CCCG 2011, Toronto ON, August 10–12, 2011

Improving Accuracy of GNSS Devices in Urban Canyons∗

Boaz Ben-Moshe† Elazar Elkin‡ Harel Levi§ Ayal Weissman¶

Abstract

This paper addresses the problem of calculating the ac-curate position of a GNSS device operating in an urbancanyon, where lines of sight (LOS) with navigation satel-lites are too few for accurate trilateration calculation.We introduce a post-processing refinement algorithm,which makes use of a 3D map of the city buildings aswell as captured signals from all traceable navigationsatellites. This includes weak signals originating fromsatellites with no line of sight (NLOS) with the device.We also address the dual problem - computing a 3D mapof the city buildings when the position of the device isgiven. This is achieved by storing LOS/NLOS rays toall navigation satellites sampled at multiple locationswithin a region of interest (ROI). These rays are thenused to compute the 3D shapes of buildings in the ROI.

A series of field experiments confirm that both algo-rithms are applicative. The position refinement algo-rithm significantly improves the device’s accuracy andthe mapping algorithm allows few users to map a com-plex urban region simply by walking through it.

1 Introduction

Receivers in Global Navigation Satellite Systems(GNSS) such as GPS, GLONASS or GALILEO tend tooutput inaccurate location estimations while operatingin urban regions, mostly due to the density of tall build-ings, which often block a receiver’s line of sight (LOS)to the navigation satellites. Modern GNSS receivers aresensitive enough to receive the indirect signal reflectedfrom the buildings. This multi-path effect is the majorfactor of poor performance of GNSS in urban canyons.A GNSS receiver approximates its position by interpo-lating the signal from each navigation satellite into apseudorange, an approximation of the distance between

∗This research was partially supported by the MAGNET pro-gram of the Israel Ministry of Industry and Trade - RESCUEconsortium (patent pending 61/426,541).†Department of Computer Science, Ariel University Center,

Ariel 40700, Israel. benmo@g.ariel.ac.il‡Department of Computer Science, Ariel University Center,

Ariel 40700, Israel§Department of Computer Science, Ariel University Center,

Ariel 40700, Israel¶Department of Computer Science, Bar-Ilan University,

Ramat-Gan, 52900 Israel

the receiver and the navigation satellite, obtained bymultiplying the speed of light by the time needed forthe signal to travel the distance. Using four pseudor-anges and their associated satellite locations, the GNSSreceiver location can be computed simply by intersect-ing the four spheres (see [2, 4] for more information re-garding GNSS principles). Figure 5 presents an actualpositioning error caused by wrong pseudoranges in anurban region.

In all but rare cases, a rule of thumb, which corre-lates a strong signal to the existence of LOS is provenvery effective. Therefore, a GNSS device operating in anon-urban area would simply sort captured signals ac-cording to their strength, then use four (or more) strongenough signals to compute its location. Since a receiverwandering around at the country-side typically has LOSwith more than four satellites for most of its journey, thedecisive majority of location computations in such ar-eas are typically based on signals originating from LOSsatellites, for which pseudoranges tend to be accurate(the error range is typically within 2-5 meters).

In urban canyons, however, the situation is funda-mentally different. It is very common for a GNSS deviceoperating in an area of this sort (e.g. downtown Man-hattan) to be surrounded by obstacles such as tall build-ings, which block LOS with most, and infrequently all,otherwise available satellites. Since at least four strong-enough signals, equivalent to four LOS satellites, arerequired for accurate positioning, the outcome of a nar-rowly available sky is inevitably a skewed computation,up to the point where the device is unable to performits task.

Prior attempts to address limited LOS in urban areas,all of the while succeed to present reasonably-accurateresults where satellites’ signals are scarce and weak,are mostly based on approaches such as Map Matching(MM) [7, 10, 17, 18] and Dead Reckoning (DR) [4, 13].A certain degree of improvement could arguably be ob-tained by assuming the GNSS receiver is located insidea car, which drives at some estimated speed on top of aroad with a known path. The fact of the matter, how-ever, is that most of these methods are evidently notsufficient in rough urban canyons, where lines of sight(LOS) can and do deteriorate up to the point where a re-ceiver only captures multipath indirect reflections (zeroLOS). In such circumstances, the decisive majority ofGNSS devices become incompetent and cannot improve

23d Canadian Conference on Computational Geometry, 2011

accuracy using these methods.

The novelty of the GNSS−refinement method pre-sented in this paper is based on two core concepts. Thefirst is that unlike existing methods, which mostly relyon information external to the line of sight (LOS) prob-lem, such as vehicle speed and road location, the dis-cussed improvement is confronting the LOS problemin a more direct manner, by applying LOS-based al-gorithms. The second inventive aspect is an effectiveleverage of supposedly-useless weak signals originatingfrom no line of sight (NLOS) satellites. By combiningcaptured signals’ strength with shading algorithms ona region of interest’s 3D map, our improved GNSS de-vice is able to determine with a high degree of assurancein which parts of the region of interest (ROI) it couldpotentially be, and likewise, in which parts of the ROIit is certain not to be, thus significantly narrowing theproblem’s error range.

The above, however, merely segments a ROI into”can-be” and ”cannot-be” partial regions. Therefore, toaddress the general case, in which intersecting the satel-lites’ binary LOS maps yields more than one ”can-be”region, we multiply each binary map with a ”likelihoodweight”. These weights are from a continuous range,where each derives from the captured signal’s strengthof the respective satellite. We later discuss how sum-ming weighted LOS maps for all satellites usually con-verges to a single ”highest likelihood” location. We alsoexplain the heuristics we use in case there are still sev-eral candidate locations subsequent to that summingprocedure.

Figure 1: The Urban Canyon effect: In red, the GPScaptured path. In blue, the actual path.

1.1 Related Work

Prior studies have shown that longer integration timesand data wipe-off enable High Sensitivity GPS (HS-GPS) receivers to acquire and track signals at lower sig-nal strengths [14, 9]. This increases satellite availabilityin weak signal environments, but in an urban canyoncomes with a baggage of positioning errors resultingfrom signal cross-correlation, multipath and echo-onlysignals [14, 8]. Most attempts to improve GNSS de-vices’ accuracy in urban canyons consider the typicalin-vehicle situation. This narrows the estimation prob-lem, since vehicles are generally restricted to travel on

roads. Nevertheless, GNSS and other absolute posi-tioning systems do not inherently locate vehicles ontoroads [12, 15]. The process of coinciding the outputof a sensor such as GPS with a road network map iscalled Map Matching (MM) and is often integratedwith Dead Reckoning (DR), which is the process of es-timating one’s current position based upon a previouslydetermined position [3, 19].

Unfortunately, the problem’s narrowing achieved byMM techniques is not sufficient in complex urbancanyons. This is mainly because limited LOS in suchareas frequently causes initial location estimates thatare off by tens of meters. Such deviations are too largefor MM techniques, which often leads to placementsonto wrong distant roads.

In this paper we demonstrate how 3D maps of anarea can be leveraged to acquire more information outof captured (both LOS and NLOS) GNSS signals. Thisadditional information can then be used in conjunctionwith existing MM techniques, or as an alternative tosuch methods. Moreover, the concepts employed to nar-row the estimation problem also form the basis of ouralgorithm for the dual 3D modeling problem (see section3).

1.2 Paper Structure

Following an introduction and a related work review,we turn to a detailed discussion of the GNSS refinementalgorithm. We then present a framework algorithm tothe dual (inverse) problem, namely the computing of thecity buildings’ 3D maps by capturing the signal strengthof all navigation satellites. Subsequently, we put thepresented algorithms to the test and discuss results fromfield experiments conducted in rough urban canyons.We conclude with suggested future work.

2 GNSS Refinement Algorithm

2.1 Overview and Definitions

In this section we present the main algorithm for im-proving the GNSS receiver’s accuracy in urban canyons.The algorithm transforms the signal strength of eachtraceable navigation satellite into a LOS/NLOS value.This value is not boolean but a continuous value in therange of [0, 1], representing the LOS clearance.

The algorithm’s detailed description begins with for-malization of (i) input parameters available from theGNSS device; (ii) some pre-defined constants (thresh-olds) and (iii) functions and data structures usedthroughout the refinement process (see Table 1). Wethen describe the mechanism by which the algorithm de-termines LOS status with each satellite. Subsequently,we explain the concepts behind LOS/NLOS partial

CCCG 2011, Toronto ON, August 10–12, 2011

maps and discuss the formation of an aggregated like-lihood map out of them. We conclude the section witha high-level pseudo-code, which encapsulates the entirealgorithm.

GNSS Algorithm Definitions

DeviceDeviceOutput : The current non-refined locationestimation, position error range, and the set(S(t)) of all traceable satellite signals.LastPosition: The last recorded refined loca-tion, and the corresponding error ratio and con-fidence level.

ConstantsSigBench: A signal-strength threshold, whichdetermines visibility (assume LOS if higher;NLOS if lower).MaxSig: A surely visible signal-strength thresh-old (used for linear transformation to [0,1]range).MinorErr : An error estimation threshold (don’tcorrect if smaller).

Functions

S(t) = S1...Sn: The set of all satellite signals ascaptured by the GNSS receiver in time t.Sv(t) ⊂ S(t): The set of visible satellites (subsetof S(t) obtained using SigBench).Su(t) ⊂ S(t): The set of invisible satellites (sub-set of S(t) obtained using SigBench).Map: A 2.5D representation of the terrain - in-cluding both earth surface and buildings on topof it.ROI : The region of interest; a minimal polygonwhich contains both: (i) all buildings which mayaffect the user.(ii) all possible locations in whichthe user could potentially be.LOS(Si, ROI): A binary shading function fromeach point of the ROI to a LOS,NLOS w.r.t.Si location.SIG(Si, ROI,Wi): A refinement of LOS(Si,ROI) to a continuous range using a signalstrength (Wi ∈ [0, 1]) weight.Approximate: The proposed GNSS refinementalgorithm (i) Creates an aggregated likelihoodmap from all SIG(Si,ROI,Wi) (ii) Picks mostlikely location with respect to the parametersDeviceOutput and LastPosition.Aggregated : An aggregation ad-hoc 2D matrixwith ROI ’s boundaries.

Table 1: Formal definitions of parameters used through-out the proposed GNSS refinement algorithm.

2.2 Approximating Satellites’ LOS Status

The strength of a signal as captured by GNSS-receiverdepends on several factors ([5]):

• Global parameters: transmission frequency, trans-mission power - these parameters are mostly fixed.

• Position and time: atmosphere and ionosphere con-dition, the angle between the satellite and the re-ceiver.

• LOS and multi-path status: the nature of propa-gate signal with respect to the possible ”radio path”to the receiver [16, 5, 6].

For a given GNSS (e.g. GPS L1, L2), the global pa-rameters are fixed. The position and time parameterscan be approximated within a small error range, usu-ally smaller then 5 dB. The typical LOS signal strengthis at least 10dB stronger than the signal strength ofa reflected signal (NLOS). It is therefore rather sim-ple to classify captured signals into Sv(t)(LOS) andSu(t)(NLOS) subsets. Moreover, the field experimentswe conducted (see section 4) demonstrate that deter-mining a signal’s LOS/NLOS status is applicable evenin highly complex urban regions.

2.3 Partial LOS Map

Computing a shading map of a city building map (ROI)w.r.t. a satellite position can be done by projecting thebuildings on the surface (the satellite position can bethought as in infinity). Our implementation encapsu-lates the LOS map of each captured signal Si in S(t) asa 2D matrix filled with (0 and 1) binary values, each in-dicating whether the receiver is likely to have LOS withthe corresponding satellite within a one square meterspot. The computation of the map’s values is a rela-tively straightforward shading algorithm, which makesuse of the satellite’s position and the 2.5D Map of thearea.

A fundamental, somewhat tricky, feature of the pro-posed algorithm concerns the leverage of weak multi-path signals captured by the receiver to obtain meaning-ful information. A weak captured signal almost alwaysindicates the absence of LOS with the respective satel-lite and is therefore classified (using SigBench) into thesubset of invisible satellites Su(t). Knowing the receivercannot see the satellite from its current location, we canconclude it is certainly not positioned in spots wherethis satellite can be seen. Derives from this observa-tion is the applicability of using the complementary LOSmaps (switching 1 and 0 values) of invisible satellites be-longing to the subset Su(t) as likelihood layers, whichare as informative as likelihood layers generated fromvisible satellite signals belonging to the Sv(t) subset.Furthermore, since the discussed algorithm is targetedat urban canyons scenarios where LOS may deteriorateeven to an empty Sv(t) subset (all captured signals areweak), the complementary LOS maps of invisible satel-lites belonging to Su(t) become an essential source ofinformation for the formation of the aggregated likeli-hood map discussed below.

2.4 Likelihood Weights

Likelihood weightening is a mechanism employed by thealgorithm to improve determinism. In the absence ofweights, which transform a LOS map from a binaryLOS/NLOS representation into a more refined likeli-hood map, the algorithm could very well narrow the

23d Canadian Conference on Computational Geometry, 2011

problem by segmenting the ROI into ”can be” and”cannot be” regions, but would not be able to resolvea scenario of multiple ”can be” spots, and pick a singlelocation to be presented on the GNSS device’s screen.By introducing signal-strength derived weights, the LOSmaps become differentiated from one another (each mapis multiplied by a weight from a continuous range).This, in turn, results in (i) a further segmented ag-gregated likelihood map, which serves the algorithm’spurpose of picking a single spot ; (ii) improved accu-racy and reliability, since greater importance is grantedto stronger signals.

2.5 Aggregated Likelihood Map

The likelihood map is implemented as a 2D matrix filledwith real numbers, each representing the likelihood ofthe receiver to be located within a location (e.g., within1 square meter). The matrix is constructed by (a) mul-tiplying each partial LOS matrix with a weight, whichsignifies the signal’s strength of the corresponding satel-lite and (b) summing all partial weighted matrices. Theoutcome of this matrix addition is a single 2D matrix,where each point represents a likelihood, and the ma-trix’s highest value(s) is the most likely spot. Sincethis likelihood matrix is being constructed by summinga considerable number (roughly 8 to 18) of partial (al-ready differentiated by weights) matrices, the max valueof the matrix tends to have a relatively small number ofappearances. In the empirically common case of a sin-gle unique max value, the algorithm concludes and thespot represented by that max value is being presented.Otherwise, if several max values are encountered, thealgorithm’s Approximate function is employing heuris-tic methods (e.g. nearest point to the non-intervenedreceiver’s output - DeviceOutput) to choose the pointto be presented.

Figure 2: Construction of a likelihood map from LOSmaps. In this example there are three satellites (S1 −S3) and four points (p1 − p4), p1 and p4 have the sameaggregated shading maps (they both can see S1, andS2). Yet p2 and p3 aggregated shading maps differ fromthe aggregated shading map of p1 (or p4).

2.6 Algorithm Formalization

Using the definitions at the beginning of this section (seeTable 1), the refinement algorithm’s high-level pseudo-

code would be:

Algorithm 1: High-Level pseudo-code for GNSS re-finement algorithm

Result: RefinedPositionif PositionError < MinorErr then

return DevicePosition;

Let S(t) be the set of all satellite signals ascaptured by the GNSS receiver in time t.Let Aggregated be a 2D matrix with ROI ’sboundaries (initialized with 0 values).for each Si in S(t) do

Use SigBench to determine whether Si ∈ Sv orSi ∈ Su.Let Wi be Si’s signal strength weight 1

Li ← SIG(Si, ROI,Wi)2

if Si ∈ Su thenInverse Li

3

Aggregated← Aggregated + Li4

Let LikelyPoints be the set of max values inAggregated.Refined Position = Nearest point in LikelyPointsto DevicePosition.return Refined Position.

1Wi is transformed into [0, 1] range using MaxSig constant.2Compute partial weighted map.3For an NLOS satellite : x = (1− x) to each x in the matrix.4Add partial weighted map to aggregated likelihood map.

3 3D Mapping Algorithm

3.1 Overview

In this section we address the problem of constructing a3D building map using the strength of the signals fromnavigation satellites. This task is the dual problem tothe improved accuracy: instead of using the 3D build-ings’ map to improve the receiver’s position, we use itsposition to approximate the buildings’ 3D map.

Most GNSS devices are able to keep detailed logfiles, which contain information about captured satel-lites’ signals along a device’s journey. Thereafter, it isa straightforward process to track down a device’s pathand the satellites’ position respective to that device ateach point in time during the journey (in sampling rateof 1-10Hz). This ability to track down signals, whenmagnified by a number of GNSS devices covering a sub-jected urban canyon, is a preliminary enabler of ournovel framework algorithm to the dual problem, whichis the generation of buildings’ 3D models out of capturedsatellites signals.

The 3D mapping problem can be defined as follows:given a GNSS log-file, which contains samples of: time,

CCCG 2011, Toronto ON, August 10–12, 2011

position, accuracy and the signal strength to each trace-able satellite, convert the log file into two sets of 3Dvectors: (i) Blue vectors: all LOS signals. (ii) Red vec-tors: all the NLOS signals. The goal is to construct thesurface, which will block all the vectors in the red setand will not block the vectors from the blue set.

3.2 2.5D Mapping Heuristics

We limit this algorithm to compute a 2.5D map repre-sentation, a surface of a terrain representation in whicheach (X,Y ) location has a single Z value associated withit. For simplicity, we divide the mapping algorithm intotwo sequential steps: (i) computing the buildings’ con-tours. (ii) approximating the height of each contour.

For the algorithm’s first step we traverse time-consecutive samples of the satellite signals. We thencompute distances between consecutive samples, using aweighted xor function (assuming LOS is 1 and NLOS is0), a change in satellite status (LOS/NLOS) contributesto the distance function according to the satellite angle(high-angle satellites contribute more). If the distanceis above some threshold, we consider this point to bean edge-point. Edge-points tend to appear in buildings’corners and next to buildings’ walls (due to the ampli-fying distance of high-angle satellites). We then filterout edge-points with potential high position error, andaggregate all the relatively accurate edge-points. Lastly,we compute contours which are bounded by the edge-points. These contours may be general polygons or someconstraint shapes (see Figure 6).

The algorithm’s second step computes the z-valueof each contour. The height value of each contour isbounded by all the LOS rays going over it. Yet becausethe LOS/NLOS data is ”noisy” by nature, the actualz-value is computed as the height for which maximalweighted-constraints (LOS/NLOS) are satisfied. As inthe first stage, the higher the ray-angle is (LOS/NLOS)the larger its weight becomes. Noteworthy is that sam-ples from the same spot taken at different times of theday are beneficial for the algorithm. This is becausefor each triplet (spot, building, satellite) if there’s a(time dependent) LOS ray from the spot to the satel-lite, which goes over the building’s contour, then thereexists a time of the day, which minimizes the verticaldistance between that ray and the building’s roof.

During our initial field experiments, the contours ofthe builds were slightly larger and shorter than in real-ity. In order to fix this effect we modified the algorithmto keep refining the 2.5D map by updating the contoursaccording to the building approximated height.

4 Experimental Results

We conducted a set of preliminary experiments to eval-uate the suggested algorithms in practice. In order to

Figure 3: 3D mapping algorithm in action. In red arethe rays which are blocked (NLOS), in blue are the rayswith LOS to the corresponding navigation satellites.

evaluate the improved accuracy algorithm two types ofexperiments were conducted (see Figures 3-5): (i) lo-cating a GPS receiver in a fixed position for few hours(at each position). (ii) walking along a fixed route. Inboth experiments the actual position was compared tothe suggested location of both (a) the GPS device (b)the refinement algorithm. In order to evaluate the 2.5Dmapping algorithm we have walked through the uni-versity campus and computed the approximated build-ing map. The algorithm was implemented in Java andtested on both Android and Linux. The algorithm wasable to refine the location (in an area of 200*200 meters)in less than 1 second, which validated its applicability torun efficiently on mobile devices (equipped with a 1HzGPS). The following GPS receivers were used: Fastrax1Hz, Wintec G-Rays 10Hz and the internal GPS of theAndroid devices. All tests were made while walking.The GPS row data was accessed via the NMEA proto-col.

Figure 4: Improved position algorithm in action: Inboth above examples the GPS suggested a position with12-18 meters error ratio. The refinement algorithm wasable to fix the position to an error of less than 1 meter.

Figure 5: Improved Position: Left: above view. Right:3D perspective view. In red, the path computed by a1Hz fastrax GPS with an average error of 31 meters andmax error of 180 meters; In green, the refined positionwith an average error of 4 meters and max error of 11meters; In yellow, the actual path.

23d Canadian Conference on Computational Geometry, 2011

Figure 6: 2.5D mapping example, Left: the actualbuildings, Middle: the 2.5D map of the buildings us-ing axis parallel rectangles contours. Right: the 2.5Dmap of the buildings with no contour constraints

5 Conclusion and Future Work

We have proposed a new framework for improving aGNSS-receiver accuracy in urban regions. We havealso presented an algorithm for constructing a 2.5Dbuilding map - using the receiver’s position and theLOS status to it from each navigation satellite. Inpractical implementations, both algorithms could berunning together - improved position accuracy assistsin improving the 2.5D map accuracy, which in turnfurther improves positioning accuracy. Such approachfor Simultaneous Localization And Mapping (SLAM)is proven to be an efficient method in many navigationand mapping tasks [1, 11]. The experimental resultspresented above show that even a basic implementationof the algorithms helps improving the GNSS accuracysignificantly in urban canyons. Using few walkingclients equipped with standard GPS devices we wereable to construct a 2.5D buildings map of a complexdowntown area; this map was then sufficient as theinput source for the accuracy improvement algorithm.For future work we intend to use GNSS-pseudorangesto compute a more accurate map of the buildings.In particular, we would like to generalize the 2.5Dmapping algorithm into a real 3D mapping method.

Acknowledgment The authors wish to thank EliyahuAriel and Prof. Avner Kidar for introducing us to thereal world of GPS.

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