Weak Signal Carrier Tracking Using Extended Coherent ... - CiteSeerX

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 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. 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 metres. In contrast, real-time kinematic (RTK) positioning capability (i.e., centimetre-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 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. Previous work in this area has investigated the use of an ultra-tight integration of a GNSS receiver with an inertial measurement unit (IMU) (e.g., Soloviev et al 2004a; Soloviev et al 2004b; Gebre-Egziabher et al 2005; Landis et al 2006; Ohlmeyer 2006; Petovello et al 2007; Petovello et al 2008). The concept of ultra-tight integration is to use the integrated GNSS and inertial navigation system (INS) navigation solution to drive the code and frequency numerically controlled oscillators (NCOs) directly, thereby exploiting the common position/velocity of the antenna to improve the aggregate signal tracking performance. This paper extends the authors’ prior work on software-based ultra-tight integration with the GPS L1 C/A-code for high accuracy positioning (Petovello et al 2007; Petovello et al 2008). These previous studies used coherent integration times of 20 ms or less to assess the relative performance of different receiver architectures in terms of carrier phase tracking and RTK positioning under degraded signal conditions. Under these conditions an ultra-tight integration strategy has been shown to provide about 7 dB of sensitivity improvement over a standard receiver implementation. However, 20 ms of coherent integration may not provide an assessment of each receiver’s “absolute” carrier phase tracking sensitivity.

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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 of signal attenuation. To address the most challenging 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 information from a nearby reference station.

Signal Processing Local Signal Generator

The main objective of the paper is to assess the sensitivity of an ultra-tight receiver in terms of carrier phase tracking and RTK positioning capability. The paper presents a Kalman filter-based tracking algorithm within an ultratight GNSS/IMU receiver architecture and investigates the effect of IMU quality, oscillator quality and coherent integration time on the filter’s performance. The paper begins with a short review of the ultra-tight integration strategy used and then proceeds to describe how extended coherent integration was performed. Covariance simulations are then presented to demonstrate the expected impact of the Kalman filter tracking model on the carrier tracking under a variety of operating conditions. A pedestrian-based test is then described and the RTK positioning results obtained using 20 to 100 ms coherent integration times, in 20 ms increments, are presented and analyzed. RECEIVER ARCHITECTURE OVERVIEW This section presents a brief overview of standard and ultra-tight GNSS/IMU receiver architectures. Standard Receiver Architecture The standard (scalar-tracking) receiver architecture utilized herein 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 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.

Discriminator & Loop Filter

Channel 1 Channel 2 Channel k

Navigation Filter Figure 1 – Standard Receiver Architecture Ultra-Tight Receiver Architecture In contrast to scalar-tracking, ultra-tight GNSS/IMU integration estimates the position and velocity of the receiver directly. This concept, in the absence of an IMU, is often termed vector-tracking (Spilker 1994; Pany & Eissfeller 2006; Lashley & Bevly 2007). In a vectortracking architecture, the individual tracking loops are effectively 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. For efficiency, many studies use/suggest a federated or cascaded approach to implement the vector-based or ultra-tight receiver architectures (Abbott & Lillo 2003; Kim et al 2003; Jovancevic et al 2004; Ohlmeyer 2006; Petovello & Lachapelle 2006; Groves et al 2007). In this case, in place of the discriminator and loop filter, each channel has an associated Kalman filter that estimates the tracking errors for that channel. Herein, this filter is referred to as the channel filter. This is illustrated in Figure 2, which shows the ultra-tight integrated receiver architecture. Direct feedback from the channel filter to the local signal generator is used for the carrier phase only, since the navigation solution accuracy (or the temporal variability of the navigation solution) is insufficient for carrier phase tracking. The architecture shown in Figure 2 has been termed a coherent ultra-tight (or deep) integration strategy by Groves et al (2007) because it uses the correlation outputs directly to update the channel filter. The channel filter is discussed in more detail later on in the paper.

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Signal Processing

Channel Filter

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 considered here.

(Kalman filter)

EXTENDING COHERENT INTEGRATION TIME Local Signal Generator

Channel 1 Channel 2 Channel k

As is well known, the most efficient means of improving post-correlation signal to noise ratio (SNR) in a GNSS receiver is to extend the coherent integration time. The coherent time cannot, however, be extended indefinitely for two main reasons (Watson et al 2006) 1.

The presence of unknown navigation data bit transitions will negatively affect the coherent integration process, thus resulting in a loss in postcorrelation SNR.

2.

Any frequency error, due most likely to receiver motion or receiver oscillator error, will induce an additional reduction in the SNR that increases with integration time.

Navigation Filter

IMU

Mechanization Equations

Figure 2 – Ultra-Tight Receiver Architecture The drawback of the ultra-tight receiver is that, because all satellite tracking channels are intimately related, any error in one channel can potentially adversely affect other channels. In terms of benefits however, the ultra-tight receiver will share the same benefits as a vector-tracking receiver, which include the following: noise is reduced in all channels making them less likely to enter the nonlinear 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 and ultra-tight integration 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 & Eissfeller 2006). That said, 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, these effects can generate measurement biases in the carrier phase. The ultra-tight integration strategy described above has been implemented in the University of Calgary’s GSNRx-ut™ (GNSS Software Navigation Receiver –

As mentioned in the previous section, the effect of receiver motion in the second point is largely reduced by the presence of the IMU in the ultra-tight integration strategy. The focus therefore shifts to the effect of IMU errors and receiver oscillator effects. However, as will be discussed below, false frequency lock will also play a critical role in this regard. The algorithms presented were developed specifically for the GPS L1 C/A-code signal, but can be applied to any other GNSS signal with minor modifications.

Estimating Navigation Data Bits The maximum likelihood approach to navigation data estimation on the fly is implemented herein. Assuming the receiver has achieved bit synchronization, 20 ms coherent integration can be safely performed within a given data bit. Assuming M consecutive 20 ms integrations, the maximum likelihood estimate of the data bits is that combination of data bit transitions that maximizes the combined energy in the in-phase, I and quadra-phase, Q channels as described, for example, in (Soloviev et al 2008). It is noted however that this approach does not determine maximum likelihood estimates of the data bits, per se. Rather, it can only determine the maximum likelihood estimate of the bit transitions, of which there are M − 1 . This effectively leads to an ambiguity that needs to be handled in the channel filter. The effect of a single bit error on the channel filter will depend on the number of 20 ms integrations. For example, over one 20 ms interval ( M = 1 ), a data bit error introduces 180° phase error. Over two 20 ms intervals ( M = 2 ), a single bit error has half the effect on 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 probability of having more than a single bit error at a time. Nevertheless, it is expected that extended integration time will reduce the bit error rate relative to the case when 20 ms integration is performed, although this remains to be confirmed analytically.

Channel Filter Model

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 error in units of rad, δf is the frequency tracking error in units of rad/s, and δa is the frequency rate error of the NCO in units of rad/s2. It is noted that in the context of an ultra-tight GNSS/IMU receiver, this latter term models the residual INS acceleration error and not the full level of line-of-sight acceleration.

False frequency lock is a phenomenon in which a GNSS receiver continues to track a signal but at a wrong frequency (Doppler offset). This occurs when a multiple of one half cycle of carrier phase error is accumulated over the coherent integration interval. For example, for a nominal 20 ms coherent integration, false frequency lock 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 time increases, the false frequency lock points tend closer to zero, which in turn make them harder to detect. In the context of this paper, a false frequency lock has two negative effects. First, because the tracking frequency is in error, the receiver’s carrier phase measurements, which are integrated receiver Doppler values, will necessarily become unusable for high accuracy applications. Second, a false frequency lock will negatively impact the post-correlation SNR because the coherent integration process introduces a power attenuation given by

 sin 2 ( π ⋅ δf ⋅ T )  coh  PAtt = 10log10   ( π ⋅ δf ⋅ T )2  coh  

In this work the channel filter state vector is given by

xT = [ A δτ

Given the above, there exists an inherent trade-off between extending the coherent integration time (to improve post-correlation SNR) and making the receiver more susceptible to the effects of false frequency lock.

CHANNEL FILTER DESCRIPTION The channel filter plays a critical role in the ultra-tight receiver architecture used in this work. It estimates the tracking errors on a channel-by-channel basis and these error estimates are used to correct the measurements used to compute the receiver’s navigation solution, which in turn are used to drive the NCOs. Alternatively, the tracking error estimates can be used to update the navigation solution directly. In either case, if the error 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 conducted to assess the filter performance under a variety of operating conditions.

δa ]

(2)

The system model for the filter is taken from Petovello & Lachapelle (2006) and is given by

 A  0  δτ  0 d     δφ  = 0 dt     δf  0  δa  0

0 0 0 0  A  0 0 β 0   δτ  0 0 1 0  ⋅ δφ     0 0 0 1   δf  0 0 0 0   δa  0 0 0   wA  1 0 0 1 β ⋅ 2πf  w  0 0    δτ  + 0 0 2πf 0 0  ⋅  wb      0 2πf 0   wd  0 0 0 0 0 0 2π λ   wa 

(1)

where δf is the frequency tracking error in units of radians per second and Tcoh is the coherent integration interval. At the nearest frequency lock point (i.e., when δf ⋅ Tcoh is half a cycle), the power attenuation will be 3.9 dB. This is an unacceptable level of loss for highsensitivity applications.

δφ δf

(3)

where β converts from units of radians to chips, f and λ are the nominal frequency and wavelength of the signal being tracked, wA is the driving noise of the amplitude, wδτ is the driving noise of the code tracking error that is included to account for code-carrier divergence due to the ionosphere, wb is the driving noise for the clock bias, wd is the driving noise for the clock drift, and wa is the driving noise to account for line-ofsight acceleration. The spectral densities for the clock bias and clock drift are taken from the h0 and h−2 parameters used to model oscillators (e.g., Van Dierendonck et al 1984; Brown & Hwang 1992). The measurements used to update the channel filter are the early, prompt and late in-phase and quadra-phase correlator outputs. Assuming a known correlator offset of ∆ (e.g., for early or late correlators), the correlator outputs are given by

I = A ⋅ N ⋅ R ( δτ − ∆ ) ⋅

Q = A ⋅ N ⋅ R ( δτ − ∆ ) ⋅

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sin ( π ⋅ δf ⋅ T ) π ⋅ δf ⋅ T sin ( π ⋅ δf ⋅ T ) π ⋅ δf ⋅ T

( )

(4)

( )

(5)

⋅ cos δφ

⋅ sin δφ

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where R is the auto-correlation function of the ranging code and δφ is the average local phase error over the integration interval. The noise power associated with these measurements is given by

σ n2I = σ n2Q =

No 2 ⋅T

(6) Simulation Tests

where N o is the noise power spectral density (PSD) in units of W/Hz. Finally, the average phase error in equations (4) and (5) can be further expanded as (similar to Psiaki 2001; Psiaki & Jung 2002)

δφ = δφend − δf end ⋅

T T2 + δaend ⋅ 2 6

(7)

where a subscript of “ end ” explicitly indicates a value at the end of the integration interval. It is noted however that this distinction is not strictly necessary because equation (2) implicitly assumes that all parameters refer to the current filter time, which will nominally be at the end of the most recent integration interval. A critical distinction must now be made between the channel filter presented above and a loop filter that is traditionally implemented in a receiver (e.g., Ward et al 2006). In the latter, every output from the discriminator is given equal weight in the determination of the loop filter output. This means that as the post-correlation SNR decreases, the filter outputs become increasingly noisy and will eventually induce a loss of lock on the signal (ibid.). In turn, this provides the motivation for extending the coherent integration time. However, the channel filter presented above weights the measurements according to equation (6). The question therefore arises as to whether it is beneficial, or even necessary, to extend the integration time in this case. Specifically, if the Kalman filter weights the measurements according to the information they contain, it follows that performing “lower quality” (i.e., lower SNR) updates more frequency (e.g., at 20 ms) may be as useful as performing “higher quality” (i.e., higher SNR) updates less frequently. Mathematically, assume the measurement noise matrix for a 20 ms coherent integration is given by R20 , then for M 20 ms coherent integrations, and assuming the correlator outputs have been normalized by 1 / N (see equations (4) and (5)), the measurement noise matrix is

RM ⋅20 =

R20 M

least-squares adjustment. These two solutions are well known to give the same results, suggesting that extended coherent integration would not be necessary. However, for the case at hand, the system model will impact filter performance. The following section presents some initial testing in this regard.

(8)

Although the covariance matrix is reduced, it must be noted that for every update using the longer coherent integration time, there would have been M updates using the 20 ms integrations. With this in mind, in the absence of a system model, the higher rate low-SNR situation would reduce to sequential least-squares and the lower rate high-SNR situation would reduce to a batch

To assess the performance of the channel filter under different situations, a series of covariance simulations were run in Matlab®. For all simulations, the tracking errors were assumed to be zero (for generating the design matrix), although the channel filter model is not overly 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 measurement updates, which allowed plenty of time for the filter to reach steady state. It is noted that the simulations assumed perfect knowledge of the navigation data bits. Although this is not normally the case for GPS L1 C/A receivers, the assumption is relevant in the context of assisted GNSS (AGNSS) or when considering pilot channel tracking, as is possible with some of the modernized GPS signals and the signals that will be available with Galileo. In this respect, the simulation results will be optimistic because they do not consider the effect of bit errors on the overall performance. That said, for strong signals, the bit error rate (BER) will be low. For weaker signals, the BER for longer integration intervals is expected to be lower than for shorter integration intervals, although this remains to be verified analytically. The primary objective of the simulation was to evaluate the expected channel filter performance as a function of IMU quality, oscillator quality, carrier to noise density ratio ( C / N o ), and coherent integration time. Of these, only the IMU and oscillator quality are reflected in the channel filter directly. Details of how this was done are discussed in the following paragraphs. Recall that the frequency rate error is due primarily to the residual inertial errors. Different IMU qualities can therefore be considered by selecting appropriate values for the spectral density of the corresponding process noise, that is, for wa . Two different spectral density values were used herein, namely 5 cm/s2/√Hz and 20 cm/s2/√Hz. These are intended to reflect a tactical and MEMS-grade IMU respectively. However, as will be seen, the IMU quality plays only a very small role in the expected tracking performance. For modelling the oscillator, the process noise values of the clock bias and clock drift parameters can be adjusted according the quality of the oscillator. The model originally presented in Van Dierendonck (1984) is used with the corrections described in Brown & Hwang (1992). Two different oscillators were considered: a Voltage Controlled Temperature Compensated Crystal Oscillator (VCTCXO) and an Oven Controlled Crystal

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Oscillator (OCXO). The corresponding parameters are given in Table 2.

model

Table 1 – Simulated Clock Parameters (NovAtel 2008) Oscillator h0 (s2/s2/Hz-1) h-2 (Hz2/Hz) VCTCXO 1.0e-21 1.0e-20 OCXO 2.51e-26 2.51e-22

To begin the analysis, Figure 3 shows the estimated steady-state standard deviation of the carrier phase and frequency errors as a function of coherent integration time using different IMUs and oscillators. As can be seen, the quality of the IMU plays a minimal role on overall channel filter performance. For the different IMUs considered, the effect on phase tracking is well below one degree (i.e., < 0.5 mm at L1) and is considered negligible. In contrast, the oscillator quality plays a very 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 postcorrelation SNR, but rather it may lie with the fact that lower bit error rates are possible.

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 Combinations of IMUs and Oscillators

Given the above, the remaining simulation results are generated assuming the poorer quality IMU and the emphasis shifts to evaluating the effect of the oscillator

and the C / N o of the received signal. With this in mind, Figure 4 and Figure 5 respectively show filter performance using the VCTCXO and OCXO oscillators for different values of C / N o . The results are similar to those presented before. Specifically, they support the conclusions that the performance with the VCTCXO 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). The effect of C / N o on filter performance is generally as expected, with stronger signals providing better performance. Interestingly, however, the VCTCXO filter performance appears to become less dependent on C / N o as the integration time increases. This suggests that for a given coherent integration interval, the oscillator may be the dominant factor in terms of filter performance, even more so than the C / N o .

Figure 4 – 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 C/No Values Using a VCTCXO Oscillator

Figure 5 – 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 C/No Values Using a OCXO Oscillator

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In all cases considered herein, the shorter the coherent integration interval provided the best performance. This is contrary to traditional wisdom which suggests that extending the coherent integration time will necessarily provide better performance (within the constraints imposed by the oscillator and IMU). The difference in 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 noted again, however, that these results assume perfect knowledge of the navigation data bits, which is obviously not case for the GPS L1 C/A signal without external aiding information. To this end, the effect of the data bits on the filter performance is still unquantified but it is expected that the extended coherent integration will provide lower BER, thus providing better performance. That said, the results presented would apply if aiding data were made available to the receiver or if a pilot channel was used.

Table 2 – 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 (Watson et al 2007). Such an oscillator is currently unfeasible for mass-market deployment due to its high cost and large size. It was included during testing to better assess the best possible performance of an ultratight receiver. The results presented below should therefore be considered in this light. Static Antenna

TEST DESCRIPTION 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

A schematic of the test setup is shown in Figure 6. 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 frontend, which in this case consisted of a NovAtel Euro 3M receiver outputting complex samples at 20 MHz. The complex intermediate frequency (IF) samples are then passed to an FPGA (Field Programmable Gate Array) that restructures the data more compactly before forwarding it to the PC via a National Instruments data acquisition card. The samples are stored on the PC and processed in postmission using the GSNRx-ut™ 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 second antenna, 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 2 (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 not affected by the variable attenuator, it is able to track all satellites in view and provide high quality carrier phase data throughout the test. This data, in turn, is used to generate a reference solution accurate to 2-3 cm.

NovAtel SPAN Receiver

NovAtel OEM4 RS-232

Variable Attenuator

RS-232

NovAtel Euro 3M

Laptop PC

External Oscillator

I/Q Samples

FPGA

PC

Software Receiver

Figure 6 – Schematic of Test Setup

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 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 east/west. 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. 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 AND ANALYSIS

The IF data samples collected from the frontend were processed using the GSNRx-ut™ software receiver described previously. The coherent integration time was 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. The 100 ms solution shows very poor performance. This is caused by several successive incorrect ambiguity fixes. Because the ambiguity resolution process is dependent on so many variables, many of which are independent of the receiver architecture, these results are not considered a reflection of the extended coherent integration time.

Figure 7 – RTK Position Errors as a Function of Signal Attenuation for Different Coherent Integration Times Assuming the VCTCXO Oscillator

Aside from the 100 ms case, however, Figure 7 shows that all integration times yield roughly the same level of RTK positioning performance. This is in complete agreement with the results of the simulations presented earlier. In this case, the RTK performance of all integration times begins to degrade after about 22 to 24 dB of attenuation. The RTK positioning errors as a function of signal attenuation when using the OCXO oscillator model (which is in closer agreement to the actual oscillator used) are shown in Figure 8. In this case, the RTK positions do not begin to degrade until 25 dB or later for all integration times. Compared with the results obtained with the VCTCXO model, this represents an improvement of 1 to 3 dB. This improvement is also consistent (in terms of trend, not necessarily magnitude) with the simulation results shown above.

Figure 8 – RTK Position Errors as a Function of Signal Attenuation for Different Coherent Integration Times Assuming the OCXO Oscillator

To better evaluate the relative performance obtained with the different coherent integration times, Figure 9 shows the 3D position error for all cases in more detail. Also 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 degradation is relatively small and may be due to a half-cycle lock error (although this remains to be determined conclusively). For the other coherent integration times, the RTK solution begins to degrade at 26 dB (100 ms), 27 dB (80 ms) and 28 dB (40 & 60 ms). No definitive conclusions can be made based on this single test. However, the results do support the idea that extended coherent integration may not be completely necessary for RTK performance in degraded environments. In particular, when comparing the results from the different integration intervals, the attenuation level at which the RTK solutions begin to degrade differs by only about 2 dB, but extending the coherent integration time would nominally provide 7 dB of SNR improvement.

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The oscillator quality can be significant. The use of an OCXO showed nearly consistent performance using coherent integration times between 20 and 100 ms. A VCTCXO oscillator, however, showed degraded performance and a greater dependence on coherent integration time, with shorter integration times giving better performance.

A pedestrian-based test was also performed to verify the simulation results. Results were generally consistent with the simulation and RTK positioning accuracy was shown to be possible with signals suffering as much as 28 dB of attenuation. Coherent integration times were found to have only a small effect on RTK performance with the attenuation at which the RTK began to fail varying by only a few dB. 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 Assuming the OCXO Oscillator CONCLUSIONS AND FUTURE WORK

This paper investigated the use of a GPS L1 C/A ultratight GNSS/IMU receiver for RTK positioning in degraded environments. The performance of the channel filter (one per satellite) was assessed using simulations in terms of IMU quality, oscillator quality, C / N o and coherent integration time. The main conclusions from this are •

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Extending the coherent integration time may not be as important as originally thought. In fact, for conditions simulated, the 20 ms integration case performed best in all cases, if only marginally. It is noted however that these results assumed perfect knowledge of the navigation data bits. Although this is not normally the case for a GPS L1 C/A receiver, the results are consistent with an aided receiver or if the receiver used a pilot channel for tracking. For the range of values considered herein, the IMU quality plays a minor role in the overall performance of the filter.

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. Brown, R.G. and P.Y.C. Hwang (1992) Introduction to Random Signals and Applied Kalman Filtering, John Wiley & Sons, Inc. 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. Groves, P.D., C.J. Mather and A.A. Macaulay (2007) Demonstration of Non-coherent Deep INS/GPS Integration for Optimised Signal-to-noise Performance, ION GNSS 2007, Fort Worth, TX, Institute of Navigation, 2627-2638. Gustafson, D., J. Dowdle and K. Flueckiger (2000) A Deeply Integrated Adaptive GPS-Based Navigator

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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. 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, 15751586.

Petovello, M.G., C. O'Driscoll and G. Lachapelle (2008) Carrier Phase Tracking of Weak Signals Using Different Receiver Architectures, ION National Technical Meeting, San Diego, CA, Institute of Navigation, In Press. Psiaki, M.L. (2001) Smoother-Based GPS Signal Tracking in a Software Receiver, ION GPS 2001, Salt Lake City, UT, Institute of Navigation, 2900-2913. 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.

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.

SiRF (2007) SiRFstarIII GSC3e/LP & GSC3f/LP, SiRF Technology, Inc. 2007, Product insert.

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.

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.

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.

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.

NovAtel (2008) OEM4 Family User Manual - Volume 2, NovAtel, Inc. 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. 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. Petovello, M.G., C. O'Driscoll and G. Lachapelle (2007) Ultra-Tight GPS/INS for Carrier Phase Positioning In Weak-Signal Environments, NATO RTO SET-104 Symposium on Military Capabilities Enabled by Advances in Navigation Sensors. Antalya, Turkey, NATO.

Soloviev, A., F. Van Grass and S. Gunawardena (2008) Decoding Navigation Data Messages from Weak GPS Signals, IEEE Transactions on Aerospace and Electronic Systems, Accepted for publication. 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., J.B. McGraw and R.G. Brown (1984) Relationship Between Allan Variances and Kalman Filter Parameters, Applications and Planning Meeting, NASA Goddard Space Flight Center, Precise Time and Time Interval, 273-293. 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.

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Watson, R., G. Lachapelle, R. Klukas, S. Turunen, S. Pietilä and I. Halivaara (2006) Investigating GPS Signals Indoors with Extreme High-Sensitivity Detection Techniques, NAVIGATION, 52(4), 199213. 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.

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