Cooperative Navigation between a GroundVehicle and an Unmanned Aerial Vehicle in

GNSS-Challenged Environments

Victor O. Sivaneri, Jason N. Gross, West Virginia University

ABSTRACTThis paper considers cooperative navigation between a Un-manned Aerial Vehicle (UAV) in a GNSS-challenged en-vironment with an Unmanned Ground Vehicle (UGV), andfocuses on the design of the optimal motion of the UGV tobest assist the UAV’s navigation solution. Our approach re-duces the uncertainty of a UAV’s navigation solution throughthe use of radio ranging updates from a cooperative UGV.In this study, we develop and compare two novel methodsfor designing a UGV’s trajectory such that the UAV’s dilu-tion of precision is reduced. To conduct this study, a simu-lation environment is used to characterize the performanceof the cooperative navigation between a UAV and a UGV.The study is conducted to evaluate the positioning accuracyduring common GNSS-challenged scenarios such as: a ve-hicle in an urban environment and flying against a build-ing. Using an Ultra Wideband (UWB) radio, the UAV in aGNSS-challenged environment, an urban canyon, is able todetermine it’s position with the support of a UGV. The useof a UGV and moving it based on the reduction of dilutionof precision, has shown to decrease the position error of theUAV.

1 INTRODUCTIONCollaborative navigation is a research area that has beenincreasingly active in recent years, especially in supportof military operations and Intelligent Transportation Sys-tems (ITS) (Stromback et al., 2010). This is due to the factthat these environments are oftentimes GNSS-challenged.In military situations, UAVs or UGVs, may go from situa-tions where GNSS is readily available to completely denied(e.g., being jammed or traversing inside a cave). The majordownside of GNSS is that it requires an open-sky (Kealyet al., 2015). In military operations, sub-meter level accu-racy and high update rates (e.g., > 10 Hz) are needed, andthis is not always possible with standalone GNSS (Zadoret al., 2000). In the context of ITS, urban canyons oftenlead to extreme multipath and GNSS outages, which cancause positioning errors as large as a few hundred meters(Ko et al., 2015). These scenarios are a few of the better-

known cases when cooperative navigation would be bene-ficial. Other cases include, UAVs for bridge inspection orstructural health monitoring (Guo et al., 2011), UAVs forsurveillance in urban environments (Alam et al., 2013), orUAVs transitioning from indoor-to-outdoor or vice versa (Ser-ranoa et al., 2014).

To improve the positioning solution, multi-sensor in-tegration has to be considered. As discussed in Tittertonand Weston (2005), a number of techniques have been in-troduced to combat the issues in GNSS-challenged condi-tions, such as Inertial Navigation Systems (INS) and odome-ters; but it is well known that these sensors diverge rapidlyover time and will not be able to handle long GNSS outagesand multipath.

Collaborative positioning techniques, such as usinglocal measurements between vehicles or nodes, have helpedtackle this problem. Collaborative navigation uses manysensors to aid in navigating when GNSS is degraded ornot available. These sensors include Inertial MeasurementUnits (IMU), inter-nodal raging, lasers, cameras, magne-tometers, and various other aides. Many collaborative nav-igation techniques focus on the use of Vehicle Ad-Hoc Net-works (VANETs), where multi-sensor fusion is used onindividual nodes, and the collaboration between nodes isopportunistic in nature. Most of the collaborative naviga-tion communication is with Dedicated Short Range Com-munications (DSRC) for vehicle-to-vehicle and vehicle-to-infrastructure communication (Kealy et al., 2015).

The typical approaches used in DSRC are Angle ofArrival (AoA) and Time of Arrival (ToA). The AoA posi-tioning technique measures the angle between the referencenodes and the target nodes. ToA, used for Ultra WideBand(UWB) radios, rely on the travel time of the measurementfrom the reference node to the target nodes (Gezici et al.,2005). An advantage of using UWB signals is they havebeen shown to work in non-LOS application, can penetratewalls, and are not significantly impacted by multipath (Gaoet al., 2014). Another benefit using the UWB radios, aretheir weight and cost.

Kassas and Humphreys (2013) used signal of oppor-

tunities, radio signals, to draw navigation and timing in-formation. The authors found that adopting a information-based optimal motion planning performed better than hav-ing a pre-described path. The optimal motion planningevaluated different actions that the receiver could take, thenmove to a location that would maximize the informationabout the environment. The use of an cooperative navi-gation algorithm to navigate vehicles through a field withobstacles, has been seen in Ferrari et al. (2011). In thiscase, the UAV provides a low resolution map to the UGV,so it can plan it’s movements based on the objects ahead.However, this requires the UGV to be in the field of viewof the UAV which does not help in urban canyons, as theGNSS information would be the same for both vehicles.

Using peer-to-peer updates for positioning is not new,as there is plenty of research that has been conducted onstationary nodes (Bais and Morgan, 2012) (Kealy et al.,2015) and on moving nodes (Gao et al., 2014) (Parker andValaee, 2007) (Kassas and Humphreys, 2013). For exam-ple, Bais and Morgan (2012) evaluated the best position forplacing base stations, to have the area covered by 4 basestations at all times. Gao et al. (2014) investigated usingUWBs on a vehicle-to-vehicle platform, where the vehi-cles exchanged their position with each other. Hardy et al.(2016) and Strader et al. (2016) focused on the design andevaluation of an estimation strategy for determining the rel-ative pose of the aircraft, between UAVs in a GPS-deniedenvironment. On the contrary, there has been less of anemphasis on the control or design for the location of thecooperative navigation nodes.

In this paper, the use of cooperative navigation is in-vestigated between a UGV and a UAV, in which a DSRCconsisting of a UWB radio, is used to provide range mea-surements between the two vehicles and the UGV is strate-gically moved in order to reduce the Position Dilution ofPrecision (PDOP) of the UAV. PDOP was chosen as ourbasis for designing the UGVs trajectory because it well-known that the PDOP is essential in determining the accu-racy of a positioning system (Misra and Enge, 2006). Inthis setting, the following is taken advantage of: (1) theUGV has a non-degraded GNSS solution, (2) a single UGVacting as a ranging source is able yield a wide range of unitvectors with respect to the location of a UAV, and (3) aUGV is naturally positioned to improve a UAV’s solutiongeometric as it emanates its ranging signal from a directionthat a GNSS transmitter cannot. By leveraging these char-acteristics, this cooperative navigation algorithm yields in-creased accuracy of the positioning of the UAV faced withGNSS-challenged conditions.

The rest of this paper is organized as follows. Sec-tion 2 motivates our cooperative approach by assessing theeffectiveness of a single ranging sources ability to reducePDOP when given the freedom of the transmitter location.Section 3 describes the algorithm formulation of the coop-erative navigation for both without the UGV and with the

UGV. Next, Sections 4 and 5 presents the results of a seriesof simulations. Finally, Section 6 discusses the conclusionof the study and future planned experimental work.

2 CONCEPT OVERVIEWFigure 1 shows the assumed set-up for the cooperative navi-gation in an urban canyon. The UAV is in a GNSS-challengedenvironment (e.g. under forest cover, urban canyon, bridgeinspection). It is furthered assumed that the cooperativevehicle is not GNSS-challenged. A UGV is initially be-ing assumed as the cooperative vehicle, but the technologybeing discussed herein is not restricted to use on a UGV.This only simplifies the ability to realize an experimentaldemonstration.

2.1 Review of PDOPDilution of Precision (DOP) provides a simple character-ization of the user-satellite geometry. The better the ge-ometry, the lower the DOP, the better the position esti-mate. Starting from the Linear Least Squares (LLS) GNSS-solution,

∆x = (GT G)−1GT∆ρ (1)

where G is the “Geometry Matrix”. The pseudorange mea-surement model is given by the equation

ρkC = rk + cδtu + ε

kρ (2)

where rk is the geometric range from satellite k to the user,c is the speed of light, δtu is the receiver clock bias, and εk

ρ

is the measurement residuals, where it is assumed that themeasurement residuals are zero-mean E[ερ], and the vari-ance of the error is given by

E[ερεTρ ] = Pε = σ

2UREI (3)

where σURE is the standard deviation of the “User RangeError” and is provided by the GPS control segment. Usingthe LLS solution, the clock bias estimation, and the zero-mean assumption, the estimation covariance matrix can beformed

cov[∆x] = σ2URE(G

T G)−1 = σ2UREH (4)

where G is the Geometry Matrix and ρ is the pseudorangemeasurement. The Geometry Matrix is constructed by cre-ating a set of unit vectors, of the distance between the satel-lites and the UAV position. Within this study, the Geome-try Matrix is augmented by the UWB measurement fromthe UGV, which effectively acts as another satellite obser-vation.

where HDOP is formed as shown in Eq. 5

HDOP = (GT G)−1 = diag[H11, H22, H33, H44

](5)

The Root Mean Square (RMS) of the 3D position is knownas the Position Dilution of Precision (PDOP),

PDOP =

√HDOP

11 +HDOP22 +HDOP

33 (6)

Figure 1. Concept Diagram for Cooperative Navigation with UWB Ranging between a UAV and UGV

2.2 Reducing PDOP with a Single Ranging Source

To motivate the potential of this approach, a simple Monte-Carlo simulation was conducted to determine the maximumamount of PDOP reduction that could be realized by the ad-dition of a single ranging source, for different GNSS satel-lite geometries. That is, the location of the simulated userlocation and the GNSS time of week was randomized inorder to realize a large number of constellation geometriesfor a given scenario. Next, to simulate a GNSS-challengedcondition, high azimuth and elevation masks were appliedto simulate a user’s GNSS visibility being impacted. Asa single example, Figure 2 shows the percentage of PDOPreduction that could occur, with the inclusion of a UWBranging source located in the best position within a 25 msquare grid surrounding the UAV’s location, as a functionof the GNSS-only PDOP.

In Figure 2, a 180 degree azimuthal mask and 50 de-gree elevation mask was used to simulate a UAV up againsta tall building. From this analysis, it is apparent that thepoorer the satellite geometry, the more beneficial the sin-gle ranging source can become. For example, the PDOPcan reduced by 90 % when the initial PDOP is 10 (i.e. thePDOP can be reduced to as low as 1). However, the min-imum potential PDOP reduction is also shown to motivatethe fact that the cooperative ranging source must be strate-gically placed. That is, the additional ranging source couldoffer little or no benefit if poorly located.

Figure 2. Monte Carlo simulation result that illustrates the poten-tial improvement of including a single additional rang-ing source that is optimally placed.

3 ALGORITHM FORMULATION

This section gives an overview of the formulations used inthis paper. First an overview of the GNSS/INS filter de-sign is discussed, then how the UWB is implemented in theGNSS/INS filter, and finally the cooperative strategy, lo-cally greedy and regionally optimal, used for the UGV andthe UAV.

3.1 Core GNSS/INS Filter DesignThe GNSS/INS integration filter adopted uses INS error-state formulation with closed-loop feedback, which cor-rects the integrated INS solution at each time step. The INSestimated navigation states are used to predict the GNSS-observable within the EKF. The estimated state vector is,

x =

δΨ

δvδrbabgδtuδtuTwN1...

N j

(7)

where δΨ is the INS attitude error, δv is the INS velocityerror, δr is the INS position error, ba is the Inertial Mea-surement Unit (IMU) tri-axial accelerometer sensor biases,bg is the (IMU) tri-axial gyroscope sensor biases, δtu is theestimated receiver clock bias, δtu is the estimated receiverclock drift, Tw is the estimated troposphere, and N1.. j is theestimated phase bias for each satellite in view. For the at-titude update, a 3rd order fixed-step Runge-Kutta integra-tion method was used for the integration of the quaternion,which represents the UAV’s body attitude in the Earth Cen-tered Inertial (ECI) frame (Jekeli, 2001). For this study,an error-state Kalman Filter is being used, where the for-mulation for the position, attitude, and velocity equationsare from Groves (2013). For the complete details of theGNSS/INS formulation adopted, the reader is referred to(Gross et al., 2015) and (Watson et al., 2016).

3.2 GNSS/INS Augmentation with UWB RangesThe GNSS observation matrix, Hobs, is dependent on thenumber of satellites in view, and the number of states es-timated, as shown above in the state vector Eq. 7, whichis 18. It represents the sensitivity of the observed mea-surement models to the state being estimated. The first 6columns of Hobs correspond to, the INS attitude and veloc-ity errors and are zero as they do not appear in the GNSSpseudorange and carrier-phase observation models. Thenext 3 columns of Hobs are the partials of user’s ECI po-sition. Columns 10-15 of Hobs are the partials of the IMUsensors biases which are modeled with random-walk dy-namics and therefore zero, and column 16 is the partialderivative of the GNSS receiver clock bias. In this study, noGNSS receiver clock drift is estimated, therefore clock driftpartial is zero. The troposphere’s zenith delay partials arecomprised of the elevation dependent mapping function,and appear in column 18 of Hobs. The rest of the columnsare populated with an identity matrix over the block of rowsthat correspond to the carrier-phase observations. This iden-

tity matrix represents the partial derivative of the carrier-phase observational model with respect to the carrier-phasebiases. This is the Hobs matrix when the UGV is not beingused. The size of the Hobs matrix is shown in Eq. 8

Hobs = [2∗S , N +S] (8)

where S is the number of GNSS satellites in view and N isthe number of non phase-bias states estimated. When theUGV is employed, Hobs only slightly differs. The UGV isconsidered as an additional GNSS satellite measurement,but this measurement only has partial for the position as itdoes not have a receiver clock bias, troposphere delay, or acarrier-phase bias.

Hobs =

01x6 uX uY uZ 01x6 1 0 Mel 0nxn

......

......

......

......

01x6 uX uY uZ 01x6 1 0 Mel Inxn...

......

......

......

...01x6 uwbX uwbY uwbZ 01x6 0 0 0 01xn

(9)

where n is the number of satellites in view. The UWBrange, distance between the UAV and UGV, is implementedas an observation in the zk vector and is shown in Eq. 10.

yuwb = ||posUAV − posUGV ||2 (10)

To include the UWB ranging source, the UWB range mustbe predicted for inclusion in the filter. Then the differencebetween the UWB predicted range and the UWB measuredrange was inserted at the end of the zk vector.

zk =

∆ρ1...

∆ρN∆Φ1

...∆ΦN

∆UWB

(11)

where ∆ρ is the Observed Minus Computed (OMC) pseu-dorange of the satellites in view, ∆Φ is the OMC carrierphase of the satellites in view, and the ∆UWB is OMCUWB range, where the computed is the distance betweenthe UAV and UGV.

A simple UWB error model was parameterized byempirically modeling the UWB ranging errors with twoTime Domain P410 Ranging and Communication RadioModules (RCM). These tests consisted of both line-of-sight(LoS) and non-line-of-sight (NLoS). The following Figures3, 4, and 5 show one of the test set-ups, the correspondingerror history, and the histogram, respectively.

The mean and standard deviation of the error were6140 mm and 28 mm, respectively. In the filter, a normaldistribution of 5 cm was added to the UWB measurementas a conservative bound of the empirically estimated distri-bution.

Figure 3. Set up for short range Non Line of Sight (NLoS) rang-ing testing.

Figure 4. Time history of ranging errors for short range NLOS.

3.3 Cooperative StrategyThe two strategies that were evaluated included: (1) hav-ing the UGV choose the minimum PDOP, of the UAV, ifit were to select from points immediately around the UGV,and (2) having the UGV calculate the minimum PDOP, ofthe UAV, it it were to be located anywhere within a 50 me-ter by 50 meter grid centered at the UAV, then moving inthe regionally optimal direction. For both approaches, themaximum distance that the UGV is assumed to move overone GNSS measurement updated interval is 1 meter.

Figure 5. Distribution of ranging errors for short range NLOS.

3.3.1 Locally Greedy Strategy

In this approach, first the UAV captures the signals from allavailable GNSS satellites to calculate is position solution.After the UAV communicates the satellites it has in view,the UGV determines which location it should move, Eq.12, in order to reduce the PDOP. This is accomplished bythe UGV calculating what the UAV’s PDOP would becomewhen incorporating a UWB ranging update from each ofthe UGV’s candidate locations. With the Locally Greedyapproach, the list of candidate position includes of all po-sitions immediately surrounding the UGV. The number ofpositions evaluated that encircle the UGV was set to 10.

To implement this approach, 10 candidate UGV head-ing angles, Ψ`=1:10 =

[0, . . . ,2π

], were selected and

candidate positions were calculated using Eq. 12.

rUGV,ENU`

k+1 =

rUGV,Ek +d ∗ cos(Ψ`)

rUGV,Nk +d ∗ sin(Ψ`)

0

(12)

where rUGV,ENU`

k+1 is the UGV’s candidate location for head-ing angle Ψ`, rUGV,E

k is the UGV’s current East position,rUGV,N

k is the UGV’s current North position, d is the movedistance of the UGV, Ψ` is the candidate heading loca-tion around the rover that is being evaluated. With eachcandidate UGV location, the UAV’s GNSS-only GeometryMatrix, G, is augmented using unit vector to the candidateUGV position and current best estimate of the UAV’s posi-tion

uuwb =rUAV

k − rUGV,ENU`

k+1

||rUAVk − rUGV,ENU`

k+1 ||2(13)

where the uuwb is the unit vector distance between the UAVand the candidate UGV position. With the set of UAV Ge-ometry matrices augmented with each UGV candidate lo-cation, the PDOP for each candidate 1 to ` is evaluated, and

the minimum PDOP is selected as indicated in Eq. 14.

minPDOP = argmin(PDOP1 ... PDOPN) (14)

Once the minimum potential PDOP of the UAV is identi-fied, the UGV is moved to the location that corresponds tothe minimum UAV PDOP. Additional UGV path planninglogic was also included to ensure that it does not get tooclose to the UAV. This is to ensure that the UGV doesn’talso enter the GNSS-challenged environment. For the timebeing, this is implemented as a simple perimeter of radius70 meters was set around the UAV’s best known locationand established a no-UGV-zone. As such, if the UGV’snext desired trajectory position falls inside the perimeter,the following steps are taken. First, the slope of the dis-tance between the UAV and UGV is found using Eq. 15.

m =∆rN

∆rE(15)

where m is the slope, ∆rN is the North component of thedistance between the UAV and UGV, and ∆rE is the Eastcomponent of the distance between the UAV and UGV.Next, the intersection of the perimeter and the UGV, is de-termined, based on the slope and the equation for a circleas shown in Eq. 16 and 17 .

rUGV,Ek+1 = sign(rUGV,E

k )

√r2

perim

(m2 +1)(16)

rUGV,Nk+1 = mrUGV,N

k (17)

where rUGV,Ek+1 is the UGV’s next East position, rperim is the

radius of the perimeter, and rUGV,Nk+1 is the UGV’s next North

position. In Eq. 16, the sign operator is to ensure roveris located in the proper quadrant of the circle. For futuredevelopment of this approach, a prior map information willbe included in this part of the trajectory design for selectionof the perimeter.

3.3.2 Regionally Optimal Strategy

For the regionally optimal cooperative UGV path planningstrategy, a 50 meter by 50 meter grid is setup with theUAV at the center. Then, UWB-augmented-PDOP fromincluding a ranging observation that is emanating from ev-ery point on the grid is computed. As an example of thisapproach, Figure 6 shows the percentage reduction possi-ble for the 50 meter by 50 meter grid at one time step, forone simulation scenario. The yellow represents a regionin which a 60 % percentage reduction is achievable. Afterevaluating this grid, the minimum overall PDOP is deter-mined as seen in Eq. 18.

minPDOPgrid = argmin(PDOP1grid ... PDOPNgrid)(18)

Once the east and north location of where the PDOP is min-imum is found, the UGV is driven in that direction. This is

Figure 6. Regional optimal strategy using a grid to calculate min-imum augmented-PDOP

Figure 7. Diagram of heading calculation between two UGV lo-cations.

accomplished by first determining the distance between thecurrent UGV position and the location where the PDOP ofthe UAV is minimum over the grid as shown in Eq. 19 and20.

∆rUGV,E = rUGV,Ek −EGrid

PDOPmin (19)

∆rUGV,N = rUGV,Nk −NGrid

PDOPmin (20)

where E,NGridPDOPmin is the location where the PDOP would

be minimized for the rover location within the grid. Fromhere, the heading angle, Ψ, is found to determine whichdirection the UGV should move, as seen in Figure 7. Theheading was calculated by Eq. 21.

Ψ = atan2(∆rUGV,N ,∆rUGV,E) (21)

Since there is a constraint that the UGV can only move amaximum of 1 meter per time step, the next UGV locationis determined based on the move distance and the heading,Eq. 22 and 23.

rUGV,Ek+1 = rUGV,E

k +d ∗ cos(Ψ) (22)

Ground Vehicle Path for Locally Greedy and Regionally Optimal

-150-100-50East (meters)

050100150

30

0

5

10

15

20

25

100

0

-100

Nort

h (

mete

rs)

Locally Greedy Path

Quadcopter Path

Start

end

Regionally Optimal Path

Figure 8. Example of locally greedy and regionally optimal pathin a GNSS-challenged environment

rUGV,Nk+1 = rUGV,N

k +d ∗ sin(Ψ) (23)

where d is the maximum move distance of the UGV and Ψ

is the heading angles. As stated above, there is a check inplace to make sure the UGV does not come too close to theUAV. If it does, the same procedure described in Section3.3.1.

4 SIMULATION ENVIRONMENTThe raw GNSS and IMU data used in the simulation wasgenerated using a commercially available SatNav-3.04 andInertial–Navigation Toolboxes (GPSoft 2003), which is aGNSS constellation simulation toolbox. Inputs that weredefined for the generation of GPS and IMU data, were theorigin in Latitude, Longitude, and Height, the time of theweek, and the length of the flight. These inputs were se-lected at random, giving each case different satellite geom-etry and atmospheric effects. For more information on thegeneration of data, please refer to (Watson et al., 2016) fora more detailed description.

The particular error source important to this studywas GNSS multipath errors. As such, for this work themultipath error was increased to simulate the GNSS- chal-lenged environment of an urban-canyon. Multipath wasmodeled as a first order Guass-Markov error source andwith a σ =8 meters and a time constant, τ of 2 minutes.Furthermore, to simulate a GNSS-challenged environment,an elevation and azimuth mask, i.e. buildings in an urbancanyon, was incorporated as seen in Figure 8. The maskswere held constant throughout the simulated flight, and forall data sets. This simulation also included an orbit er-ror model to represent the errors in the GNSS broadcastephemeris. The satellite ephemeris errors were modeled bydifferencing the broadcast products provided by the Inter-national GNSS Service (IGS) and the Center for Orbit De-termination (CODE). A multi-sinusoidal model was fitted

No UGV UGV Locally Greedy UGV Regionally Optimal

Po

sitio

n E

rro

r (m

ete

rs)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5Average RMS of Position Error of 10 Data Sets

East

North

Vertical

Figure 9. Average RMS of 10 data sets

to the error, and based on the time of day. More informationcan be found in Watson et al. (2016). The UAV and UGVwere assumed to start at arbitrary positions. Within thisstudy Monte-Carlo design was implemented and 10 datasets were generated.

5 RESULTSThe generated data sets were run through the GNSS/INSfilter with and without augmentation from the UGV in or-der to characterize the performance of including a coopera-tive UGV. Next, both cooperative strategies were attemptedsuch that any differences between the two different approacheswould become apparent. In Figure 9, the first graph showsthe GPS position error when having a UGV employing thelocally greedy cooperative strategy, the second is when theUGV is using the regionally optimal strategy, and the lastone is without having a UGV. Table 1 shows the averageRMS values for the East, North, and Vertical position er-ror. It can be seen that having a UGV employing the locallygreedy strategy is better than having no UGV, and having aUGV employing the regionally optimal strategy is the bestscenario.

Table 1. Average RMS of 10 data setsE. (m) N. (m) V. (m)

No Ground Vehicle 1.89 1.47 4.46Locally Greedy 0.92 0.55 2.96

Regionally Optimal 0.48 0.47 1.92

In Figure 10, the first graph shows the multi-constellation,GNSS, position error when having a UGV employing thelocally greedy cooperative strategy, the second is when theUGV is using the regionally optimal strategy, and the lastone is without having a UGV. Table 2 shows the averageGNSS RMS values for the East, North, and Vertical posi-tion error. As with the GPS case, having no UGV is theworst scenario, but for the GNSS case, the locally greedyscenario was the best case. In all scenarios for GNSS, theRMS values were less than the GPS-only case.

The next figures detail a specific example of one sim-ulation trial in which the UGV’s path and the reduction inPDOP are shown. Figure 11 shows the path that the UGV

No UGV UGV Locally Greedy UGV Regionally Optimal

Po

sitio

n E

rro

r (m

ete

rs)

0

0.2

0.4

0.6

0.8

1

1.2

1.4Average RMS of Position Error of 10 Data Sets

East

North

Vertical

Figure 10. Average RMS of 10 data sets

Table 2. Average RMS of 10 data setsE. (m) N. (m) V. (m)

No Ground Vehicle 0.47 0.19 1.30Locally Greedy 0.19 0.16 1.03

Regionally Optimal 0.22 0.19 0.99

takes when employing both the locally greedy path and theregionally optimal path. The ∗ is where the UGV starts,and the x is where it ends. The blue line indicates the lo-cally greedy path, and the green line indicates the region-ally optimal path. The circle is the perimeter that the UGVis not allowed to cross. The locally greedy UGV, movestoward the UAV in the East direction, but has no change inthe North direction. Whereas the regional optimal strategymoves toward the UAV, then moves along the constraintboundary. This is expected, as we can see from Figure 6,the largest reduction of PDOP matches the path of the UGVwith regionally optimal strategy employed.

Figure 12 shows the PDOP over the entire flight forhaving no UGV,the UGV employing the locally greedy al-

Nort

h (

mete

rs)

Ground Vehicle Path for Locally Greedy and Regionally Optimal Strategy

-100

100

0

-150-100-50East (meters)

050100150

0

5

10

15

20

Locally Greedy Path

Quadcopter Path

Start

End

Regionally Optimal Path

Figure 11. UGV’s path, Regionally Optimal and Locally Greedy,in a GNSS-challenged environment

Time

0 2000 4000 6000 8000 10000 12000

PD

OP

0

1

2

3

4

5

6

7

8PDOP of Locally Greedy, Regionally Optimal, and No Ground Vehicle

Locally Greedy

Regionally Optimal

No Ground Vehicle

Figure 12. PDOP without UGV, UGV locally greedy, and UGVRegionally Optimal

Time

0 2000 4000 6000 8000 10000

PD

OP

1.95

2

2.05

2.1

2.15

2.2

2.25PDOP of Locally Greedy and Regionally Optimal

Locally Greedy

Regionally Optimal

Figure 13. PDOP when using a UGV Locally Greedy, and UGVRegionally Optimal

gorithm, and the UGV employing the regionally optimalapproach. The PDOP when having the UGV is much lessthan when there is no UGV. It can be seen how much an ef-fect having a UGV’s ranging source can have on the PDOP.Figure 13 shows the comparison of PDOP while using aUGV with a regionally optimal strategy and the locallygreedy strategy. The PDOP for the regionally optimal al-gorithm is reduced further than that of the locally greedypath planning approach.

6 CONCLUSIONSA cooperative navigation strategy has been employed toimprove the positioning of a UAV in a GNSS-challengedenvironment. This paper described the filter design, co-operative techniques, and a simulation evaluation. As ex-pected, having a UGV ranging source has been shown tohelp in the positioning of the UAV whenever it was co-operatively located. This work has shown that employing

different cooperative strategies for trajectory planning ofthe UGV has an effect on the vehicle positioning. The re-gionally optimal strategy performed better than the locallygreedy strategy. Future work will consider implementinga differential-type filter between the two vehicles, and anexperimental flight-test evaluation.

ACKNOWLEDGEMENTSThis work was supported in part NGA Academic ResearchProgram (NARP) Grant # HM0476-15-1-0004. Approvedfor public release under case number 16-523.

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