Cycle Slip Detection and Correction for Precise Point Positioning

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1 1 Cycle Slip Detection and Correction for Precise Point Positioning Pedro Silva Technical University of Lisbon - Instituto Superior Técnico pedro.silva@ist.utl.pt Abstract Over the last years precise point positioning (PPP) has been receiving more attention as it provides a cheaper way to achieve decimetre and centimetre precision levels when compared to the typical differential techniques. While differential techniques rely on two or more receivers to differentiate their observations and cancel out most errors, PPP only uses undifferenced observations from a single receiver, leading to a more complex and difficult error modelling. One of the major sources of error in the observations, besides the atmospheric and relativistic effects, are the satellite ephemerides and clocks broadcast by the Global Positioning Service (GPS) system. This, however, can be corrected by using precise ephemerides and clocks made available by International GNSS Service (IGS). PPP then relies not only on precise products but also on the millimetre precise but ambiguous carrier phase measurements. Despite the presence of an ambiguity term, carrier phase measurements are also susceptible to other effects such as cycle slips. Cycle slips are a discontinuity in carrier phase that can cause a momentary loss of lock. Detection and correction of cycle slips will allow the estimation process to continue outputting precise solutions, without having to be reinitialised. It is then important to look out for these discontinuities in the carrier phase measurements before using them to acquire a solution, something that can be done through several methods that provide with a certain confidence level a detection mechanism for such discontinuities. Using inertial measurement unit (IMU) can also help understand in some cases if a cycle slip occurred or not, by knowing how much the carrier phase measurements should have changed due to the receiver s dynamics. This work aims to discuss the contribution of IGS s precise products in the increase of performance of the GPS system. Besides that it provides a solution to detect and correct cycle slips using predicted Doppler measurements, to which IMUs are essential in order to estimate the receiver s velocity and displacement in between GPS measurements. This information is also used in order to provide a data regeneration mechanism to minimise the impact of constellation changes throughout the observation period. Index Terms GPS, PPP, IMU, Least Squares, Sequential Filter, EKF, Doppler I. INTRODUCTION GNSS positioning is quite common and popular nowadays specially by its proliferation in devices such as smart phones and tablets. Smart phones have replaced most common car receivers offering a solution that can handle personal navigation as well as communication. With common GNSS receivers it is normal to obtain several metres of error, although in a car receiver this is not problematic as the receiver s software knows where the road is. Although, with the current GNSS enabled devices people are using them to navigate not only in roads, but also in sidewalks, cycling trails and even light indoors. This means that a common GNSS receiver will not be able to provide a reasonable performance, especially in an urban context where multipath, signal interferences and a reduced sky visibility take a toll on the receiver s performance. A metre level positioning can be achieved with a single receiver if auxiliary data is pulled from the Internet or is obtained from an UHF signal broadcast by a nearby station. This is usually referred to as assisted GPS (AGPS). Improvements can also be obtained from using a satellite based augmentation system (SBAS), which relies on geosynchronous satellites to transmit more accurate information to the users that are able to see these satellites. Another alternative is differential GPS (DGPS) that uses information from at least two receivers to remove the common errors through double differencing the observations, allowing high precision and accuracy levels to be achieved. Despite the good results provided by DGPS, it is quite expensive to own and maintain a reference station, therefore AGPS alternatives are receiving more attention due to their reduced cost and independence from a (nearby) reference station. PPP is one of such techniques in the AGPS world that is being seen as a good alternative to DGPS [1]. This technique uses undifferenced code and carrier phase observations with precise products, such as orbit and clock information, to achieve centimetre level solutions. Precision is highly related to the success estimating the integer ambiguities present in the carrier phase measurements and detecting and correcting cycle slips. Performance metrics There are several performance metrics that can be used to infer the system s precision and accuracy. In this case the metrics rely on the standard deviation of the estimated position and it is normal to consider a 2D precision (east and north coordinates) and 3D precision (east, north and up/down coordinates). CEP, DMRS, SEP and MRSE are the most commons metrics used in the GNSS industry. CEP represents a circular region which will contain the solution with a given probability, for example, CEP50 represents a 50% probability circular region. The same goes for SEP, although instead of a circular region this metrics represents a sphere. As the name implies, DMRS is the square root of the average of the squared horizontal position errors and defines an approximate 60% probability circular region. MRSE

2 2 TABLE I: Precision metrics 2D 3D Metric Formula Probability DMRS σx 2 + σ2 y 60% CEP σ x σ y 50% CEP CEP50 95% MRSE σx 2 + σy 2 + σz 2 60% SEP (σ x + σ y + σ z) 50% SEP MRSE 95% is the square root of the average of the squared horizontal and vertical position errors and represents a sphere that contains the position estimates with an approximate 60% probability. II. POSITIONING WITH GPS Point positioning is the most traditional way of obtaining the receiver s coordinates using the GPS system and since only one receiver is used, to achieve high precision levels all errors that the signal is subject to must be taken into account. One of the fundamental requirements to have a GPS solution is for the receiver to lock at least four satellites. Having four satellites, the receiver can present a solution for latitude, longitude, altitude and receiver time offset. Code and carrier phase measurements to these satellites can be used to provide such solution. Pseudoranges are obtained from the code measurements and are modelled by equation 1. Equation 2 is used for modelling the carrier phase measurements, which is similar to the previous one despite the ambiguity term. The index regarding the measurement frequency it refers to was ignored for readability purposes. In other words, these equations describe the GPS measurements as a function of the geometrical range from the receiver to the satellite (ρ), receiver clock delay (d r ), satellite clock delay (d s ), a tropospheric (T ) and ionospheric (I) delay, an integer ambiguity (N) for carrier phase measurements and other unmodeled errors (ɛ). The geometric range can be computed by equation 3, where the receiver position is given by r r = (x r, y r, z r ) and the satellite position by r s = (x s, y s, z s ). P = ρ + c(dt s + dt r ) + I + T + ɛ (1) Φ = ρ + c(dt s + dt r ) + I + T + λn + ɛ (2) ρ = (x s x r ) 2 + (y s y r ) 2 + (z s z r ) 2 (3) A common approach to obtain a position solution is to use a least squares (LSQ) filter. Although, the model is not linear and to use it in LSQ a linearisation around a known point must be done and solve it iteratively. Detailed steps for the linearisation can be found at [2] [3]. The linearised model results in equation 4. P = H X (4) P is the observed minus computed (OMC) vector, H is the design matrix containing the partial derivatives of the observation equations in respect to X the unknowns vector and k is the number of satellites used. P is defined as the difference between the error free measurements (P o ) and the measurements computed for the linearised point (P l ) plus an error vector (P ε ). Vector X can be seen as the difference between an error free position (X o ) and the position defined for the linearisation point (X l ) plus an error vector (X ε ). For the following analysis the error vectors from equation 4 are ignored and its expansion results in equation 5. P o (1) P (1) l P o (2) P (3) l P (k) o. P (k) l e (1) 1 δx e (2) 1 δy =.. δz e (k) 1 δdt r In order to use the carrier phase measurements the H will need to expand by k rows to allow the estimation of each ambiguity. These ambiguities will not be an integer value, as the dual frequency measurements are combined to remove the ionospheric delay, resulting in a combined N 1 N 2 ambiguity. The vector of unknowns will also be updated accordingly. Precise Point Positioning PPP is a point positioning technique that uses undifference measurements from one GPS receiver and precise products such as those provided by IGS. This technique allows centimetre level results in static mode and a decimetre level in kinematic mode (one sigma) both in accuracy and precision anywhere in the world, under good receiving conditions [4]. Its disadvantages are the long convergence times to estimate carrier phase ambiguities and the accuracy limitation imposed by the unmodeled errors and the precise products available. The product availability is another issue as it can take up to two weeks for the precise products to be available [5]. Several errors and effects can be modelled by following the recommendations provided in [5] [6]. Under PPP the measurements are also modelled as in standard point positioning (SPP) (equations 1 and 2). It stands out from SPP by taking into account more error sources and especially by using precise products. If only precise products are used decimetre level solutions can already be obtained [5]. Another difference is that it usually employs Kalman filtering or sequential filters in order to obtain a better solution due to the variance propagation between epochs. Equation 6 show the traditional filter used for PPP, where W 0 is the a priori weighted parameter constraints, W P is the measurements weight and W X is the estimated parameters weight matrix. W X can be set as seen in [7]. On the other side, both W 0 and W X are the inverse of covariance matrices and W 0 is be successfully updated with the last estimated parameters (5)

3 3 weight matrix W X. The initialisation can be done by using an identity matrix as the first covariance matrix. X = (W 0 + H T W P H) 1 H T P W P W X = (W 0 + H T W P H) Dilution of Precision - The impact of satellite availability GPS solution is not only affected by the pseudorange error but also by the geometry of the observed satellites. Therefore the error in the GPS solution can be seen as the product of a pseudorange error factor and a geometry factor. This geometry factor is known as dilution of precision (DOP) and can be divided in several factors that indicate the horizontal, vertical and time impact of the seen constellation [8]. The most common DOP value used is the position dilution of precision (PDOP), a metric associated to the east, north and up error (equation 7). PDOP = (6) Tr(S [3 3] ) with S = (H T H) 1 (7) An ideal constellation should have the satellites dispersed throughout the sky and not concentrated in one single region. If this is maintained the DOP values should be relatively small near 1 or 2 (adimensional). In open sky conditions using GPS standalone, near a dozen satellites should be seen by the receiver, but with multipath, shadowing and signal to noise range (SNR) degradation due to low elevation angles, no more than 8 to 10 satellites should be usable in practice. Going for stronger multipath environments this value quickly drops to 4 or 5 usable satellites, due to the receiver s difficulty obtaining carrier phase information. Therefore, in such context it is valuable to look for ways to increase the satellite availability during periods of loss of lock. A. Fusing IMU with GPS IMUs are commonly used in conjunction with GPS to provide dead reckoning in between GPS observations and when it is not available, something quite common in urban areas, where the GPS signal is either shadowed by the city buildings or destroyed by strong multipath. In these kind of applications the IMU and GPS work together to reduce the error in each processing loop with feedback being sent both ways. In a more simple and focused approach the IMU can be used in order to aid the cycle slip detectors by providing an estimate of the receiver displacement observed between epochs. In a cycle slip free situation the carrier phase between two consecutive epochs are increased by the travelled satellite and receiver distance. On the contrary, when a cycle slip happens, the carrier phase will be additionally increased by its value. With an accurate displacement information this detection can be easily achieved. III. CYCLE SLIP DETECTION AND CORRECTION In general, cycle slip detection is done by comparing the residuals of a predicted value to an observed value, if this residual is above a certain threshold, then a cycle slip is declared. The main difference in the detectors is which measurements or combinations of those to use. The geometry-free combination detector uses carrier phase data to decide when a cycle slip is present in the data. The Melbourne-Wbbena detector uses a code and phase measurement combination to obtain a signal with a larger wavelength. The TECR detector estimates the Total Electron Content (TEC) in the atmosphere to declare a cycle slip. On the other hand the proposed solution uses predicted Doppler measurements to estimate the expected change in the carrier phase. Geometry-free combination Relying on the two frequency GPS signals (L1 P(Y) and L2 P(Y)) it is possible to make the carrier phase geometry free combination (equation 8). As the name implies, this combination allows the removal of the geometry impact, clocks and all non dispersive effects. This combination is very precise and with few changes between closely epochs, so that when a cycle slip is present the jump will be amplified as well as the signal noise [6]. The amplification of signal noise can lead to false detection and a way to reduce its effect is to apply a low order polynomial on the previous epochs information. The polynomial fitted estimate is then subtracted to the current geometry free combination and a cycle slip is signalled if this residual is bigger than the defined threshold. The threshold to be used should take into account the sampling rate used, which is translated by t = t t t t 1 in equation 9. T 0 is taken as 60 seconds, a 1 = a 0 2 and a 0 = 3 4 (λ 2 λ 1 ) [6]. Using the standard deviation of the combination, the threshold can also be set as 3σ Φgf [9]. Φ gf = Φ L1 Φ L2 (8) ( T hreshold = a 0 a 1 exp t ) T 0 Melbourne-Wübbena This detector uses the Melbourne-Wübbena combination (MW ) which is computed by using dual frequency carrier phase and code measurements (Equation 10). This combination has two major advantages, a larger wavelength (λ MW = c f 1 f 2 ) and a reduced signal noise level due to the usage of code measurements. The larger wavelength is important as the spacing between ambiguities will be increased, making it easier to detect jumps. The code measurements allow the removal of the noise incresead by the linear combination of the carrier phase, therefore there is no need to use a polynomial as in the geometry-free detector. The detection is done by comparing the mean value of the previous epochs with an aproximation of the standard deviation (σ MW ) times a sensitivity factor (K) (9)

4 4 [10]. The mean (µ MW ) and standard deviation can be obtained through equations 12 and 11, respectively. MW = Φ L1 Φ L2 f 1 f 2 f 1 + f 2 ( P 1 λ 1 + P 2 λ 2 ) (10) σmw 2 (t) = t 1 σmw 2 (t 1) t + (MW (t) µ MW (t 1)) 2, t > 0 (11) t µ MW (t) = t 1 µ MW (t 1) + t Total Electron Content MW (t), t > 0 (12) t In this detector, the Total Electron Content Rate(TECR) inferred from Link 1 (L1) and Link 2 (L2) carrier phase measurements is compared with an estimation provided by previous epochs [11]. With that information, TEC can be derived from dual frequency carrier phase measurements (equation 13). The same way, TECR for the current epoch can be obtained by differentiating the TEC from two epochs separated by t (equation 14). If a cycle slip has happened at epoch t, its value can be determined by equation 16, which results from rearranging the previous two equations. TEC(t 1) = f 2 1 [[λ 1 Φ 1 (t 1) λ 2 Φ 2 (t 1)] [λ 1 N 1 λn 2 ]] (γ 1) TECR observed (t) = TEC(t) TEC(t 1) t (13) (14) [λ 1 N 1 (t) λ 2 N 2 (t)] = (γ 1) ttecr(t) f 2 1 λ 1 [Φ 1 (t) Φ 1 (t 1)] + λ 2 [Φ 2 (t) Φ 2 (t 1)] (15) (16) In the end, if the TECR for the current epoch is known, then the cycle slip value can be easily computed. TECR can then be estimated by using equation 17. The detection of the cycle slip can then be done by comparing the residual from the TECR calculated by 14 and the estimation computed by equation 17, with the detection threshold. The standard deviation and a sensitivity factor can be used as the threshold, in a similar manner to the Melbourne-Wübbena detector [11]. TECR estimate (t) = TECR(t 1) + TECR(t 1) t TECR(t TECR(t 1) TECR(t 2) (17) 1) = t Proposed algorithm The Doppler effect describes the shift in the center frequency of an incident waveform due to the relative target motion with respect to the source of radiation [12]. Equations 18 describe the Doppler effect, where f is the observed frequency, f 0 the emitted frequency with wavelength λ 0, v s the satellite velocity [13], v r the receiver velocity and c as the propagation speed of the wave, which in this case is considered to be the speed of light in vacuum. When the speed of light is greater than the relative speed of the source and the observer the Doppler computation can be simplified by using the line of sight velocity defined as v s,r [12]. f = c + v r c + v s f 0 f D = (1 c + v r c + v s )f 0 = (1 v s,r c )f 0 (18a) (18b) f = ( v s,r c )f 0 (18c) The proposed algorithm uses an IMU to compute the Doppler shift ( f) observed between observation epochs (equation 18c). Integrating the Doppler shift over the observation period (usually one second) an expected carrier phase and code measurements can be determined. This value will be close to the actual value but it will accumulate error due to the integration process, so it is important to reset the prediction with measured data when possible. By continuously tracking changes in the satellite constellation these predicted values can be used when the lock to a satellite is loss and if the prediction is still considered valid, it is used to fill in the missing measurement. The loss of lock can be permanent or momentary as it is can be caused by shadowing, multipath or atmospheric effects, although in either cases losing a satellite will increase the DOP values. For a static receiver the change in the measured carrier phase is the result of the satellite s motion along its orbit (equation 7). By differentiating two time adjacent carrier phase measurements (from now on, carrier phase time difference) the number of cycles obtained scaled by the frequency gives the total displacement the satellite suffered during that period of time. If the satellite [13] and receiver velocity is known, the expected change in carrier phase measurement (predicted Doppler) can be computed and should approximate the carrier phase time difference (ideally it should be equal to it). To clarify, the predicted Doppler should be equal to the carrier phase time difference as long as the measurement is cycle slip free. Therefore, when a cycle slip happens, the difference between these two will reflect the actual carrier phase jump which can then be used to correct it. Since the predicted Doppler will have an error associated to its prediction, the cycle slip detection is done against a threshold times the standard deviation of the residual observed until the previous epoch. In a familiar manner to the other algorithms the threshold will set a sensitivity threshold which should be in accordance to the measurements and prediction quality. The direction cosines in a static application can be considered the ones from the previous epoch, however in a dynamic situation this could lead to an increased error level.

5 5 Comparison Each of these detectors has its shortfalls when detecting cycle slips. The Melbourne-Wübbena detector can detect most cycle slips, but it will not be able to detect cycle slips of equal value happening in both frequencies at the same time or a cycle slip less than or equal to three widelane cycles [14]. For the TECR detector the detection is very difficult when the combination is a multiple of (77, 60) in L1 and L2 respectively [11]. In the LG detector the detection is prone to false positives under ionospheric scintillation. On the other hand the predicted Doppler detector is also limited by the quality of the predictions and the measurements used, otherwise it can detect any cycle slip combination on the L1 and L2 signal, as it only relies on single frequency data. In the end, all these cycle slip detector will be influenced by the wind up effect that isn t being removed. As this effect can lead to errors up to one wavelength (one cycle slip), correcting the carrier phase when such value is detected can degrade the solution as it might not be an actual cycle slip. To minimise this, the detection should only be done when at least two of these detectors assume that a cycle slip is present in the data. Using more than one detector also allows the detection mechanism to be less prone to false positives. Testing the solution In order to test the effectiveness of the proposed solution, one set of data was modified in order to contain an artificial cycle slip at a random time and the several algorithms were used to detect and correct that slip. To ease with the discussion only one satellite was chosen for this discussion. The cycle slip detection is important in order to reinitialise the ambiguity estimation process or correct the carrier phase value, otherwise the impact on it can be quite dramatic. To understand this, figure 1(a) shows the ambiguity N 1 N 2 estimated with the effect of a cycle slip introduced on the L2 carrier phase measurement. On the other hand, figure 1(b) displays the N 1 N 2 with the cycle slip corrected. The impact of the cycle slip is noticeable and when corrected, the estimation does not diverge and shows the same behaviour as if the cycle slip was not introduced (Figure 1(c). (a) Cycle slip left without correction (b) Cycle slip detected and corrected IV. GAP REGENERATOR The loss of lock can be permanent or momentary as it can be caused by shadowing, multipath and atmospheric effects. In some cases this can lead to a significant deterioration of the estimated solutions as it was observed on April. At this time, the receiver was hanging over the laboratory s window with an acceptable view of the sky but in a strong multipath environment. As a consequence of that, a loss of lock to one of the satellites was seen during brief periods of time repeated in short succession, causing discontinuities in the estimated solutions (Figure 2(a)). With the intervention of the gap regenerator the epochs with missing data were filled with the computed predictions, removing the discontinuities (Figure 2(b)). In the same way, precision also improved showing approximately an increase of 50% in CEP95 and 65% for SEP95 (Table II). These (c) No cycle slip added Fig. 1: Influence on the ambiguity estimation by the cycle slip (10 cycles) on L1

6 6 TABLE II: Precision values obtained with and without the gap regenerator (April) (a) Without regeneration (b) With regeneration Fig. 2: Regeneration impact on ENU coordinates metrics were obtained using a SPP algorithm, more precisely a weighted least squares (WLSQ). The code and carrier phase measurements predictions quality will have an impact on the regeneration and if they are done for a long period of time the error will increase drastically. To avoid that it is important to reset them whenever possible, that is, by using an observed measurement as a prediction for the next epoch. Apart from the measurements noise the next prediction is quite precise and near the actual observed value. If such precaution is not taken the error will increase. Kinematic data In the previous example the receiver was immobilised in IST s north tower roof, however to validate the proposed solution the receivers were transported to a car and several trips were done inside Lisbon. During the first trials two receivers were taken from the laboratory, Pro Flex and ublox, and several trips were done inside IST in order to be present in a strong multipath environment. However, mostly due to that the Pro Flex had a difficult time obtaining at least four satellites and only a few epochs contained data (this was 2D 3D Metric Standard Deviation Without Regeneration (m) With Regeneration (m) DMRS CEP CEP MRSE SEP SEP σ east σ north σ up already something observed in the laboratory, while using it in the window s ledge, without the wood support). Therefore, only the ublox receiver (single frequency receiver) was used for these trials. Besides this, the velocity computed using the IMU was highly unstable, with the velocity quickly changing with the car s braking, turning and quick changes in velocity. Because of that, new trials were repeated on a open road where speed could be maintained constant in order to have an approximation of the velocity that would have been reported by the IMU. With that in mind, IP7 was chosen for these test due to its length, low traffic and a particularly of this road, a small tunnel. The tunnel is something interesting it causes a natural loss of lock, thus enabling the data regeneration to be evaluated. The following results refer to an approximate five minute travel that started near the connection with IC-17 and stopped near Telheiras (South direction). When approaching the tunnel, multipath starts to increase as more reflections are present, which leads to a lower accuracy level until no solution is provided, when inside the tunnel (Figure 3(a)). On the other hand, using the data regeneration mechanism the accuracy should improve as more data is available (Figure 3(b)). Comparing both figures it can be seen that the regeneration mechanism actually produced a more accurate result. Despite being an expected result, when comparing the predictions with the actual measurements the error is sometimes much bigger than in static operation, something to which the lack of an accurate velocity contributes too. However, to understand if this is really a problem of the predictions and the inaccurate velocity, the data regeneration was also done using the receiver s Doppler measurement. Looking at Figure 5 it is possible to see for four satellites that the pseudorange error in both cases is close to each other, meaning that the predictions are in agreement with the receiver s measurements. Although, in some epochs, especially after the loss of lock, the error using the receiver s Doppler measurement is quite high. This might be due to the reacquisition process which might explain a reduced quality in the measurements. To end this discussion, figure 4 shows the actual path obtained using the receiver s Doppler measurements and in comparison to the

7 7 (a) Without data regeneration (a) Prediction error for satellite with PRN 3 (b) With data regeneration Fig. 3: Benefits of data regeneration for kinematic data TM (Google Earth mapping service) (b) Prediction error for satellite with PRN 11 Fig. 5: Pseudorange error near IP7 s tunnel Fig. 4: Data regeneration using receiver s Doppler measuretm ments (Google Earth mapping service) previous two, it is even worse. V. P RECISE P OINT P OSITIONING Better precision and accuracy can be achieved by estimating the carrier phase ambiguities, therefore cycle slip removal is important as mentioned before. If such effect is removed from the carrier phase measurements, the performance of the PPP algorithm is not affected. In order to understand how different algorithms affect performance metrics, tables III and IV show these metrics for a recursive least squares and an extended Kalman filter. The following description is based on the recursive least squares values and the differences between the extended Kalman filter are pointed out. Comparing the 2D metrics when using IGS s final products to the ones obtained by using only broadcast information there is an increase of precision around 35%. The usage of GMV s higher precise clock is also showing benefits regarding the final products. A similar observation can be done when using the extended Kalman filter. Following a similar trend, the 3D metrics are also improved by the precise products with an increase in precision over 50%. However in this case GMV s products are outperformed by IGS s final products, approximately by 15% less. In the extended Kalman filter this is also happening but the percentage is smaller, however it is still approximately 10% higher. Regarding the standard deviations the value for the horizontal coordinates, east and north, is similar in almost every case.

8 8 TABLE III: Recursive Least Squares - Performance metrics 2D 3D Standard Deviation Metric Broadcast (m) IGS (m) GMV (m) DMRS DMRS CEP CEP MRSE MRSE SEP SEP σ east σ north σ up TABLE IV: Extended Kalman Filter - Performance metrics 2D 3D Standard Deviation Metric Broadcast (m) IGS (m) GMV (m) DMRS DMRS CEP CEP MRSE MRSE SEP SEP σ east σ north σ up Apart from that, the precise products are providing better north and up deviations, with the exception of the sequential filter which is also showing a smaller deviation in the up coordinate. Finally, each algorithm seems to be performing equally well and within decimetre levels. VI. CONCLUSIONS Achieving PPP requires the use of precise products that can be obtained from the Internet from several sources, however, the most common and used is IGS which has been functioning since PPP is being seen as a successor to the common DGPS techniques, especially for areas of difficult access. Nevertheless, the push for more rapid and accurate precise products are seen as a great motivation to further develop and improve PPP techniques with a shift for real time operation. However one of the main pitfall for PPP is the presence of cycle slips in the data, which should increase with the approaching solar maximum in A solution was proposed in this work in order to detect and repair cycle slips in GPS data and to benchmark its performance, this solution was compared to several known detectors under different situations. The testing was done with real data modified with false cycle slips in order to test the detection and repair mechanism. The predicted Doppler offered a good performance and allowed the detection and correction of every artificial cycle slip. Regarding its flaws, the predicted Doppler detector, as the others is prone to mis detection due to changing receiving conditions, higher noise levels and wind up effect. The wind up effect can cause small changes (up to one cycle) in the carrier phase and thus be interpreted as a cycle slip. To avoid that, the several algorithms are used together to decide when a cycle slip is observed or not. As mentioned before, the precision is affected by the receiving conditions and the observed satellite constellation. When such changes happen the precision can be greatly decreased. If this loss of lock is brief it might be possible to regenerate the signal and improve the final precision. Such thing was observed in April and the results showed that the regeneration mechanism works for small periods, as the prediction error is still small. Finally an IMU was used to test the developed solution in the road, but due to slopes, turns and bumps in the road the velocity obtained in the IMU was not reliable thus its results were abandoned. The car s cruise control was used instead in order to have an approximate value of the real velocity. IP7 was chosen as the road to make this test with the cruise control. However, the predictions in this environment were not as good as expected and the error reached several metres of error with the same being observed using the receiver s Doppler measurements. This higher error did not allow the performance of cycle slip detection. In the end, the proposed solution seems to work both in static and kinematic, however under kinematic operation the Doppler measurement seem to be quite unpredictable and cycle slip detection could not be done, but data regeneration still seems to be possible as observed. ACHIEVEMENTS This work allowed the development of a research set up for MATLAB that can easily help users observe and analyse GPS data, through the several implemented algorithms, the graphical user interface (GUI) and the automated reports. However, the major achievements are resumed to the data regenerator and predicted Doppler cycles slip detector. These two algorithms provide a way to increase the satellite availability by predicting absent epochs of data and detecting and correcting cycle slips in the carrier phase data. The predicted Doppler detector can also be used under single frequency operation and allows detection of most cases if the quality of the provided measurements are good. FUTURE WORK The developed software allows future work to be developed under PPP, cycle slip detection and correction, usage of IMU and atmosphere monitoring. For PPP, more filters can be used along with other masks and metrics to allow a better precision to be achieved. Besides that, there is still room to improve by correcting the geophysical fluids interaction, moon and sun interaction, phase wind up,

9 9 among others. Integer ambiguity fixing and back smoothing can also lead to better results and should be investigated. As for cycle slip detection and correction, the usage of IMUs can be improved in order to provide not only support to the detection and correction loop, but also for navigation purposes. A tight or loose integration technique might be used to continuously try to track the IMU s drift using filters such as an extended Kalman filter. However, these devices seem to be better at attitude determination rather than estimating the velocity of a vehicle. Atmosphere monitoring is also something quite interesting that PPP has been used for over the last years. Most recently a service by the UNB provides precise troposphere products in a similar manner to IGS. Therefore, PPP can be used to model the troposphere and ionosphere, especially in the last case to remove the second order error which can still be quite large for PPP applications. Finally, the developed software can be used to develop an online PPP service to provide the community with another (free) alternative for the current deployed ones. ACKNOWLEDGMENT This research was partially supported by the scientific project PTDC/EEATEL/122086/2010. The authors gratefully acknowledge IGS for providing GPS data and ephemerides. GMV for the support given throughout the work. REFERENCES [1] J. Ray, D. Dong, and Z. Altamimi, IGS reference frames: status and future improvements, GPS Solutions, vol. 8, no. 4, pp , Sep [Online]. Available: s x [2] G. Strang and B. Borre, Linear Algebra, Geodesy and GPS, 1st ed. Wellesley-Cambridge Press, [3] P. Misra and P. Enge, Global Positioning System, 2nd ed., [4] S. Bisnath and Y. Gao, Current state of precise point positioning and future prospects and limitations, Observing our Changing Earth, pp , [Online]. Available: index/l u1r7.pdf [5] J. Kouba, A guide to using International GNSS Service (IGS) products, [Online]. Available: resource/pubs/usingigsproductsver21.pdf [6] B. Hofmann-Wellenhof, H. Lichtenegger, and E. Wasle, GNSS - Global Navigation Satellite Systems. Austria: Springer Wien New York, [7] B. Witchayangkoon, Elements of GPS precise point positioning, Ph.D. dissertation, Maine, [Online]. Available: com/uploads/167\ 0.pdf [8] E. D. Kaplan and C. J. Hegarty, Eds., Understanding GPS - Principles and Applications, 2nd ed. Artech House, [9] R. Fang, C. Shi, Y. Lou, and Q. Zhao, Real Time Cycle-slip Detection of GPS Undifferenced Carrier-phase Measurements, Proc. SPIE 7285, International Conference on Earth Observation Data Processing and Analysis (ICEODPA), [Online]. Available: https: //proceedings.spiedigitallibrary.org/proceeding.aspx?articleid= [10] G. Blewitt, An Automatic Editing Algorithm For GPS Data, GEOPHYSICAL RESEARCH LETTERS, vol. 17, no. 3, pp , [Online]. Available: GL017i003p00199.pdf [11] Z. Liu, A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver, Journal of Geodesy, vol. 85, no. 3, pp. 1 13, Nov [Online]. Available: http: // [12] B. R. Mahafza, Radar Systems - Analysis and Design Using MATLAB, 2nd ed. Chapman & Hall/CRC, [13] B. W. Remondi, Computing satellite velocity using the broadcast ephemeris, GPS Solutions, vol. 8, no. 3, pp , Aug [Online]. Available: upn03yqpajtf9m91/ [14] S. Bisnath, Efficient, automated cycle-slip correction of dual-frequency kinematic GPS data, proceedings of ION GPS, [Online]. Available: