Weak Signal Carrier Tracking Using Extended Coherent Integration with an Ultra-Tight GNSS/IMU Receiver
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 of RTK positioning include precise relative positioning of two (or more) vehicles (e.g., for autonomous vehicle Dr. Mark Petovello is an Assistant Professor in the operation), precise relative motion over time (e.g., for Position, Location And Navigation (PLAN) group in the system/sensor calibration) and enhanced personal Department of Geomatics Engineering at the University navigation/personnel tracking accuracy. Even if RTK of Calgary. Since 1998, he has been involved in various positioning is not possible, the use of a float ambiguity navigation research areas including software receiver solution (instead of fixed ambiguity solution with RTK) development, satellite-based navigation, inertial would provide tremendous improvements over navigation, reliability analysis and dead-reckoning sensor pseudorange-based algorithms, primarily in terms of integration. multipath mitigation. Unfortunately, carrier phase tracking requirements are much more stringent than those Dr. Cillian O’Driscoll received his Ph.D. in 2007 from for pseudorange or carrier frequency, and loss of carrier the Department of Electrical and Electronic Engineering, lock is likely when the received GNSS signals are weaker University College Cork. His research interests are in the than normal. As such, RTK positioning is generally area of software receivers for GNSS, particularly in reserved for environments where the GNSS signals relation to weak signal acquisition and ultra-tight received at the user’s antenna have minimal attenuation. GPS/INS integration. He is currently with the Position, Location And Navigation (PLAN) group at the Given the above, it is highly desirable to investigate Department of Geomatics Engineering in the University means to extend the carrier phase tracking capability of of Calgary. GNSS receivers to include weaker signal environments. Previous work in this area has investigated the use of an Dr. Gérard Lachapelle is a Professor of Geomatics ultra-tight integration of a GNSS receiver with an inertial Engineering at the University of Calgary where he is measurement unit (IMU) (e.g., Soloviev et al 2004a; responsible for teaching and research related to location, Soloviev et al 2004b; Gebre-Egziabher et al 2005; Landis positioning, and navigation. He has been involved with et al 2006; Ohlmeyer 2006; Petovello et al 2007; GPS developments and applications since 1980. He has Petovello et al 2008). The concept of ultra-tight held a Canada Research Chair/iCORE Chair in wireless integration is to use the integrated GNSS and inertial location since 2001 and heads the PLAN Group at the navigation system (INS) navigation solution to drive the University of Calgary. code and frequency numerically controlled oscillators (NCOs) directly, thereby exploiting the common INTRODUCTION position/velocity of the antenna to improve the aggregate signal tracking performance. This paper extends the High-sensitivity GNSS (HSGNSS) receivers are capable authors’ prior work on software-based ultra-tight of providing satellite measurements for signals attenuated integration with the GPS L1 C/A-code for high accuracy by approximately 30 dB (Fastrax 2007; SiRF 2007; ublox positioning (Petovello et al 2007; Petovello et al 2008). 2007). This capability is impressive and extends These previous studies used coherent integration times of positioning applications dramatically. However, the 20 ms or less to assess the relative performance of focus of HSGNSS is generally on pseudorange different receiver architectures in terms of carrier phase measurements, thus limiting obtainable positioning tracking and RTK positioning under degraded signal accuracy to the order of tens of metres. conditions. Under these conditions an ultra-tight integration strategy has been shown to provide about In contrast, real-time kinematic (RTK) positioning 7 dB of sensitivity improvement over a standard receiver capability (i.e., centimetre-level) in degraded implementation. However, 20 ms of coherent integration environments has not received as much attention, even may not provide an assessment of each receiver’s though many systems require – or could benefit from – “absolute” carrier phase tracking sensitivity. such high positioning accuracy. Some potential benefits
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In contrast, this paper uses coherent integration times up to 100 ms to assess the absolute carrier phase tracking limit and corresponding RTK positioning capabilities for an ultra-tight receiver. Furthermore, the analysis is performed with real data collected under different levels Signal Discriminator of signal attenuation. To address the most challenging Processing & Loop Filter situation, integration beyond 20 ms is accomplished by estimating the navigation data bits (or at least the data bit transitions) in real-time, as opposed to using aiding Local Signal Generator information from a nearby reference station. Channel 1 The main objective of the paper is to assess the sensitivity Channel 2 of an ultra-tight receiver in terms of carrier phase tracking Channel k and RTK positioning capability. The paper presents a Kalman filter-based tracking algorithm within an ultra- tight GNSS/IMU receiver architecture and investigates the effect of IMU quality, oscillator quality and coherent Navigation Filter integration time on the filter’s performance.
Figure 1 – Standard Receiver Architecture The paper begins with a short review of the ultra-tight integration strategy used and then proceeds to describe Ultra-Tight Receiver Architecture how extended coherent integration was performed. Covariance simulations are then presented to demonstrate In contrast to scalar-tracking, ultra-tight GNSS/IMU the expected impact of the Kalman filter tracking model integration estimates the position and velocity of the on the carrier tracking under a variety of operating receiver directly. This concept, in the absence of an conditions. A pedestrian-based test is then described and IMU, is often termed vector-tracking (Spilker 1994; Pany the RTK positioning results obtained using 20 to 100 ms & Eissfeller 2006; Lashley & Bevly 2007). In a vector- coherent integration times, in 20 ms increments, are tracking architecture, the individual tracking loops are presented and analyzed. effectively eliminated and are replaced by the navigation filter. With the position and velocity of the receiver RECEIVER ARCHITECTURE OVERVIEW known, the feedback to the local signal generators is obtained from the computed range and range rate to each This section presents a brief overview of standard and satellite. ultra-tight GNSS/IMU receiver architectures. For efficiency, many studies use/suggest a federated or Standard Receiver Architecture cascaded approach to implement the vector-based or ultra-tight receiver architectures (Abbott & Lillo 2003; The standard (scalar-tracking) receiver architecture Kim et al 2003; Jovancevic et al 2004; Ohlmeyer 2006; utilized herein is shown in Figure 1. Down-converted Petovello & Lachapelle 2006; Groves et al 2007). In this and filtered samples are passed to each channel in case, in place of the discriminator and loop filter, each parallel. The samples are then passed to a signal channel has an associated Kalman filter that estimates the processing function where Doppler removal (baseband tracking errors for that channel. Herein, this filter is mixing) and correlation (de-spreading) is performed. The referred to as the channel filter . This is illustrated in correlator outputs are then passed to an error Figure 2, which shows the ultra-tight integrated receiver determination function consisting of discriminators architecture. Direct feedback from the channel filter to (typically one for code, frequency and phase) and loop the local signal generator is used for the carrier phase filters. The loop filters aim to remove noise from the only, since the navigation solution accuracy (or the discriminator outputs without affecting the desired signal. temporal variability of the navigation solution) is It is noted that the receiver will have discriminator and insufficient for carrier phase tracking. The architecture loop filter pairs for code tracking and one or both for shown in Figure 2 has been termed a coherent ultra-tight carrier phase and frequency tracking. More information (or deep) integration strategy by Groves et al (2007) on discriminators and loop filters is available in Ward et because it uses the correlation outputs directly to update al (2006). Finally, the local signal generators – whose the channel filter. The channel filter is discussed in more output is used during Doppler removal and correlation – detail later on in the paper. 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.
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Ultra-Tight) software package. The program is written in C++ and currently acquires and tracks GPS L1 C/A code signals. Other versions of the software also implement different receiver architectures, although these are not Signal Channel Filter considered here. Processing (Kalman filter) EXTENDING COHERENT INTEGRATION TIME
Local Signal As is well known, the most efficient means of improving Generator Channel 1 post-correlation signal to noise ratio (SNR) in a GNSS receiver is to extend the coherent integration time. The Channel 2 coherent time cannot, however, be extended indefinitely Channel k for two main reasons (Watson et al 2006)
1. The presence of unknown navigation data bit transitions will negatively affect the coherent Navigation Filter integration process, thus resulting in a loss in post- correlation SNR.
Mechanization IMU 2. Any frequency error, due most likely to receiver Equations motion or receiver oscillator error, will induce an additional reduction in the SNR that increases with Figure 2 – Ultra-Tight Receiver Architecture integration time.
The drawback of the ultra-tight receiver is that, because As mentioned in the previous section, the effect of all satellite tracking channels are intimately related, any receiver motion in the second point is largely reduced by error in one channel can potentially adversely affect other the presence of the IMU in the ultra-tight integration channels. In terms of benefits however, the ultra-tight strategy. The focus therefore shifts to the effect of IMU receiver will share the same benefits as a vector-tracking errors and receiver oscillator effects. However, as will receiver, which include the following: noise is reduced in be discussed below, false frequency lock will also play a all channels making them less likely to enter the non- critical role in this regard. linear tracking regions, it can operate with momentary blockage of one or more satellites, and it can be better The algorithms presented were developed specifically for optimized than scalar-tracking approaches (Spilker 1994). the GPS L1 C/A-code signal, but can be applied to any Vector-tracking and ultra-tight integration is also able to other GNSS signal with minor modifications. improve tracking in weak-signal or jamming environments, especially when integrated with inertial Estimating Navigation Data Bits sensors (Gustafson et al 2000; Ohlmeyer 2006; Pany & Eissfeller 2006). That said, the ultra-tight receiver should The maximum likelihood approach to navigation data outperform the vector-based receiver because the inertial estimation on the fly is implemented herein. Assuming sensors can measure the actual antenna motion between the receiver has achieved bit synchronization, 20 ms navigation filter updates whereas the vector receiver coherent integration can be safely performed within a would have to predict the navigation solution forward given data bit. Assuming M consecutive 20 ms using past estimates, thus introducing more error. This is integrations, the maximum likelihood estimate of the data particularly important when coherently integrating over bits is that combination of data bit transitions that longer time intervals where predicting the navigation maximizes the combined energy in the in-phase, I and solution may introduce additional attenuation. quadra-phase, Q channels as described, for example, in It should be noted that the inertial sensors are only able to (Soloviev et al 2008). compensate for changes in the antenna-to-satellite geometry; including lever-arm effects between the IMU It is noted however that this approach does not determine and GPS antenna and phase wind-up effects. In other maximum likelihood estimates of the data bits, per se . words, it provides no benefit if the received signal varies Rather, it can only determine the maximum likelihood because of “non-geometric” effects such as receiver clock estimate of the bit transitions , of which there are M −1. errors, multipath or interference. Although this would This effectively leads to an ambiguity that needs to be seem to be a positive effect, care should be exercised handled in the channel filter. since it has been observed that, in some instances, these effects can generate measurement biases in the carrier The effect of a single bit error on the channel filter will phase. depend on the number of 20 ms integrations. For example, over one 20 ms interval ( M = 1 ), a data bit The ultra-tight integration strategy described above has error introduces 180° phase error. Over two 20 ms been implemented in the University of Calgary’s intervals ( M = 2 ), a single bit error has half the effect on GSNRx-ut™ (GNSS Software Navigation Receiver – the phase, namely 90°, and so on. However, it must be
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borne in mind that for M ≥ 2 , there is a non-zero Channel Filter Model probability of having more than a single bit error at a time. Nevertheless, it is expected that extended In this work the channel filter state vector is given by integration time will reduce the bit error rate relative to the case when 20 ms integration is performed, although xT = [ A δτ δφ δ f δa] (2) this remains to be confirmed analytically.
Effect of False Frequency Lock where A is the signal amplitude, δτ is the code phase tracking error in units of chips, δφ is the phase tracking False frequency lock is a phenomenon in which a GNSS error in units of rad, δf is the frequency tracking error in receiver continues to track a signal but at a wrong units of rad/s, and δa is the frequency rate error of the frequency (Doppler offset). This occurs when a multiple NCO in units of rad/s 2. It is noted that in the context of of one half cycle of carrier phase error is accumulated an ultra-tight GNSS/IMU receiver, this latter term models over the coherent integration interval. For example, for a the residual INS acceleration error and not the full level nominal 20 ms coherent integration, false frequency lock of line-of-sight acceleration. points occur at multiples of 25 Hz (i.e., 25 Hz x 0.02 s = 0.5 cycles). This means that as the coherent integration The system model for the filter is taken from Petovello & time increases, the false frequency lock points tend closer Lachapelle (2006) and is given by to zero, which in turn make them harder to detect.
In the context of this paper, a false frequency lock has A0 0 0 0 0 A two negative effects. First, because the tracking δτ000 β 0 δτ d frequency is in error, the receiver’s carrier phase δφ=0 0 0 1 0 ⋅ δφ measurements, which are integrated receiver Doppler dt values, will necessarily become unusable for high δf 0 0 0 0 1 δf accuracy applications. Second, a false frequency lock δa 0 0 0 0 0 δa will negatively impact the post-correlation SNR because (3) 10 0 0 0 wA the coherent integration process introduces a power attenuation given by 01β⋅ 2 π f 0 0 wδτ +002πf 0 0 ⋅ w b 2 sin ()π⋅ δ f ⋅ T 00 0 2πf 0 wd P = 10log coh (1) Att 10 2 00 0 02 π λ wa ()π⋅ δ f ⋅ T coh
where β converts from units of radians to chips, f and where δf is the frequency tracking error in units of λ radians per second and T is the coherent integration are the nominal frequency and wavelength of the coh signal being tracked, w is the driving noise of the interval. At the nearest frequency lock point (i.e., when A amplitude, wδτ is the driving noise of the code tracking δf⋅ T coh is half a cycle), the power attenuation will be 3.9 dB. This is an unacceptable level of loss for high- error that is included to account for code-carrier sensitivity applications. divergence due to the ionosphere, wb is the driving noise
for the clock bias, wd is the driving noise for the clock Given the above, there exists an inherent trade-off drift, and w is the driving noise to account for line-of- between extending the coherent integration time (to a improve post-correlation SNR) and making the receiver sight acceleration. The spectral densities for the clock more susceptible to the effects of false frequency lock. bias and clock drift are taken from the h0 and h−2 parameters used to model oscillators (e.g., Van CHANNEL FILTER DESCRIPTION Dierendonck et al 1984; Brown & Hwang 1992).
The channel filter plays a critical role in the ultra-tight The measurements used to update the channel filter are receiver architecture used in this work. It estimates the the early, prompt and late in-phase and quadra-phase tracking errors on a channel-by-channel basis and these correlator outputs. Assuming a known correlator offset error estimates are used to correct the measurements used of (e.g., for early or late correlators), the correlator to compute the receiver’s navigation solution, which in outputs are given by turn are used to drive the NCOs. Alternatively, the tracking error estimates can be used to update the sin (π⋅ δ f ⋅ T ) I=⋅⋅ ANR ()δτ −∆⋅ ⋅ cos δφ (4) navigation solution directly. In either case, if the error π⋅ δ f ⋅ T () estimates are incorrect, the overall performance of the receiver will suffer. This section describes the local filter in detail and presents the results of some simulations sin (π⋅ δ f ⋅ T ) Q=⋅⋅ AN R ()δτ −∆⋅ ⋅ sin δφ (5) conducted to assess the filter performance under a variety π⋅ δ f ⋅ T () of operating conditions.
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where R is the auto-correlation function of the ranging least-squares adjustment. These two solutions are well code and δφ is the average local phase error over the known to give the same results, suggesting that extended coherent integration would not be necessary. However, integration interval. The noise power associated with for the case at hand, the system model will impact filter these measurements is given by performance. The following section presents some initial testing in this regard. 2 2 No σn= σ n = (6) I Q 2⋅ T Simulation Tests where No is the noise power spectral density (PSD) in To assess the performance of the channel filter under units of W/Hz. different situations, a series of covariance simulations were run in Matlab®. For all simulations, the tracking Finally, the average phase error in equations (4) and (5) errors were assumed to be zero (for generating the design can be further expanded as (similar to Psiaki 2001; Psiaki matrix), although the channel filter model is not overly & Jung 2002) sensitive to typical tracking errors. At the conclusion of each simulation, the final steady-state covariance matrix was stored. Each simulation run consisted of 2000 T T 2 δφ= δφend − δ f end ⋅+δa end ⋅ (7) measurement updates, which allowed plenty of time for 2 6 the filter to reach steady state. where a subscript of “ end ” explicitly indicates a value at It is noted that the simulations assumed perfect the end of the integration interval. It is noted however knowledge of the navigation data bits. Although this is that this distinction is not strictly necessary because not normally the case for GPS L1 C/A receivers, the equation (2) implicitly assumes that all parameters refer assumption is relevant in the context of assisted GNSS to the current filter time, which will nominally be at the (AGNSS) or when considering pilot channel tracking, as end of the most recent integration interval. is possible with some of the modernized GPS signals and the signals that will be available with Galileo. In this A critical distinction must now be made between the respect, the simulation results will be optimistic because channel filter presented above and a loop filter that is they do not consider the effect of bit errors on the overall traditionally implemented in a receiver (e.g., Ward et al performance. That said, for strong signals, the bit error 2006). In the latter, every output from the discriminator rate (BER) will be low. For weaker signals, the BER for is given equal weight in the determination of the loop longer integration intervals is expected to be lower than filter output. This means that as the post-correlation SNR for shorter integration intervals, although this remains to decreases, the filter outputs become increasingly noisy be verified analytically. and will eventually induce a loss of lock on the signal (ibid. ). In turn, this provides the motivation for extending The primary objective of the simulation was to evaluate the coherent integration time. However, the channel filter the expected channel filter performance as a function of presented above weights the measurements according to IMU quality, oscillator quality, carrier to noise density equation (6). The question therefore arises as to whether ratio ( C/ N o ), and coherent integration time. Of these, it is beneficial, or even necessary, to extend the only the IMU and oscillator quality are reflected in the integration time in this case. Specifically, if the Kalman channel filter directly. Details of how this was done are filter weights the measurements according to the discussed in the following paragraphs. information they contain, it follows that performing “lower quality” (i.e., lower SNR) updates more frequency Recall that the frequency rate error is due primarily to the (e.g., at 20 ms) may be as useful as performing “higher residual inertial errors. Different IMU qualities can quality” (i.e., higher SNR) updates less frequently. therefore be considered by selecting appropriate values Mathematically, assume the measurement noise matrix for the spectral density of the corresponding process for a 20 ms coherent integration is given by R20 , then for noise, that is, for wa . Two different spectral density M 20 ms coherent integrations, and assuming the values were used herein, namely 5 cm/s 2/√Hz and correlator outputs have been normalized by 1/ N (see 20 cm/s 2/√Hz. These are intended to reflect a tactical and equations (4) and (5)), the measurement noise matrix is MEMS-grade IMU respectively. However, as will be seen, the IMU quality plays only a very small role in the R expected tracking performance. R = 20 (8) M ⋅20 M For modelling the oscillator, the process noise values of Although the covariance matrix is reduced, it must be the clock bias and clock drift parameters can be adjusted noted that for every update using the longer coherent according the quality of the oscillator. The model integration time, there would have been M updates originally presented in Van Dierendonck (1984) is used using the 20 ms integrations. With this in mind, in the with the corrections described in Brown & Hwang absence of a system model, the higher rate low-SNR (1992). Two different oscillators were considered: a situation would reduce to sequential least-squares and the Voltage Controlled Temperature Compensated Crystal lower rate high-SNR situation would reduce to a batch Oscillator (VCTCXO) and an Oven Controlled Crystal
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Oscillator (OCXO). The corresponding model and the C/ N o of the received signal. With this in mind, parameters are given in Table 2. Figure 4 and Figure 5 respectively show filter performance using the VCTCXO and OCXO oscillators Table 1 – Simulated Clock Parameters (NovAtel 2008) for different values of C/ N . The results are similar to Oscillator h (s 2/s 2/Hz -1) h (Hz 2/Hz) o 0 -2 those presented before. Specifically, they support the VCTCXO 1.0e-21 1.0e-20 conclusions that the performance with the VCTCXO OCXO 2.51e-26 2.51e-22 oscillator is dependent on the integration time whereas the performance with the OCXO is virtually independent of integration time (for the time intervals simulated here). To begin the analysis, Figure 3 shows the estimated The effect of C/ N on filter performance is generally as steady-state standard deviation of the carrier phase and o frequency errors as a function of coherent integration expected, with stronger signals providing better time using different IMUs and oscillators. As can be performance. Interestingly, however, the VCTCXO filter seen, the quality of the IMU plays a minimal role on performance appears to become less dependent on C/ N o overall channel filter performance. For the different as the integration time increases. This suggests that for a IMUs considered, the effect on phase tracking is well given coherent integration interval, the oscillator may be below one degree (i.e., < 0.5 mm at L1) and is considered the dominant factor in terms of filter performance, even negligible. In contrast, the oscillator quality plays a very more so than the C/ N o . significant role. For the VCTCXO, the estimated accuracy is considerably larger than with the OCXO. Furthermore, performance with the VCTCXO shows a much larger dependence on coherent integration time than does the OCXO. This is expected because the VCTCXO is a lower quality oscillator.
Finally, and perhaps most surprisingly, the filter performance is best, if only marginally, for shorter coherent integration intervals. The reader is reminded, however, that these results are optimistic for the unaided GPS L1 C/A code because they assume perfect knowledge of the navigation data bits. With this in mind, it is expected that extending the coherent integration time will provide better bit estimation performance. In other words, according to these results, the benefit of extended coherent integration is not that it improves the post- correlation SNR, but rather it may lie with the fact that Figure 4 – Simulation Results Showing the Estimated lower bit error rates are possible. Steady-State Standard Deviation of the Carrier Phase (top) and Carrier Frequency (bottom) Errors as a Function of Integration Time for Different C/N o Values Using a VCTCXO Oscillator
Figure 3 – Simulation Results Showing the Estimated Steady-State Standard Deviation of the Carrier Phase (top) and Carrier Frequency (bottom) Errors as a Function of Integration Time for Different Figure 5 – Simulation Results Showing the Estimated Combinations of IMUs and Oscillators Steady-State Standard Deviation of the Carrier Phase (top) and Carrier Frequency (bottom) Errors as a Given the above, the remaining simulation results are Function of Integration Time for Different C/N o generated assuming the poorer quality IMU and the Values Using a OCXO Oscillator emphasis shifts to evaluating the effect of the oscillator
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In all cases considered herein, the shorter the coherent Table 2 – Honeywell HG1700AG11 Specifications integration interval provided the best performance. This Specified Value Parameter is contrary to traditional wisdom which suggests that Gyro Accelerometer extending the coherent integration time will necessarily Bias (1 σ) 1 deg/h 1 milli -G provide better performance (within the constraints Scale Factor (1 σ) 150 ppm 300 ppm imposed by the oscillator and IMU). The difference in Misalignment (1 σ) 500 rad 500 rad this case is that the Kalman filter can integrate measurements at a higher rate and weight the measurements according to their expected quality. It is The NovAtel Euro 3M receiver was driven by an external noted again, however, that these results assume perfect oscillator, in this case a Symmetricom 1000B OCXO. knowledge of the navigation data bits, which is obviously This oscillator is very stable over time intervals of several not case for the GPS L1 C/A signal without external seconds (Watson et al 2007). Such an oscillator is aiding information. To this end, the effect of the data bits currently unfeasible for mass-market deployment due to on the filter performance is still unquantified but it is its high cost and large size. It was included during testing expected that the extended coherent integration will to better assess the best possible performance of an ultra- provide lower BER, thus providing better performance. tight receiver. The results presented below should That said, the results presented would apply if aiding data therefore be considered in this light. were made available to the receiver or if a pilot channel was used. Static TEST DESCRIPTION Antenna Backpack Live pedestrian-based GPS data was collected in order to confirm the results presented in the previous section. The setup is described in more detail in the following. HG1700 IMU
Equipment NovAtel SPAN A schematic of the test setup is shown in Figure 6. The Receiver 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 frontend, which in NovAtel this case consisted of a NovAtel Euro 3M receiver OEM4 outputting complex samples at 20 MHz. The complex RS-232 intermediate frequency (IF) samples are then passed to an Variable RS-232 FPGA (Field Programmable Gate Array) that restructures Laptop PC the data more compactly before forwarding it to the PC Attenuator via a National Instruments data acquisition card. The samples are stored on the PC and processed in post- NovAtel External mission using the GSNRx-ut™ software. Euro 3M Oscillator I/Q Samples The rover equipment consisted of a test antenna, as well as a NovAtel SPAN™ (Synchronized Position Attitude FPGA Navigation) system. The SPAN™ system consists of a second antenna, a NovAtel OEM4 receiver and an IMU; in this case a Honeywell HG1700AG11 (“HG1700”). Software The HG1700 is a tactical-grade IMU with specifications PC listed in Table 2 (Honeywell 1997). It is important to Receiver note that the SPAN™ antenna was not connected to the attenuator, thus the data consists of strong signals only. Figure 6 – Schematic of Test Setup Raw GPS measurements were logged from the SPAN™ system at 1 Hz and raw IMU data was logged at 100 Hz. In addition to the rover equipment, a NovAtel OEM4 The role of the SPAN™ system is two-fold. First, the receiver was setup on a nearby pillar with known inertial data is time tagged and can therefore be more coordinates to act as a base station. The receiver’s raw easily integrated into the (post-mission) ultra-tight GPS measurements were logged to file and were used for receiver software. Second, because the SPAN antenna is RTK processing. The base station data logging PC was not affected by the variable attenuator, it is able to track also used to control the variable attenuator. The base all satellites in view and provide high quality carrier station receiver maintains accurate time throughout the phase data throughout the test. This data, in turn, is used test (i.e., not affected by the attenuator) and was therefore to generate a reference solution accurate to 2-3 cm. used to accurately time tag the changes in the attenuator levels.
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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.
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 Figure 7 – RTK Position Errors as a Function of east/west. The rectangular pattern was traversed in both Signal Attenuation for Different Coherent Integration clockwise and counter-clockwise directions. After Times Assuming the VCTCXO Oscillator approximately 4.5 min of walking, the signals were attenuated at a rate of 1 dB every four seconds until a Aside from the 100 ms case, however, Figure 7 shows maximum attenuation of 60 dB was reached. The same that all integration times yield roughly the same level of rectangular walking pattern was maintained during the RTK positioning performance. This is in complete attenuation phase of the test. agreement with the results of the simulations presented earlier. In this case, the RTK performance of all The maximum speed of the antenna during the test was integration times begins to degrade after about 22 to just below 1.6 m/s. However, the measured acceleration 24 dB of attenuation. had a peak-to-peak range of about 10 m/s 2 in each coordinate direction. Furthermore, because this The RTK positioning errors as a function of signal acceleration was induced mostly from the walking motion attenuation when using the OCXO oscillator model (and less so from the actual trajectory), it is present (which is in closer agreement to the actual oscillator throughout the data set with a period of roughly 2 Hz. used) are shown in Figure 8. In this case, the RTK positions do not begin to degrade until 25 dB or later for DATA PROCESSING AND ANALYSIS all integration times. Compared with the results obtained with the VCTCXO model, this represents an The IF data samples collected from the frontend were improvement of 1 to 3 dB. This improvement is also processed using the GSNRx-ut™ software receiver consistent (in terms of trend, not necessarily magnitude) described previously. The coherent integration time was with the simulation results shown above. varied from 20 to 100 ms in 20 ms increments (but was held constant for any given processing session). The receiver generated pseudorange, carrier phase and carrier Doppler measurements were then processed, along with the corresponding data from the base station receiver, using the University of Calgary’s FLYKIN+™ software. The FLYKIN+™ software performs carrier phase ambiguity resolution and thus provides RTK positioning capability.
Figure 7 shows the FLYKIN+™ RTK positioning errors as a function of signal attenuation for the different integration times when using the VCTCXO oscillator model. It is noted that the VCTCXO model is pessimistic relative to the oscillator actually used during testing. This was done intentionally in order to get an idea of the effect of a poorer quality oscillator. Figure 8 – RTK Position Errors as a Function of Signal Attenuation for Different Coherent Integration The 100 ms solution shows very poor performance. This Times Assuming the OCXO Oscillator is caused by several successive incorrect ambiguity fixes. Because the ambiguity resolution process is dependent on To better evaluate the relative performance obtained with so many variables, many of which are independent of the the different coherent integration times, Figure 9 shows receiver architecture, these results are not considered a the 3D position error for all cases in more detail. Also reflection of the extended coherent integration time. shown is the level of attenuation. As can be seen, the 20 ms coherent integration results perform worst and
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begin to degrade with 24 dB of attenuation. However, • The oscillator quality can be significant. The use of the degradation is relatively small and may be due to a an OCXO showed nearly consistent performance half-cycle lock error (although this remains to be using coherent integration times between 20 and determined conclusively). For the other coherent 100 ms. A VCTCXO oscillator, however, showed integration times, the RTK solution begins to degrade at degraded performance and a greater dependence on 26 dB (100 ms), 27 dB (80 ms) and 28 dB (40 & 60 ms). coherent integration time, with shorter integration times giving better performance. No definitive conclusions can be made based on this single test. However, the results do support the idea that A pedestrian-based test was also performed to verify the extended coherent integration may not be completely simulation results. Results were generally consistent with necessary for RTK performance in degraded the simulation and RTK positioning accuracy was shown environments. In particular, when comparing the results to be possible with signals suffering as much as 28 dB of from the different integration intervals, the attenuation attenuation. Coherent integration times were found to level at which the RTK solutions begin to degrade differs have only a small effect on RTK performance with the by only about 2 dB, but extending the coherent attenuation at which the RTK began to fail varying by integration time would nominally provide 7 dB of SNR only a few dB. improvement. It is noted that the field results presented are based on a single test and further testing is underway to verify these results. In addition, future work will also look at evaluating the BER over different coherent integration times and assessing the results in terms of receiver performance.
ACKNOWLEDGEMENTS
The authors would like to kindly acknowledge and thank Defence Research and Development Canada (DRDC) for funding this work. The authors would also like to express their gratitude to Dr. Daniele Borio of the PLAN group for his assistance with the bit estimation algorithm.
REFERENCES Figure 9 – 3D RTK Position Errors as a Function of Time for Different Coherent Integration Times Abbott, A.S. and W.E. Lillo (2003) Global Positioning Assuming the OCXO Oscillator Systems and Inertial Measuring Unit Ultratight Coupling Method , Patent, US 6,516,021 B1, United CONCLUSIONS AND FUTURE WORK States, 22 pages.
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