Research Article  Open Access
FlightTest Evaluation of Kinematic Precise Point Positioning of Small UAVs
Abstract
An experimental analysis of Global Positioning System (GPS) flight data collected onboard a Small Unmanned Aerial Vehicle (SUAV) is conducted in order to demonstrate that postprocessed kinematic Precise Point Positioning (PPP) solutions with precisions approximately 6 cm 3D Residual Sum of Squares (RSOS) can be obtained on SUAVs that have short duration flights with limited observational periods (i.e., only ~≤5 minutes of data). This is a significant result for the UAV flight testing community because an important and relevant benefit of the PPP technique over traditional Differential GPS (DGPS) techniques, such as RealTime Kinematic (RTK), is that there is no requirement for maintaining a short baseline separation to a differential GNSS reference station. Because SUAVs are an attractive platform for applications such as aerial surveying, precision agriculture, and remote sensing, this paper offers an experimental evaluation of kinematic PPP estimation strategies using SUAV platform data. In particular, an analysis is presented in which the position solutions that are obtained from postprocessing recorded UAV flight data with various PPP software and strategies are compared to solutions that were obtained using traditional doubledifferenced ambiguity fixed carrierphase Differential GPS (CPDGPS). This offers valuable insight to assist designers of SUAV navigation systems whose applications require precise positioning.
1. Introduction
The Precise Point Positioning (PPP) technique was introduced in the late nineties [1, 2] and uses statespace GNSS satellite orbit and clock bias solutions with significantly greater accuracy than their broadcast ephemeris counterparts in order to enable the usersegment to obtain accurate positioning with undifferenced data. The use of undifferenced data means that no GNSS reference station is required to form differential data combinations. To date, PPP technology has matured to the extent that there are now multiple realtime orbit and clock solution products offered by government organizations [3], commercial entities [4, 5], and the International GNSS Service [6]. The PPP technique has revolutionized many geophysical research applications that involve static reference stations and Earth orbiting spacecraft; however, it has not been heavily exploited for applications involving lowcost small UAVs (SUAVs).
Many authors have conducted studies to compare the solution accuracy of the PPP technique with doubledifference CPDGPS solutions or other ground “truths.” For example, Colombo et al. show that once a PPP filter has converged, it agrees with doubledifferenced GPS to within 10 cm [7]. Likewise, for a kinematic vehicular application, Honda et al. demonstrate a few decimeterlevel performance with respect to CPDGPS [8]. In another study, Zhang and Forsberg consider the use of PPP to support missions that require accuracy over very longranges (i.e., on the order of many hundreds of kilometers), thereby making doubledifferences to an individual reference station impractical [9]. In their assessment, Zhang and Forsberg use comparisons of airborne laser altimetry and satellite altimetry products to assess height solution accuracy from PPP and conclude that PPP can produce accuracy at the decimeterlevel. In 2009, Bisnath and Gao [10] offered insight on the stateoftheart of PPP and, in their assessment, demonstrate decimeterlevel kinematic PPP of a static reference station after an initial convergence period. Bisnath and Gao conclude that more algorithm development and additional observables are needed to reduce PPP’s convergence period before it can be considered as an RTK alternative. Many have shown that PPP can achieve accuracy levels consistent with CPDGPS but point out its slow convergence.
More recent studies have also considered the impact of multiconstellation GNSS or other navigation systems, such as Inertial Navigation Systems (INS), to yield better accuracy with the PPP approach. For example, Cai et al. evaluated multiconstellation GNSS using the GPS, GLONASS, Galileo, and Beidou and showed improvements in kinematic PPP position solution accuracy and convergence [11]. Likewise, Yigit et al. demonstrated better positioning performance with multiconstellation GNSS, especially whenever there is a relatively short observation duration [12]. In addition, Zhang and Gao include INS within a PPP filter for a kinematic application and show faster solution convergence and accuracy comparable to conventional RTK/INS solutions [13]. More recently, Gross et al. [14] reaffirmed better overall solution accuracy as well as solution robustness to rapid changes in the tropospheric delay induced by abrupt changes in aircraft altitude by comparing both a fused PPP/INS and a PPPonly solution to a postprocessed reference solution that was the NASA Jet Propulsion Laboratory’s submission to the US National Geodetic Survey’s Kinematic GPS Processing Challenge [15]. Finally, Watson et al. [16] provided a comprehensive evaluation of the benefit of incorporating INS under various common PPP error sources by using a Monte Carlo simulation environment and showed that incorporating INS becomes more important depending on the quality of the troposphere model, multipath environment, and quality of PPP orbit and clock products.
Despite the extensive literature that offers performance comparisons of different GNSS processing techniques, there is a lack of published studies that demonstrate the obtainable PPP positioning accuracy of SUAV flights that have very limited flight durations. Furthermore, while several past studies point to the slow solution convergence as a pitfall of using PPP technique, the need for realtime solutions is often irrelevant for many SUAV scientific applications (e.g., remote sensing, aerial mapping) that can simply wait for postprocessed solutions. However, because some SUAVs have very limited flight durations, which are on the order of fifteen minutes, or often less, some uncertainty remains as to whether PPP’s slow solution convergence will impact the accuracy of the postprocessed (i.e., filtered and backwards smoothed) short duration SUAV solutions.
As such, to fill this knowledge gap, the contribution of this paper is to offer an experimental analysis of PPP techniques when compared to CPDGPS with data collected onboard SUAV that has very short duration flights. This is particularly relevant to the field robotics community as SUAVs are being more regularly used for more ambitious scientific applications that have stringent requirements on platform positioning. For example, recent experimental evaluations have demonstrated the use of Light Detection and Ranging (LIDAR) for finescale mapping with UAVs [17–19]. Accurate georegistration requires platform positioning accuracy in the cmscale, as these LIDAR systems have cmscale or better resolution. Additionally, researchers at the University of Kansas have recently instrumented SUAV for radar sounding of remotely located Antarctic ice sheets [20]. While the current Kansas ice sounding UAV is operating at radar frequencies with large wavelengths, it is not a stretch to envision a similar SUAV radar system operating higher frequencies (e.g., microwave) and thus needing cmscale positioning precision, such as a miniaturized version of NASA’s LBand UAVSAR instrument [21]. For these SUAV applications, which are typically cited to offer the benefit of being rapidly deployable and useful for remote regions, eliminating the need for GNSS differential reference station and thus reducing overall cost and complexity of the navigation system by leveraging PPP will further open the use of SUAVs for hosting scientific payloads that have stringent positioning requirements.
The rest of this paper is organized as follows. Section 2 reviews the GNSS observational models for both PPP, which is being evaluated, and doubledifferenced ambiguity fixed CPDGPS, which is being used to estimate reference position solutions. In addition, the details of the software implementation employed in this study are discussed. Section 3 discusses the experimental SUAV, GNSS equipment, and flighttest environment used for this study. The results of an experimental comparison study are then detailed in Section 4, and the study’s findings are summarized in Section 5.
2. Methodology
2.1. Observational Models
We start by considering the generic observation models for GNSS pseudorange and carrierphase measurements as shown in (1) and (2), which are found in many textbooks [22, 23]. ConsiderIn (1) and (2), the subscript is used to denote the user and superscript denotes the GNSS satellite index. Common to both pseudorange and carrierphase are several error sources, where is the unknown GNSS receiver clock bias in units of seconds, is the GNSS transmitter’s clock bias in units of seconds, is the speed of light in a vacuum in units of meters per second, is the GNSS signal delay due to the refraction in the neutral atmosphere in units of meters, and is the phaseadvance/pseudorange delay caused by signal refraction through traversing the Earth’s ionosphere (note the sign change between (1) and (2)) in units of meters. The remaining unmodeled error sources are denoted by and are in units of meters. Within the carrierphase model (2), there is also unknown integer phase tracking ambiguity that is denoted by and is taken from units of carrierphase cycles to meters through a multiplication with the GNSS carrier wavelength , where and cm and cm for the case of GPS. Furthermore, in (1) and (2), the geometric range between the user’s receiver antenna phase center and the satellite’s transmitter antenna phase center is denoted as and given bywhere both the user’s position and satellite’s position are modeled in the same Cartesian reference frame, typically either an EarthCenteredEarthFixed frame or an EarthCenteredInertial frame. For the PPP technique, accurate solutions to each GNSS transmitter’s clock bias, , and orbital location are determined using a global network of tracking reference stations and are used in lieu of the GNSS broadcast ephemeris. However, typically, the satellite locations are provided with respect to the center of gravity of each GNSS spacecraft. Therefore, to be consistent with (3), the attitude of each satellite must be modeled such that the lever arm offset between each satellite’s antenna phase center and its center of gravity is properly considered. To do this, GNSS satellite type dependent known lever arm offsets and attitude models [24, 25] must be included in the processing strategy.
In this study, we assume access to dualfrequency GNSS data. As such, we use the dispersive nature of the ionosphere’s delay and form a linear combination of the dualfrequency signals in order to cancel the effect of the ionosphere signal refraction to the first order. This linear combination is denoted as ionosphericfree (IF) combination [22] and given by (4) and (5), for pseudorange and carrierphase observations, respectively:Note that the coefficients in (4) and (5) (i.e., 2.546 and −1.546 for GPS) sum to 1.0, and thus the modeled common mode error sources, including clock biases and the troposphere delay, remain unchanged in the IF observations. However, when using the IF combination, the unmodeled random errors denoted by become amplified. For GNSS, the unmodeled error sources consist of thermal noise and receiver front end noise and multipath. For pseudorange observables is on the order of 1 meter and for carrierphase is on the order of 1 millimeter. As such, when using the IF combination, the measurement noise is ~3 meters for pseudorange and 3 millimeters for carrierphase (i.e., ).
In (1) and (2), the tropospheric delay is typically modeled by scaling the zenith direction delay using an elevation angle dependent mapping function to reduce the number of model parameters. Furthermore, this is composed of both wet and dry components of which the dry component is ~90% of the total delay and can be well approximated with a model. As such, the zenith dry delay is typically modeled and the zenith wet delay is estimated as an unknown parameter such that the delay is modeled as shown inwhere is the elevation angle from the nominal user location to satellite . Within this study, different mapping functions, , are utilized depending on the solution strategy and software used as will be detailed in the next section.
The remaining modeled error sources are the carrierphase ambiguities. Traditionally, with kinematic PPP techniques, despite the fact that these are known to be an integer number, these are modeled as floating point parameters in the PPP filter/smoother. However, PPP ambiguity resolution techniques have been developed [26, 27] and this remains an active research area.
An important unmodeled error source within the terms is present in (1) and (2) which are the errors induced by multipath reflections. These errors are attributed to reflections of the GNSS signals being present in the received signal in addition to the line of sight signal. Unfortunately, multipath leads to errors that are nonGaussian and nonWhite in nature, such that Kalman or leastsquares type estimators are not best suited to mitigate them. Instead, a total leastsquares processing technique could be employed, such as the one mentioned in Juang [28]. However, the multipath induced errors for carrierphase are multiple orders of magnitude smaller than those for pseudorange. Further, for many airborne applications, multipath induced errors, due to signal reflections from manmade objects, are less of a potential problem. In this study, to mitigate multipath induced errors, our PPP estimators will heavily rely on carrierphase data relative to pseudorange data.
2.2. Kinematic PPP with JPL’s GIPSYOASIS
The first PPP approach considered in this study uses Caltech JPL’s GNSSInferred Positioning System and Orbit Analysis Simulation Software (GIPSYOASIS) 6.2 [29]. GIPSY has been the primary geodetic and positioning software for NASA’s TOPEX/Poseidon [30] and JASON [31] and GRACE [32] low Earth orbiting spacecraft and is operationally used to generate JPL’s precise GPS orbits and clock products for the IGS [33]. GIPSY is licensed for free by Caltech to institutions for use in academic research.
When using GIPSY for kinematic PPP, our strategy in this study is to iteratively process the position solution while varying GIPSY configuration parameters in order to converge it to an optimal solution that is free of data outliers. A block diagram of the processing strategy is shown in Figure 1, which requires defining some GIPSY terms.
(i) GNSS Data to Positioning (GD2P). It is GIPSY’s main user interface script for PPP.
(ii) Pseudorange Data to Positioning (PR2P). It is GIPSY’s script for pseudorangeonly point positioning.
(iii) Time Dependent Parameter (TDP). It is GIPSY’s output format for positioning solutions and other solved for parameters (e.g., clock biases, troposphere, and phase biases).
(iv) QM File. It is GIPSY’s native binary GNSS measurement format.
As indicated in Figure 1, for the first iteration, a position solution is estimated using only pseudorange measurement with GIPSY’s PR2P. In addition, the data is translated from the Receiver Independent Exchange Format (RINEX) to a GIPSY binary QM file. During this process, a GNSS data editor is used to flag carrierphase breaks and remove gross data outliers [34]. For data editing, the GIPSY defaults were used with the exception of the editor requiring a minimum data arc length for a given transmitter. This is due to the short overall observation window of the flights.
For the remaining iterations, a subset of GIPSY processing options are varied while accepting the previous position solution (TDP file) as the a priori position solution. Within Figure 1, the configuration options that are varied for each run are as follows.
(i) Data Weights. They are measurement noise ratio between pseudorange and carrierphase measurements. This starts as onetoone and varies to onehundredtoone, where carrierphase data are modeled as 100 times more precise than pseudorange data.
(ii) Postfit Residual Window. Within each GIPSY processing run, multiple passes of a Kalman filter and smoother are conducted. Between each pass, postfit data residuals are evaluated and data are marked as outlier based on defined thresholds and excluded from the next pass. At each pass, the residuals of all data, inlier and outlier, are evaluated and either added back in or excluded from the run. This process is repeated until all data meet the postfit window criteria or a maximum number of iterations are exceeded.
(iii) Stochastic Models. The position and wet troposphere delay estimates can be modeled using either white noise about the nominal solution or random walk process noise. Additionally, the a priori magnitude and rate of process noise updates can be set. In particular, the wet zenith delay was estimated as a random walk process, given that the SUAV evaluated is not flying over great distances. Position is initially estimated using random walk, and after a few iterations it is estimated using white noise about an a priori nominal solution.
(iv) Minimum Slip. After each filter iteration, jumps in the postfit phase residuals are used to identify the possibility of a carrierphase break that was missed by the data editor. New breaks are flagged for the next iteration.
In addition to the configuration parameters listed above that are varied for each iteration, several other GIPSY options were selected and held fixed in this study. In particular, the troposphere mapping function used is the Niell mapping function [35] and the nominal troposphere delays were set using the atmospheric model populated with a nominal height for scaling and pressure and temperature from the Global Pressure and Temperature model [36]. For the several remaining available GD2P options (e.g., elevation cutoff, tide models), the defaults provided by JPL were used.
The specific strategy used for this study with respect to Figure 1 is listed in Table 1, for the 10 iterations conducted.

While the outlier deletion windows are selected ad hoc based upon experience, in order to assess the effectiveness of postfit data residual analysis and outlier deletion, the GIPSY log files report an approximate statistic of the residuals for each filter/smoother and data editing iteration. The value reported is only approximate, because it is reported as if the entire data set were processed as leastsquares batch as opposed to a sequential filter. More formally, the Residual Standard Error (RSE) of the estimator for each outlier editing iteration is reported as follows:where is the Residual Sum of Squares normalized to the data weight of each type of observation, is the total number of GNSS observations, and is the total number of parameters estimated. In addition, while it may seem problematic to delete data based upon user selected thresholds, in practice only gross outliers are removed from the filter run. This is because the residual analysis is done in a sequential narrowing window manner, such that such that, first, only gross outliers are deleted and then the residuals are reevaluated, with the possibility of adding data that was flagged as outlier on a previous run as being marked as inlier again (e.g., to handle the case in which one large outlier pollutes all of the residuals for a given epoch). Figure 2 shows an example for the RSE as well as the total percentage of data deleted during a GIPSY run, where the RSE is shown to converge and less than 1.5% of data is shown to have been deleted.
2.3. Kinematic PPP with RTKLIB
The second software package used for PPP in this study is the opensource RTKLIB [37, 38]. When using RTKLIB, several processing options are available for the user. The following list describes the adopted processing strategy of this study.
(i) Kalman Filter SetUp. The Kalman estimator was configured for both forward filtering and then backwards smoothing.
(ii) Elevation CutOff. A 5° elevation angle cutoff was used.
(iii) Troposphere Model. The troposphere was modeled using the Saastamoinen model and a residual wet zenith delay was estimated.
(iv) Ionosphere. The ionosphere free linear combination was used.
(v) Misc. Solid Earth tides and ocean loading tides were modeled. Phase windup was considered.
(vi) Process Noise. The SUAV dynamics were modeled using a double integrator with process noise driving the acceleration states of 10 m/s^{2}.
These options were selected using RTKLIB’s graphical user interface.
2.4. CarrierPhase DoubleDifferenced Processing for Reference Solutions
To provide reference position solutions for the kinematic PPP solutions, a carrierphase doubledifferenced integer ambiguity fixed processing strategy was used. In this case, the GNSS error sources present in (2), in common with a GNSS base station, which is located at a wellknown location within a short baseline separation, are canceled via data differencing [22]. In this scenario, the relative position of the UAV with respect to the base station, , is estimated, and the known location of the base station is added to recover an absolute position estimate of the UAV. For this technique, first, two carrierphase measurements from the same satellite, , are differenced between the two user receivers, denoted here as , for UAV, and , for base station, to form singledifferenced carrierphase measurements:where the satellite clock bias errors, the troposphere delay, and ionosphere delay are eliminated, and the ambiguity remains an integer. Next, to further eliminate the error attributed to the combined users’ receiver clock biases, , two of the singledifferenced carrierphase measurements from satellites and are subtracted to form doubledifferenced carrierphase measurements, . The doubledifferencing process requires the selection of a reference satellite which is typically selected to be a highelevation satellite (indicated herein with index ) and subtracting its singledifferenced measurement from all other available singledifferenced measurements. With doubledifferenced measurements, the only errors that remain are the multipath errors, which are small for carrierphase observables and airborne applications, and the ambiguity, which is known to be an integer number of wavelengths of the carrier frequency.
To resolve the integer ambiguity, a Kalman filter first estimates the carrierphase ambiguities as floating point parameters, and, then, a separate technique is used to to take advantage of the fact that these states are an integer number of wavelengths. In particular, the de facto technique that is used in this study is known as the Leastsquares AMBiguity Decorrelation and Adjustment (LAMBDA) method [39, 40]. The objective of the LAMBDA method is to find an Integer Least Squared Solution (ILS) with respect to the estimated float ambiguities, , and a corresponding variancecovariance estimate of the phase ambiguities, [39]. This is done by finding an orthogonal transformation that preservers integer values and decorrelates to a diagonal covariance matrix, such that simple rounding can be employed to estimate the integer states. Following the rounding process, the transformation is reversed to get back into the statespace domain. The cost function that the LAMBDA method optimizes is given by [41]where the integer grid search space is defined by . Once the integer fixed biases have been determined, the relative navigation states are adjusted by assuming that the integerfixing process is deterministic, such that the nonambiguity states are corrected aswhere refers to the variancecovariance matrix for the floating point ambiguities that were estimated by the Kalman filter, of which particular sections are identified by the subscripts position, which refers to the position states, and , which refers to phase ambiguity states.
It is important to point out that integer bias fixing will not always be a success in the presence of errors. As such, there must be a validation process. The specific acceptancetest employed in the RTKLIB implementation used in this study was the ratiotest [42]. The ratiotest evaluates how close the float ambiguity estimates are to the best integer ambiguity estimates when compared to the next best integer ambiguity candidate. The best candidate, , and the second best candidate, , are defined as those that minimize the cost function of (9):where is the critical value, which can be derived on the fly to allow a fixed failure rate or set to a constant [42]. For this study, was set to 3 and held constant. Three is often used in practice, though this is only empirically justified [42]. Throughout this study, only the epochs that were successfully fixed and passed the ratiotest criterion, which ranged from 65 to 85% of all epochs of each flight, were used as the reference solution for conducting the error analysis presented below.
3. Experimental SetUp
The Phastball SUAV airframe [43] was developed as a modular research platform and has been used for multiple sensorfusion studies [44–46]. The Phastball Zero SUAV is shown in Figure 3.
For this study, its payload features two Novatel OEM615 dualfrequency GNSS receivers with antennas separated 85.3 cm along the airframe’s longitudinal axis. A block diagram of Phastball Zero’s data acquisition structure is shown in Figure 4.
In this setup, one Novatel Receiver is GPS and GLONASS capable and the other is GPS only. Raw GNSS dualfrequency pseudorange and carrierphase observables are recorded at a rate of 10 Hz using OpenLog serial microSD dataloggers. The GPS/GLONASS Novatel OEM615 receiver is wirelessly connected through a 900 MHz modem to a base station that sends up RTK differential correctors. Additionally, a mechanical vertical gyroscope that directly measures the UAV’s pitch and roll is included onboard, as well as the pilot input and four Analog Devices ADIS16405 Microelectromechanical Systems (MEMS) IMUs, which are interfaced through two Netburner MOD5213 microcontrollers logging data with OpenLog serial stream dataloggers. For postprocessing, the recorded GNSS data and data streams that are interfaced through the Netburner MOD5213 microcontroller are synchronized by recording the state of the PulsePerSecond (PPS) signal from one of the GNSS receivers.
In addition to the Phastball SUAV, the experimental setup consisted of another Novatel OEM615 dualfrequency receiver serving as a static reference receiver with the antenna mounted on a tripod. Experimental flighttests for this study were conducted at WVU’s Jackson’s Mill airfield. A typical flight pattern is shown in Figure 5.
In total, six data sets of short duration SUAV flights were collected for this study. These consisted of three flighttests with two data sets per flight. Table 2 lists the total flight duration from takeoff to landing of the three flights.

4. Results and Discussion
4.1. Validation of Reference Position Solutions
For comparing the estimation performances of various PPP and single receiver point positioning algorithms, Kalman filter/smoother CPDGPS solutions were generated for each flighttest with respect to a local GPS reference station setup at the airfield. When processing the CPDGPS data, in order to obtain the absolute coordinates of the base station’s tripod, ~6 hours of static data was processing using GIPSYOASIS PPP in static mode. The software that was used for generating the CPDGPS reference solutions was RTKLIB 2.4.2.
While it is well known that doubledifference integer fixed CPDGPS solutions can obtain cmlevel accuracy and precision, the Phastball flighttest configuration provides the opportunity to validate this level of accuracy and precision for the reference position solutions. In particular, the Phastball SUAV is outfitted with two GPS antennas separated by a known baseline distance of 83.5 cm. Note that, with this setup, it is possible to further leverage the known baseline constraint between the multiple antennas to improve estimation performance of position and attitude [47], which can further be extended to improvements with an array of multiple antennas (i.e., more than 2) [48, 49]. While the arrayaided PPP is an interesting research direction that the authors intend to pursue with this SUAV platform, for the present study, the goal is to assess the accuracy of single antenna PPP for SUAVs. Therefore, in order to validate the reference solutions used for each separate antenna, the two ambiguity fixed CPDGPS solutions for each receiver on the SUAV were differenced, and the magnitude of the difference was used to evaluate how well the known antenna separation distance is estimated. Figure 5 shows an example of the result of this analysis for our second SUAV flighttest.
As shown in Figure 6, the separation between the two antennas was estimated with both cmlevel accuracy and precision. Table 3 shows the antenna separation estimation error for all three flights, where subcm accuracy and cmlevel precision were obtained.

4.2. Performance Comparison Study
In order to provide a context, in addition to the PPP solution methods described in Section 2, position solutions obtained by processing the pseudorange data only with the GPS broadcast ephemeris using both the GIPSY software and the RTKLIB software are presented. These solutions represent the expected level of accuracy one would obtain from a GPS receiver position solution without any DGPS or PPP products. Short name identifiers for the processing strategies that were compared are shown in Table 4.

Table 5 shows the mean and standard deviation error statistics for the four processing methods considered over the six data sets, and Table 6 shows the overall average mean error and standard deviation error over the six flights, where all solutions are compared to the ambiguity fixed CPDGPS reference solutions.


As shown in Tables 5 and 6, when using pseudorange based point positioning, 23 meterslevel precision and accuracy can be expected. However, when adopting kinematic PPP, decimeterlevel accuracy and centimeterlevel precision were obtained, despite the fact that these are flight data sets with only a few minutes of observations. Further, to obtain this level of positioning performance, all the user needs to do is collect the raw GNSS measurements for postprocessing.
While the level of precision on short duration SUAV flights is centimeterlevel, decimeterlevel biases remain in the solution. It is expected that these are likely due to the short duration data set and the known slow convergence of PPP. However, an important insight provided by this study is that when considering short duration postprocessing applications of PPP, the slow convergence yields a constant bias, that is, when considering the error sources that must be modeled or mitigated by PPP in (1) and (2) (e.g., troposphere, orbit, clock, and phase ambiguities). Despite the fact that there is no enough data to converge upon the absolute values of these error sources, each of these error sources remains quite constant over the few minutes’ timescale. Therefore, these decimeterlevel biases can easily be mitigated by starting the SUAV at a known location (e.g., by placing a receiver at a takeoff location for static PPP) or simply allowing the SUAV to sit static on the runway for an initialization period.
To further substantiate why kinematic PPP with short observational periods is still very precise but biased, an additional fiveminute SUAV flight that was simulated using a PPP simulation tool developed for a previous study [16] was analyzed. With this tool, all of the GNSS error sources discussed in Section 2.1 are modeled, but because they are simulated, perfect knowledge about all error sources is available for analysis. As such, the performance with respect to a perfectly known truth was assessed. Figure 7 shows an example kinematic PPP forward filter’s position solution errors and phase bias estimation errors, as well as the backwards RauchTungStriebel [50] Kalman smoothed position and phase bias errors.
(a)
(b)
As shown in Figure 7, a similar level of positioning performance as presented in the flight data analysis is shown for the simulated flight, that is, decimeterlevel accuracy with centimeterlevel precision. Further, the phase biases, which are estimated as random constants, do converge but maintain approximately 10 to 15 cm biases after the 5 minutes. Then, during the backwards smoother, the phase bias estimates are nearly constant, leading to considerably smoother positioning errors, as shown, but with decimeterlevel biases remaining present. In particular, the mean errors between the forward filter and smoother are only reduced by 1% from 44 cm to 45 cm; however, the standard deviation of the position errors was reduced by more than 25% with a 3D reduction from 14.7 cm to 11 cm.
5. Conclusions
An experimental evaluation of kinematic PPP using short duration SUAV data has been presented, as such a study was missing in the literature and the PPP approach has yet to be heavily leveraged in the field robotics and SUAV communities. Through comparison with CPDGPS reference solutions, it has been shown that approximately 6 cm 3D positioning precision with decimetertometerlevel 3D accuracy is obtainable when using PPP even when the flights are only a few minutes in duration. This is of benefit because PPP does not require the user to have access to a differential reference station. This result has been demonstrated with six SUAV flight data sets and two popular GNSS processing software packages. The results of this study are of benefit to many potential SUAV science applications that require precise positioning.
Competing Interests
The authors declare no conflict of interests with the publication of this paper.
Acknowledgments
This research was partially supported by the US National Geospatial Intelligence Agency Academic Research Program (NARP) Grant no. HM04761510004. Approved for public release, case no. 16195.
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Copyright © 2016 Jason N. Gross et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.