS receiver to enhance its ing information from the blending dorange rate, accelerations, and gyro performance. Specifically, the velocity filter into the GNSS tracking loops. measurements are used to generate a (and possibly acceleration) informa- Furthermore, in this tight integra- single blended navigation solution. tion from the blending filter (shown in tion architecture the GNSS receiver is In general, the classical tight archi- red in Figure 3) is used to aid the code no longer independent from the INS; tecture provides a more accurate solu- and carrier tracking loops in the GNSS consequently, a faulty INS sensor can tion than loose integration. Another receiver. affect the blended solution which, in advantage it has over the loose inte- This allows the GNSS receiver to turn, will affect the GNSS receiver’s gration scheme is that tight integra- remain in lock (that is, continue to performance. tion can continue to extract useful track the signal) in high-dynamic Deep INS/GNSS Integration. In cur- information from a GNSS receiver in maneuvers, which would not be possi- rent usage, the term deep integration situations where fewer than four sat- ble, or would at least be difficult, with- (or ultra-tight, which is a specific vari- ellites are visible. Loose integration, out the aiding information. Another ant of deep integration) refers to the however, has the advantage of redun- benefit of tight integration is that it kind of architecture shown in Figure dancy because the INS and GNSS can be used to narrow the tracking 4. Two important features distinguish receiver still produce independent loop bandwidths of the GNSS receiver, this integration scheme from the oth- navigation solutions. thereby reducing noise and increasing ers discussed so far. First, the architec- Tight INS/GNSS Integration: Alternate the system’s robustness to wideband ture of the GNSS receiver is fundamen- Definition. An alternate definition of interference or jamming. tally different from that traditionally
GPS | GALILEO | GLONASS
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Signal tion architecture is that it enhances the Preprocessing Correlators robustness of GNSS to interference and and Sampling and Tracking jamming. Loop #1 Velocity The enhancement afforded by this GNSS Receiver Estimate architecture exceeds that provided by
r tight integration. It also represents an r n 1 optimal fusion of the information from Blending Software an INS and a GNSS receiver. However, the major, readily apparent drawback Inertial Sensor Navigation Blended Navigation Measurement and Filtering Solution of the deep integration scheme is the Pre-processing Algorithms complexity involved in integrating INS information with GNSS information deep inside the receiver. In summary, in going from the loose to the deep integration archi- Accelerometers tectures, we gain robustness to GNSS outages either due to vehicle dynamics, INS interference, or jamming. However, this increased robustness comes at the Gyros sacrifice of system simplicity, redun- dancy, and independence of the INS
FIGURE 3 INS/GNSS Tight Integration (Alternate Definition) and GNSS navigators.
Vector Delay Lock Loop Signal Preprocessing Correlators Dr. Gebre-Egziabher and is an assistant professor Sampling of aerospace engineer- ing and mechanics at Code and Carrier the University of Minnesota, in Minneapolis, Generator Minnesota. His research is in the areas naviga- tion, guidance and control with a particular emphasis on application of estimation theory to Accelerometers avionics sensor fusion and system integration Navigator issues. and INS Blending Discriminators Algorithms Correction Gyros Two recent Inside GNSS articles carried references to “Narrow Correlator,” which is a registered trademark of NovAtel, Inc., referring to the company’s patented Blended Navigation technology. These articles were the GNSS Solution Solution article on multipath mitigation GPS | GALILEO | GLONASStechnology in the October 2006 issue and FIGURE 4 INS/GNSS Deep Integration “The Garda Project” article in the November/ December issue. Use of this terminology used in the loose and tight integration The second distinguishing feature should not have been made without reference schemes. In this case, the traditional of deep integration arises from the use to NovAtel and its trademark. The Garda receiver architecture consisting of a of the INS or information from the Project article also includes a reference to bank of independent code and carrier INS as an integral part of the GNSS “multi-correlator delay lock loop,” which tracking loops is replaced by some- receiver. That is, the GNSS receiver should not be confused with NovAtel’s patented and trademarked Multipath thing akin to a single vector delay lock can no longer be viewed as a naviga- Estimating Delay Lock Loop (MEDLL) loop (VDLL). The VDLL is enclosed in tor independent of the INS. One of the technology. Inside GNSS regrets the oversight the dashed box shown in Figure 4. many advantages of the deep integra-
32 InsideGNSS january/february 2007 www.insidegnss Further Reading Processing,” Proceedings of the ION-GNSS 18th and Applications, Editors Parkinson, Spilker, International Technical Meeting, Long Beach, Enge, and Axelrad . AIAA, Washington, D.C., For those interested the mechanics of INS/GNSS California, September 2005, pp. 1095–1102. 1996. Vol. 1. pp. 245–328. integration, the trade-offs involved in the Gebre-Egziabher, D., and A. Ravzi, P. Enge, Pany, T., and B. Eissfeller, “Use of Vector Delay various integration schemes, and the workings J. Gautier, S. Pullen, B. Pervan, and D. Akos, Lock Loop Receiver for GNSS Signal Power of advanced GNSS receiver designs such as the “Sensitivity and Performance Analysis of Analysis in Bad Signal Conditions,” Proceedings VDLL, a representative (but not exhaustive) list Doppler-Aided GPS Carrier Tracking Loops”, of the IEEE-ION Position, Location and of references are given below. Navigation, Vol. 52, No. 2, 2005, pp. 49–60. Navigation Symposium (PLANS) 2006, San INS/GNSS Integration: Vector Delay Lock Loops Diego, California, 2006. Phillips, R., and G.T. Schmidt, “GPS/INS Spilker, J., “Fundamentals of Signal Tracking Integration,” AGARD Lecture Series on System Demoz Gebre-Egziabher Theory,” in Global Positioning System: Theory Implications and Innovative Application of Satellite Navigation, Paris, France, July 1996. Cox, D. B., “Integration of GPS with Inertial Navigation Systems,” reprinted in Global Mark Petovello is a Senior Professor Gérard Lachapelle Positioning System: Papers Published in Research Engineer in the holds a CRC/iCORE Chair NAVIGATION, Institute of Navigation, Virginia, Department of Geomatics in Wireless Location in the Vol. I, 1980, pp. 144–153. Engineering at the University of Department of Geomatics Calgary. He has been actively Engineering at the University of Greenspan, R. L., “GPS and Inertial Integration,” involved in many aspects of Calgary. He has been involved in Global Positioning System: Theory and positioning and navigation with GNSS since 1980 and has Applications, Editors B. Parkinson, J. Spilker, since 1997 including GNSS received numerous awards for P. Enge and P. Axelrad. AIAA, Washington, D.C., algorithm development, inertial his contributions in the area of 1996, Vol. 2, pp. 187–220. navigation, sensor integration, differential kinematic GPS and Benefits of INS-Aiding of GNSS Receivers and software development. indoor location. Pany, T., and R. Kaniuth and B. Eissfeller, “Deep Email: mpetovello@geomatics. Email: lachapel@geomatics. Integration of Navigation Solution and Signal ucalgary.ca ucalgary.ca
GPS | GALILEO | GLONASS
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