Carrier Phase Tracking of Weak Signals Using

Carrier Phase Tracking of Weak Signals Using Different Receiver Architectures M.G. Petovello, C. O’Driscoll and G. Lachapelle Position, Location and Navigation (PLAN) Group Department of Geomatics Engineering Schulich School of Engineering University of Calgary

BIOGRAPHIES Dr. Mark Petovello is an Assistant Professor in the Position, Location and Navigation (PLAN) group in the Department of Geomatics Engineering at the University of Calgary. Since 1998, he has been involved in various navigation research areas including software receiver development, satellite-based navigation, inertial navigation, reliability analysis and dead-reckoning sensor integration. Dr. Cillian O’Driscoll received his Ph.D. in 2007 from the Department of Electrical and Electronic Engineering, University College Cork. His research interests are in the area of software receivers for GNSS, particularly in relation to weak signal acquisition and ultra-tight GPS/INS integration. He is currently with the Position, Location and Navigation (PLAN) group at the Department of Geomatics Engineering in the University of Calgary. Dr. Gérard Lachapelle is a Professor of Geomatics Engineering at the University of Calgary where he is responsible for teaching and research related to location, positioning, and navigation. He has been involved with GPS developments and applications since 1980. He has held a Canada Research Chair/iCORE Chair in wireless location since 2001 and heads the PLAN Group at the University of Calgary. ABSTRACT This paper investigates four receiver architectures and their ability to track the carrier phase signal under attenuated environments. The receiver architectures considered include a standard receiver, an estimator-based receiver, a vector-based receiver and an ultra-tight GPS/IMU receiver. The receiver architectures were implemented in software and tested using pedestrianbased data collected in open-sky environments but attenuated using a variable signal attenuator. To assess the performance of the different receivers, their phase

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lock indicator values and carrier phase-based positioning quality were compared. Unexpectedly, the vector-based receiver did not perform very well and more work is needed to understand why this is the case. Of the remaining receivers, the ultra-tight receiver performed best, the estimator-based receiver performed second best and the standard receiver performed the worst. The ultra-tight receiver provided about 7 dB and 3 dB of sensitivity improvement over the standard and estimator-based receivers. INTRODUCTION High-sensitivity GNSS (HSGNSS) receivers are capable of providing satellite measurements for signals attenuated by approximately 30 dB (Fastrax 2007; SiRF 2007; ublox 2007). This capability is impressive and extends positioning applications dramatically. However, the focus of HSGNSS is generally on pseudorange measurements, thus limiting obtainable positioning accuracy to the order of tens of meters. In contrast, real-time kinematic (RTK) positioning capability (i.e., centimeter-level) in degraded environments has not received as much attention, even though many systems require – or could benefit from – such high positioning accuracy. Some potential benefits of RTK positioning include precise relative positioning of two (or more) vehicles (e.g., for autonomous vehicle operation), precise relative motion over time (e.g., for system/sensor calibration) and enhanced personal navigation/personnel tracking accuracy. Even if RTK positioning is not possible, the use of a float ambiguity solution (instead of fixed ambiguity solution with RTK) would provide tremendous improvements over pseudorange-based algorithms, primarily in terms of multipath mitigation. Unfortunately, carrier phase tracking requirements are much more stringent than those for pseudorange or carrier frequency, and loss of carrier lock is likely when the received GNSS signals are weaker than normal. As such, RTK positioning is generally

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reserved for environments where the GNSS signals received at the user’s antenna have minimal attenuation. Given the above, it is highly desirable to investigate means to extend the carrier phase tracking capability of GNSS receivers to include weaker signal environments. In this paper, four receiver architectures are investigated in terms of their carrier phase tracking and RTK positioning capabilities. The first is a standard receiver architecture employing individual tracking loops for each satellite being tracked. The second is a Kalman filterbased (or, more generally, estimator-based) tracking loop architecture where the traditional discriminators and loop filters are replaced by a Kalman filter (e.g., Psiaki 2001; Psiaki and Jung 2002). The third architecture is a vectorbased approach that uses the navigation solution (i.e., position, velocity and estimated clock errors) to drive the code and frequency numerically controlled oscillators (NCOs) directly (Spilker 1994; Petovello and Lachapelle 2006; Lashley and Bevly 2007). The idea here is that by exploiting the common position/velocity of the antenna receiving the signals, the signal tracking performance can improve. Although the carrier phase tracking is not performed explicitly in this manner, carrier phase tracking should be improved because of better frequency tracking. Finally, an ultra-tight receiver is used. The ultra-tight receiver is similar to the vector-based receiver except that it includes an inertial measurement unit (IMU) to improve overall performance (e.g., Gebre-Egziabher et al. 2005; Landis et al. 2006; Ohlmeyer 2006). All four receiver architectures were implemented in a software-based receiver. Use of a software-based receiver allows the relevant receiver parameters to be set equal, thus allowing for a fair comparison of results. A pedestrian-based test was conducted to assess the relative performance of the different receiver architectures. Using PLL lock indicators as a performance metric, results show that for strong signals the ultra-tight receiver is best, the estimator-based receiver was second best, the vector-based receiver is third best and the standard receiver is worst. For the same test however, once the received signal power is decreased (using a variable signal attenuator), the vector-based approach shows poorer performance than the standard receiver, while the ultra-tight receiver continues to provide the best results followed closely by the estimatorbased architecture. In terms of RTK positioning capability, the ultra-tight receiver shows about 4 dB sensitivity improvement over the estimator-based receiver, 7 dB improvement over the standard receiver and about 14 dB improvement over the vector-based receiver. The main objective of the paper is to compare the relative performance of the different receiver architectures. As ION NTM 2008 Conference - San Diego, CA, Jan 28-30, 2008

such, the coherent integration times are limited to 20 ms. Although this will limit the weakest signal that can be tracked, it will provide a good understanding of the strengths and weaknesses of the different architectures. This information can then be used when extending coherent integration times beyond the 20 ms considered herein. The paper begins with a quick review of the different receiver architectures used. The pedestrian-based test is then described and the results are presented and analyzed. METHODOLOGY In terms of tracking, the basic objective of any GNSS receiver is to generate a local signal that most accurately matches the one being received. In standard receiver architectures, this is done on a satellite-by-satellite basis (one satellite per channel) with no information being shared or communicated between tracking channels. This approach is therefore sometimes called “scalar tracking”. Estimator-based receivers try to improve on traditional receiver implementations by replacing the code, carrier and frequency discriminators and loop filters with a single Kalman filter (Psiaki 2001; Shin 2001; Psiaki and Jung 2002). However, because all of the signals are being received by a common antenna they are inherently related to each other via the position and velocity of the antenna. Vectortracking receiver architectures aim to observe the position and velocity of the antenna directly in an attempt to improve signal tracking (Spilker 1994; Pany and Eissfeller 2006; Petovello and Lachapelle 2006). Ultratightly integrated GNSS/IMU receivers are, in many ways, an extension of vector-tracking wherein an IMU is used to improve positioning capability (Sennott and Senffner 1997b; Sennott and Senffner 1997a; Gustafson et al. 2000; Kreye et al. 2000; Alban et al. 2003; Gustafson and Dowdle 2003; Kim et al. 2003; Jovancevic et al. 2004; Soloviev et al. 2004a; Soloviev et al. 2004b; Gebre-Egziabher et al. 2005; Pany et al. 2005; Landis et al. 2006; Ohlmeyer 2006). Standard (scalar), estimator-based, vector-based and ultratight receiver architectures are presented in the following sections along with a brief discussion of their relative merits and drawbacks. Standard Receiver The standard (scalar-tracking) receiver architecture is shown in Figure 1. Down-converted and filtered samples are passed to each channel in parallel. The samples are then passed to a signal processing function where Doppler removal (baseband mixing) and correlation (de-spreading) is performed. The correlator outputs are then passed to an 2/11

error determination function consisting of discriminators (typically one for code, frequency and phase) and loop filters. The loop filters aim to remove noise from the discriminator outputs without affecting the desired signal. It is noted that the receiver will have discriminator and loop filter pairs for code tracking and one or both for carrier phase and frequency tracking. More information on discriminators and loop filters is available in Ward et al. (2006). Finally, the local signal generators – whose output is used during Doppler removal and correlation – are updated using the loop filter output. As necessary, each channel’s measurements are incorporated into the navigation filter to estimate position, velocity and time.

Signal Processing Local Signal Generator

Discriminator & Loop Filter

The benefit of the Kalman filter for error estimation is that is allows for weighting of the measurements (correlator outputs, in this case) based on their estimated accuracy. In this case, the weighting is based on the receiver’s estimate of the carrier-to-noise density ratio ( C / N o ). This contrasts with traditional loop filters which assume all measurements (from the discriminators) contain an equal amount of information. This “adaptive” measurement weighting associated with the Kalman filter should improve signal tracking performance in weaker signal environments.

Signal Processing Local Signal Generator

Channel 1 Channel 2 Channel k

Kalman Filter

Channel 1 Channel 2 Channel k

Navigation Filter Navigation Filter

Figure 2 – Estimator-Based Receiver Architecture Figure 1 – Standard Receiver Architecture The benefits of scalar-tracking are the relative ease of implementation and a level of robustness that is gained by not having one tracking channel corrupt another tracking channel. However, on the downside, the fact that the signals are inherently related via the receiver’s position and velocity is completely ignored. Furthermore, the possibility for one tracking channel to aid another channels is lost. For more information on scalar-tracking, refer to Spilker (1994), Van Dierendonck (1995), Misra and Enge (2001) or Ward et al. (2006). Estimator-Based Receiver In the estimator-based receiver architecture, the discriminator and loop filters for the code, carrier and/or frequency tracking loops in a standard receiver are replaced by a single Kalman filter. Other comparable estimators could also be used, although the Kalman filter is well suited for this purpose. The overall receiver architecture is shown in Figure 2; the red elements highlight differences relative to the standard receiver.

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The structure of the Kalman filters can take any suitable form, as for example, in Psiaki (2001), Jee et al. (2002), Psiaki and Jung (2002), Abbott and Lillo (2003), Ziedan and Garrison (2004) or Petovello and Lachapelle (2006). For this work, option #1 from the latter citation is adopted because it provides reasonable results and is relatively easy to implement.

Vector-Based Receiver In contrast to scalar-tracking (using either a standard or estimator-based approach), vector-tracking estimates the position and velocity of the receiver directly. The vectortracking architecture implemented for this study is shown in Figure 3; the red elements highlight differences relative to the estimator-based receiver. Effectively, the individual tracking loops are eliminated and are replaced by the navigation filter. With the position and velocity of the receiver known, the feedback to the local signal generators is obtained from the computed range and range rate to each satellite. It is also noted that, for efficiency, many studies use/suggest a federated or cascaded approach to implement the vector-based or ultra-tight receiver 3/11

architectures (Abbott and Lillo 2003; Kim et al. 2003; Jovancevic et al. 2004; Ohlmeyer 2006; Petovello and Lachapelle 2006). In this case, each channel has an associated Kalman filter that estimates the tracking errors for that channel. This is illustrated in Figure 3. The advantage of this is two fold. First, depending on the implementation of the navigation filter, it can reduce the order of the navigation filter state vector. Second, the output from the local filter can be sent to the navigation filter at a lower rate, thus improving efficiency. It is noted that in Figure 3, feedback to the NCO is made from the Kalman filter and the navigation solution. The Kalman filter is used for the carrier phase, since the navigation solution accuracy (or the temporal variability of the navigation solution) is insufficient for carrier phase tracking.

a set of mechanization equations. The navigation filter is also updated to include the inertial error states.

Signal Processing Local Signal Generator

Kalman Filter

Channel 1 Channel 2 Channel k

Navigation Filter

Signal Processing Local Signal Generator

Kalman Filter IMU

Mechanization Equations

Figure 4 – Ultra-Tight Receiver Architecture

Channel 1 Channel 2 Channel k

Navigation Filter Figure 3 – Vector-Based Receiver Architecture The primary advantages of vector-tracking are; noise is reduced in all channels making them less likely to enter the non-linear tracking regions; it can operate with momentary blockage of one or more satellites; and it can be better optimized than scalar-tracking approaches (Spilker 1994). Vector-tracking is also able to improve tracking in weak-signal or jamming environments, especially when integrated with inertial sensors (Gustafson et al. 2000; Ohlmeyer 2006; Pany and Eissfeller 2006). The primary drawback is that all satellites are intimately related, and any error in one channel can potentially adversely affect other channels.

The drawbacks of the ultra-tight receiver are the same as those listed for the vector-based receiver. In terms of benefits however, the ultra-tight receiver should outperform the vector-based receiver because the inertial sensors can measure the actual antenna motion between navigation filter updates whereas the vector receiver would have to predict the navigation solution forward using past estimates, thus introducing more error. This is particularly important when coherently integrating over longer time intervals where predicting the navigation solution may introduce additional attenuation. It should be noted that the inertial sensors are only able to compensate for changes in the antenna-to-satellite geometry; including lever-arm effects between the IMU and GPS antenna and phase wind-up effects. In other words, it provides no benefit if the received signal varies because of “non-geometric” effects such as receiver clock errors, multipath or interference. Although this would seem to be a positive effect, care should be exercised since it has been observed that, in some instances, this can generate measurement biases in the carrier phase.

Ultra-Tight Receiver

Software Implementation

The ultra-tight integrated receiver architecture is similar to that of the vector-based receiver and is shown in Figure 4; red elements highlight difference from the vector-based approach. The difference is the inclusion of an IMU and

The above four receiver architectures have been implemented in different versions of the University of Calgary’s GSNRx™ (GNSS Software Navigation Receiver) software suite. The software is configurable to select the maximum coherent integration time, tracking

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loop filter parameters, the type of navigation solution (least squares or Kalman filter), etc. The source code is modular to allow extensive code re-use; an important consideration given the comparisons to be made later.

not affected by the variable attenuator, it is able to track all satellites in view and provide high quality carrier phase data therefrom. This data, in turn, is used to generate a reference solution.

The software is currently configured to acquire and track GPS L1 C/A code only. For the vector-based and ultratight cases, the receiver was initialized using the estimator-based tracking architecture. Once the receiver was able to extract system time and a valid ephemeris, it switched to vector-based or ultra-tight mode. For the ultra-tight implementation, the INS mechanization equations were implemented in the local-level frame (Jekeli 2000). The Kalman filter estimated the position, velocity and attitude errors as well as the IMU gyro and accelerometer biases. The latter were modeled as first order Gauss-Markov processes as in, for example, Petovello (2003).

Data from a MEMS-grade Crista IMU was also collected, but unfortunately was later found to be corrupt due to data logging problems.

DATA COLLECTION Live pedestrian-based GPS data was collected in order to assess the performance of the system. The following sections described the setup in more detail.

Equipment A schematic of the test setup is shown in Figure 5. The data was collected in an open sky environment with a few nearby multipath sources. In order to decrease the received signal power, a variable attenuator with a range of 0-60 dB was inserted prior to the front-end, which in this case consisted of a NovAtel Euro 3M receiver outputting complex samples at 20 MHz. The complex samples are then passed to an FPGA (Field Programmable Gate Array) that restructures the data more compactly before forwarding them to the PC via a National Instruments data acquisition card. The samples are stored on the PC and can be processed in post-mission using the GSNRx™ software. The rover equipment consisted of a test antenna, as well as a NovAtel SPAN™ (Synchronized Position Attitude Navigation) system. The SPAN™ system consists of a NovAtel OEM4 receiver and an IMU; in this case a Honeywell HG1700AG11 (“HG1700”). The HG1700 is a tactical-grade IMU with specifications listed in Table 1 (Honeywell 1997). It is important to note that the SPAN™ antenna was not connected to the attenuator, thus the data consists of strong signals only. Raw GPS measurements were logged from the SPAN™ system at 1 Hz and raw IMU data was logged at 100 Hz. The role of the SPAN™ system is two-fold. First, the inertial data is time tagged and can therefore be more easily integrated into the (post-mission) ultra-tight receiver software. Second, because the SPAN antenna is ION NTM 2008 Conference - San Diego, CA, Jan 28-30, 2008

Table 1 – Honeywell HG1700AG11 Specifications Specified Value Parameter Gyro Accelerometer Bias (1σ) 1 deg/h 1 milli-G Scale Factor (1σ) 150 ppm 300 ppm Misalignment (1σ) 500 μrad 500 μrad The NovAtel Euro 3M receiver was driven by an external oscillator; in this case a Symmetricom 1000B OCXO. This oscillator is very stable over time intervals of several seconds and has been shown to allow coherent integration of up to 15 s with only about 1 dB worth of attenuation due to phase and frequency errors (Watson et al. 2007). Such an oscillator is currently unfeasible for massdeployment due to its high cost. It was included during testing to better assess the best possible performance of an ultra-tight receiver. The results presented below should therefore be considered in this light. Ultimately, the performance (and thus benefit) of the ultra-tight receiver for weak-signal tracking will also be influenced by the oscillator (Watson et al. 2007). In addition to the rover equipment, a NovAtel OEM4 receiver was setup on a nearby pillar with known coordinates to act as a base station. The receiver’s raw GPS measurements were logged to file and were used for RTK processing. The base station data logging PC was also used to control the variable attenuator. The base station receiver maintains accurate time throughout the test (i.e., not affected by the attenuator) and was therefore used to time tag the changes in the attenuator levels.

Test Description In total, the test lasted just over 14 minutes and seven satellites were in view. The rover was initialized in a static position for approximately 4.25 min. The initialization was performed without any signal attenuation (i.e., attenuation of 0 dB) to allow sufficient time for the software receiver to acquire all available satellites and their ephemeris. More importantly however, the initialization provides a time period during which the ambiguities can be reliably fixed to integers prior to motion.

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Static Antenna

Backpack Variable Attenuator

HG1700 IMU

RS-232

NovAtel OEM4 RS-232

NovAtel Euro 3M

NovAtel SPAN Receiver

Laptop PC

I/Q Samples

PPS

FPGA

Crista IMU RS-232

PC

PC/104

Software Rx (GSNRx™)

External Oscillator

Figure 5 – Schematic of Test Setup Following the initialization, and with the attenuator still set at 0 dB, the system was carried in a rectangular pattern spanning roughly 8 m north/south and 3 m east/west, as shown in Figure 6. The rectangular pattern was traversed in both clockwise and counter-clockwise directions. After approximately 4.5 min of walking, the signals were attenuated at a rate of 1 dB every four seconds until a maximum attenuation of 60 dB was reached. The same rectangular walking pattern was maintained during the attenuation phase of the test.

only GPS data and to wait 60 seconds before trying to resolve the ambiguities. Unfortunately, the data from the base station was logged at 1 Hz, instead of at 20 Hz. Although this poses no significant problem (it merely limits the RTK output rate), it means that fewer solutions are available at each attenuation level.

The maximum speed of the antenna during the test was just below 1.6 m/s. However, the measured acceleration had a peak-to-peak range of about 10 m/s2 in each coordinate direction. Furthermore, because this acceleration was induced mostly from the walking motion (and less so from the actual trajectory), it is present throughout the data set with a period of roughly 2 Hz.

Data Processing As mentioned before, the complex samples were processed using the University of Calgary’s GSNRx™ software. To reduce processing time, the data were down-sampled from 20 MHz to 5 MHz. For the standard receiver an FLL-assisted-PLL was used for carrier tracking. Relevant receiver settings are shown in Table 2. The output from each software receiver implementation was then processed using the University of Calgary’s FLYKIN+™ processing software, as described in Liu et al. (2003). FLYKIN+™ uses double difference processing and on-the-fly carrier phase ambiguity resolution to obtain centimeter-level positioning accuracies. The software was configured to process L1ION NTM 2008 Conference - San Diego, CA, Jan 28-30, 2008

Figure 6 – Trajectory Relative to Base Station The reference solution was obtained using the University of Calgary’s SAINT™ (Satellite And Inertial Navigation Technology) software, as described in Petovello (2003) and Petovello et al. (2003). The SAINT™ software processes GPS and IMU data and is able to resolve the carrier phase ambiguities on-the-fly. For the test considered here, the GPS data logged by the SPAN™ receiver was used to generate the reference solution because it is not affected by the signal attenuator and is also independent of the data generated by the GSNRx™

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software. The solution was then translated to the second antenna using the measured lever-arm (roughly 0.5 m long) and the estimated INS attitude. The carrier phase ambiguities were resolved prior to, and remained fixed throughout, the kinematic portion of the test. The accuracy of the solution is on the order of 1-2 cm.

Table 2 – Software Receiver Settings Standard Ultra-Tight Parameter Receiver Receiver Max Coherent 20 ms Integration Carrier-Aided DLL 0.05 Hz N/A Loop Bandwidth FLL Loop Bandwidth 8 Hz N/A PLL Loop Bandwidth 5 Hz N/A Measurement Output 20 Hz

considerably more signal dynamics than on PRN 22. This is evidenced by the observed sharp decreases in the PLI values. These decreases in PLI correlate with changes in walking direction, which cause the signal Doppler to vary and thus cause phase tracking errors. The most surprising result in Figure 8 is that the vector-tracking receiver appears to be the most sensitive to these periods of increased signal dynamics. In fact, the vector-based receiver actually loses lock around time 415195 (note the time offset in the x-axis of the figure). This behavior was unexpected and more investigation is needed to fully explain why it is occurring.

DATA ANALYSIS Analysis of the results is performed in two ways. First, the phase lock indicator (PLI) values estimated from the receiver are assessed to determine each receiver’s ability to track the carrier phase. Second, the FLYKIN+™ positioning results are analyzed to determine RTK positioning performance of each receiver architecture.

Phase Lock Indicator Results

Figure 7 – PLI for PRN 22 without Attenuation

The PLI is a metric of carrier phase tracking performance generated internal to the receiver. The PLI algorithm used in this work is the one described in Van Dierendonck (1995), which is shown to be proportional to the cosine of twice the phase tracking error. However, since the PLI is itself sensitive to noise, the results considered a smoothed with a time constant of 0.4 s. To begin the analysis, we first consider the PLI values during strong signal conditions, that is, prior to attenuating the signal. To this end, Figure 7 shows the PLI for PRN 22, which had an azimuth and elevation of about 90° and 61° respectively. The satellite’s high elevation means that the level of signal dynamics experienced is minimal because motion was primarily in the horizontal plane. As a result, all receiver architectures show very good phase tracking results. The standard receiver shows the poorest performance; although still very good with a PLI of about 0.95. The other three architectures perform noticeably better, with the ultratight receiver providing marginally better performance than the others, as expected. A similar set of results for PRN 11 are shown in Figure 8. The azimuth and elevation of PRN 11 during the test was 307° and 24° respectively. The low elevation angle of the satellite means that the walking motion induces ION NTM 2008 Conference - San Diego, CA, Jan 28-30, 2008

Figure 8 – PLI for PRN 11 without Attenuation Aside from the poor performance of the vector-tracking receiver, the other receivers are still able to maintain lock throughout the data set. As with PRN 22, the PLI values are better for the ultra-tight receiver. Interestingly however, the estimator-based receiver shows similar, although slightly worse, performance compared to the ultra-tight receiver. We now shift the analysis to investigate the PLI values during signal attenuation. Figure 9 and Figure 10 show 7/11

the PLI values for PRN 22 and 11 respectively during signal attenuation. Recall that the attenuation is increased at a rate of 1 dB every four seconds, starting at time 415210 (i.e., where the results are first plotted). As expected from our previous analysis during strong signal conditions, the vector-based receiver is not able to track the carrier phase very well at all. In contrast, as signal attenuation increases, the relative improvement of the ultra-tight receiver becomes more noticeable. However, as before, the estimator-based receiver does show comparable performance. For PRN 11, both the estimator-based and the ultra-tight receiver are able to track the signal for roughly 20 s longer (equivalent to about 5 dB) than the standard receiver before losing lock.

represents a more cost effective means of improving receiver tracking performance.

Positioning Results The PLI analysis of the previous section suggests that the receivers are able to track the carrier phase of the signal with varying levels of quality. However, the PLI metric is generated internal to the receiver and does not provide an “absolute” assessment of the carrier phase data quality. To do this, the RTK positioning accuracy must be investigated. Only if the absolute phase tracking performance is good will the positioning accuracy be at the centimeter level. It is noted that for all receiver architectures, the ambiguities were able to be resolved as integers prior to attenuating the signal. The analysis that follows therefore shows how well each receiver architecture is able to maintain carrier phase tracking and the corresponding impact on RTK positioning performance. Figure 11 shows the RTK position errors for all receiver architectures as a function of signal attenuation. The signal attenuation is used in this case in order to give a quantitative assessment of performance. Although the vertical scale is relatively large (compared to expected RTK accuracy), the results are quite clear and can be summarized as follows

•

The vector-based receiver performs the worst, as expected from the PLI analysis. This is not expected and more investigation is needed to better understand why the results are so poor.

•

The standard receiver performs second worst and is able to provide centimeter-level positioning accuracy for signals attenuated by about 15 dB or less.

•

The estimator-based receiver performs second best and provides RTK-quality positions for signals attenuated by up to about 20 dB. This represents a sensitivity improvement over the standard receiver of about 5 dB.

•

The ultra-tight receiver yields the best performance. Positioning accuracy remains at the centimeter-level for signals attenuated by no more than about 23 dB. This is about 8 dB better than the standard receiver and about 3 dB better than the estimator-based receiver.

Figure 9 – PLI for PRN 22 during Signal Attenuation

Figure 10 – PLI for PRN 11 during Signal Attenuation Based on the above PLI results, the ultra-tight receiver architecture does appear to perform best. This is expected because the IMU is able to measure receiver motion and help to compensate for that motion at the tracking level. However, the estimator-based receiver provides a level of performance similar to the ultra-tight receiver. This is particularly interestingly because the estimator-based receiver does not require the use of an IMU and therefore ION NTM 2008 Conference - San Diego, CA, Jan 28-30, 2008

These positioning results agree well with the PLI analysis of the previous section. This suggests that the PLI is a reasonable indicator of the receiver’s ability to provide centimeter-level positioning accuracy (assuming the carrier phase ambiguities are resolved as integers). 8/11

Figure 11 – RTK Position Errors of Different Receiver Architectures as a Function of Signal Attenuation To get a better understanding for how the position degrades, Figure 12 shows a “histogram” for the horizontal position error as a function of maximum attenuation for different receivers. Results for the vectorbased receiver are not shown since these have already been shown to be poor. Furthermore, results are only plotted for the time period during which the attenuator was activated (before activation, position errors are always less than the lowest threshold for all receivers). The plot shows the number of epochs whose horizontal error exceeds a given threshold for all attenuation values less than the maximum. For example, for epochs with an attenuation of 20 dB or less, the standard receiver has about 24 epochs where the horizontal error exceeds 0.1 m. In contrast, for the same level of attenuation, the ultratight receiver has zero epochs where the horizontal error exceeds 0.1 m. An alternative analysis is to say that if a horizontal position error of better than 0.1 m is required, the standard receiver can tolerate no more than 14 dB of attenuation. For the same level of accuracy, the ultratight receiver can tolerate no more than 22 dB of attenuation. This represents a sensitivity improvement of 8 dB. Overall, for the different horizontal positioning thresholds, the ultra-tight receiver provides between 5 and 8 dB (average of about 7 dB) of sensitivity improvement over the standard receiver. Using a similar analysis as above, the estimator-based receiver is found to provide an average of about 3 dB improvement over the standard receiver; or about 4 dB less sensitivity than the ultra-tight receiver. A histogram of the vertical errors is shown in Figure 13. Sensitivity improvements are similar to those observed in Figure 12 for the horizontal position.

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Figure 12 – Horizontal Position Histogram for Standard, Estimator-Based and Ultra-Tight Receivers as Computed during Signal Attenuation (lines are plotted in order of increasing position error and thus histograms for larger error results may hide smaller error results)

Figure 13 – Vertical Position Histogram for Standard, Estimator-Based and Ultra-Tight Receivers as Computed during Signal Attenuation (lines are plotted in order of increasing position error and thus histograms for larger error results may hide smaller error results) It is noted that the results presented herein are based on one set of data and should not be directly extrapolated to other cases. That said, the ultra-tight receiver architecture is expected to continue to outperform the other approaches in other situations. This is particularly so in 9/11

situations where there may be a few strong signals and a few weak signals. This contrasts with the current results which looked at the case where all satellite signals were attenuated simultaneously.

CONCLUSIONS This paper investigated four different receiver architectures and their ability to track the carrier phase under attenuated signal environments; a standard receiver, an estimator-based receiver, a vector-based receiver and an ultra-tight GPS/IMU receiver. All receivers used a maximum coherent integration time of 20 ms. This was done to assess the relative performance of the different architectures. An absolute assessment (i.e., what is the weakest possible signal that can be tracked) will be conducted later based on the findings herein. Of the four receivers, the vector-based approach showed the poorest performance and further investigations are needed to understand why this is the case. The standard receiver was shown to be able to track the carrier phase and generate centimeter-level positioning accuracy for signal attenuations up to about 14 dB. In contrast, the estimator-based and ultra-tight receivers respectively provided about 4 dB and 7 dB of sensitivity improvement relative to the standard receiver. The main conclusion of this work is that the ultra-tight receiver architecture provides the best performance, as expected due to the presence of the IMU. However, the performance of the estimator-based receiver is promising and suggests that considerable tracking improvement is possible without having to radically change the receiver architecture. Furthermore, the estimator-based receiver does not require purchasing additional hardware (e.g., an IMU) and thus is a more cost-effective means of improving receiver performance.

ACKNOWLEDGMENTS The authors would like to kindly acknowledge and thank Defence Research and Development Canada (DRDC) for funding of this work.

REFERENCES Abbott, A.S. and W.E. Lillo (2003) Global Positioning Systems and Inertial Measuring Unit Ultratight Coupling Method, Patent, US 6,516,021 B1, United States, 22 pages. Alban, S., D. Akos, S.M. Rock and D. Gebre-Egziabher (2003) Performance Analysis and Architectures for INS-Aided GPS Tracking Loops, ION National Technical Meeting. Anaheim, CA, Institute of Navigation, 611-622. ION NTM 2008 Conference - San Diego, CA, Jan 28-30, 2008

Fastrax (2007) iTrax300 OEM GPS Receiver Module, Fastrax Ltd. 2007, iTrax300 datasheet. Gebre-Egziabher, D., A. Razavi, P. Enge, J. Gautier, S. Pullen, B.S. Pervan and D. Akos (2005) Sensitivity and Performance Analysis of Doppler-Aided GPS Carrier-Tracking Loops, NAVIGATION, 52(2), 4960. Gustafson, D. and J. Dowdle (2003) Deeply Integrated Code Tracking: Comparative Performance Analysis, ION GPS/GNSS 2003, Portland, OR, Institute of Navigation, 2553-2561. Gustafson, D., J. Dowdle and K. Flueckiger (2000) A Deeply Integrated Adaptive GPS-Based Navigator with Extended Range Code Tracking, IEEE PLANS, San Diego, CA, IEEE, 118-124. Honeywell (1997) Document DS34468-01 - Critical Item Development Specification HG1700AG Inertial Measurement Unit, Honeywell International, Inc. Jee, G.I., H.S. Kim, Y.J. Lee and C.G. Park (2002) A GPS C/A Code Tracking Loop Based on Extended Kalman Filter with Multipath Mitigation, ION GPS 2002, Portland, OR, Institute of Navigation, 446-451. Jekeli, C. (2000) Inertial Navigation Systems with Geodetic Applications, Berlin, Walter de Gruyter. Jovancevic, A., A. Brown, S. Ganguly, J. Noronha and B. Sirpatil (2004) Ultra Tight Coupling Implementation Using Real Time Software Receiver, ION GNSS 2004, Long Beach, CA, Institute of Navigation, 1575-1586. Kim, H.S., S.C. Bu, G.I. Jee and C.G. Park (2003) An Ultra-Tightly Coupled GPS/INS Integration Using Federated Filtering, ION GPS/GNSS 2003, Portland, OR, Institute of Navigation, 2878-2885. Kreye, C., B. Eissfeller and J.O. Winkle (2000) Improvements of GNSS Receiver Performance Using Deeply Coupled INS Measurements, ION GPS 2000, Salt Lake City, UT, Institute of Navigation, 844-854. Landis, D., T. Thorvaldsen, B. Fink, P. Sherman and S. Holmes (2006) A Deep Integration Estimator for Urban Ground Navigation, ION Annual Meeting/IEEE PLANS, San Diego, CA, Institute of Navigation and IEEE, 927-932. Lashley, M. and D.M. Bevly (2007) Analysis of Discriminator Based Vector Tracking Algorithms, ION National Technical Meeting, San Diego, CA, Institute of Navigation, 570-576. 10/11

Liu, J., M.E. Cannon, P. Alves, M.G. Petovello, G. Lachapelle, G. MacGougan and L. deGroot (2003) A Performance Comparison of Single and DualFrequency GPS Ambiguity Resolution Strategies, GPS Solutions, 7(2), 87-100. Misra, P. and P. Enge (2001) Global Positioning System Signals, Measurement, and Performance, Lincoln, MA, Ganga-Jamuna Press. Ohlmeyer, E.J. (2006) Analysis of an Ultra-Tightly Coupled GPS/INS System in Jamming, ION Annual Meeting/IEEE PLANS, San Diego, CA, Institute of Navigation and IEEE, 44-53. Pany, T. and B. Eissfeller (2006) Use of a Vector Delay Lock Loop Receiver for GNSS Signal Power Analysis in Bad Signal Conditions, ION Annual Meeting/IEEE PLANS, San Diego, CA, Institute of Navigation and IEEE, 893-902. Pany, T., R. Kaniuth and B. Eissfeller (2005) Deep Integration of Navigation Solution and Signal Processing, ION GNSS 2005, Long Beach, CA, Institute of Navigation, 1095-1102. Petovello, M.G. (2003) Real-Time Integration of a Tactical-Grade IMU and GPS for High-Accuracy Positioning and Navigation, Ph.D. Thesis, Geomatics Engineering, University of Calgary. Petovello, M.G., M.E. Cannon and G. Lachapelle (2003) Benefits of Using a Tactical Grade INS for High Accuracy Positioning, NAVIGATION, 51(1), 1-12. Petovello, M.G. and G. Lachapelle (2006) Comparison of Vector-Based Software Receiver Implementations with Application to Ultra-Tight GPS/INS Integration, ION GNSS 2006, Fort Worth, TX, Institute of Navigation, 1790-1799. Psiaki, M.L. (2001) Smoother-Based GPS Signal Tracking in a Software Receiver, ION GPS 2001, Salt Lake City, UT, Institute of Navigation, 29002913. Psiaki, M.L. and H. Jung (2002) Extended Kalman Filter Methods for Tracking Weak GPS Signals, ION GPS 2002, Portland, OR, Institute of Navigation, 25392553. Sennott, J. and D. Senffner (1997a) A GPS Carrier Phase Processor for Real-Time High Dynamics Tracking, ION Annual Meeting, Institute of Navigation, 299308.

ION NTM 2008 Conference - San Diego, CA, Jan 28-30, 2008

Sennott, J. and D. Senffner (1997b) Robustness of Tight Coupled Integrations for Real-Time Centimeter GPS Positioning, ION GPS 1997, Kansas City, MO, Institute of Navigation, 655-663. Shin, E.W. (2001) Accuracy Improvement of Low Cost INS/GPS for Land Applications, M.Sc. Thesis, Geomatics Engineering, university of Calgary. SiRF (2007) SiRFstarIII GSC3e/LP & GSC3f/LP, SiRF Technology, Inc. 2007, Product insert. Soloviev, A., S. Gunawardena and F. Van Grass (2004a) Deeply Integrated GPS/Low-Cost IMU for Low CNR Signal Processing: Flight Test Results and Real Time Implementation, ION GNSS 2004, Long Beach, CA, Institute of Navigation, 1598-1608. Soloviev, A., F. van Grass and S. Gunawardena (2004b) Implementation of Deeply Integrated GPS/Low-Cost IMU for Reacquisition and Tracking of Low CNR GPS Signals, ION National Technical Meeting, San Diego, CA, Institute of Navigation, 923-935. Spilker, J.J., Jr. (1994) Fundamentals of Signal Tracking Theory, Global Positioning System: Theory and Applications, B. W. Parkinson and J. J. Spilker, Jr., American Institute of Aeronautics and Astronautics, Inc. I, 245-327. ublox (2007) UBX-G5010, UBX-G5000, ublox ag. 2007, Product summary. Van Dierendonck, A.J. (1995) GPS Receivers, Global Positioning System: Theory and Applications, B. W. Parkinson and J. J. Spilker, Jr., American Institute of Aeronautics and Astronautics, Inc. I, 329-407. Ward, P.W., J.W. Betz and C.J. Hegarty (2006) Satellite Signal Acquisition, Tracking, and Data Demodulation, Understanding GPS Principles and Applications, E. D. Kaplan and C. J. Hegarty, Norwood, MA, Artech House, Inc., 153-241. Watson, R., M.G. Petovello, G. Lachapelle and R. Klukas (2007) Impact of Oscillator Errors on IMU-Aided GPS Tracking Loop Performance, European Navigation Conference, Geneva, Swizterland. Ziedan, N.I. and J.L. Garrison (2004) Extended Kalman Filter-Based Tracking of Weak GPS Signals under High Dynamic Conditions, ION GNSS 2004, Long Beach, CA, Institute of Navigation, 20-31.

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