
Working Papers • May/June 2012
An indoor positioning test configuration. At left, a geodetic antenna is mounted above the presurveyed point, and an IFEN employee is using a software receiver to log GNSS signals.
Difference CorrelatorsDoes Indoor Carrier Phase Tracking Allow Indoor RTK?Difference correlators represent effective means to remove signal dynamics from correlator values and to dramatically increase the coherent integration time, thus, also increasing the carrier phase tracking sensitivity. In this article, a difference correlator software algorithm is tested both indoors and in a forested area with promising new results. Findings from both single and doubledifference correlator tests are presented.
Share via: Slashdot Technorati Twitter Facebook Working Papers explore the technical and scientific themes that underpin GNSS programs and applications. This regular column is coordinated by Prof. Dr.Ing. Günter Hein, head of Europe's Galileo Operations and Evolution. The carrier phase observable is generally considered to be the most precise GNSS measurement, yielding millimeterlevel positioning accuracy outdoors. However, measuring this observable indoors or in a forest has long been thought to be impossible or, at best, very difficult. A new carriertracking algorithm used in the research on which this column is based changes this situation and enables us to measure the received carrier phase even in highly degraded environments. The algorithm adapts a wellknown positioning concept (single/double difference) to the level of GNSS signal processing. Single and doubledifference (code and carrier) correlators eliminate common mode errors and thereby reduce the signal dynamics. Applying much smaller tracking loop bandwidths or longer integration times can then reduce noise and eliminate multipath contributions during signal tracking. For static applications, a coherent integration time of 30 seconds allows singlechannel carrier tracking without cycleslips well below zero decibel/hertz (!), provided that code and Doppler lock can be achieved by, for example, vector tracking. This column will show that the estimated carrier phase apparently relates to the received electromagnetic wave. In forest and indoor test trials that we conducted, the carrierphase tracking stability is extremely high and the number of cycle slips is very much smaller compared to standard phaselocked loop (PLL) tracking. Furthermore, the numerical value of the slips is small, perhaps only one cycle. On the other hand, a received phase tracked indoors is influenced by all the possible complex propagation effects that may occur there. This complicates use of the received phase in positioning, and classical real time kinematic (RTK) positioning algorithms cannot be applied in a straightforward manner. However, a processing software that we used in our trials yields indoor positioning with about onemeter accuracy using only carrier phase data. Difference Processing Methodology The reference station retrieves navigation data bits of the tracked satellite signals and stores them into a file. Furthermore, the reference station generates a RINEX observation file. The rover collects intermediate frequency (IF) samples and stores them onto a hard disc. All data from the reference station and the rover are input to the postprocessing, which produces a new (improved) RINEX observation file for the rover. A data processing software then analyzes the reference and rover RINEX files to estimate the rover position. Loosely speaking, the prompt correlator of a GNSS tracking channel is the exponential of the estimated carrier phase. Thus, a (receiver) singledifference correlator is obtained by multiplying the rover prompt correlator with the exponential of the corresponding reference station carrier phase and the broadcast navigation data bit. This principle extends to double (receiver and satellite) differences and is described in greater detail later in this article. The signal dynamics in a doubledifference correlator can be very low. For example, for a static user and baseline length of 50 meters, the remaining acceleration is around 50 micrometers/second2. Thus, we can form coherent batches of several hundreds of seconds and use those batches to estimate the doubledifference carrier phase. (In our test we used batches of a maximum of 90 seconds.) Ideally, the doubledifference correlators within one batch represent a tone signal, and the frequency is the (doubledifference) Doppler frequency. The phase of the tone signal relates to the user position. An adaptive filter detects the dominant frequency contribution of the lineofsight signal and applies a linear filter. Ideally, only the lineofsight signal passes through and multipath signals (having a slightly different Doppler) and noise are filtered out. The frequency selectivity is inversely proportional to the batch length. In our approach the separation of those components takes place entirely in the frequency domain, whereas a conventional PLL smoothes carrier phase estimates in the time domain. Finally, an estimator derives the Doppler frequency and the carrier phase at a given reference epoch from the filtered signal and writes them into a RINEX file. This process includes unwrapping and undoing the differencing process with certain assumptions on the receiver clock. A typical standard PLL works with a tracking loop bandwidth of 5–15 hertz to cope with user oscillator variations, even if the receiver is operated in a static mode. In contrast, a batch length of 90 seconds corresponds to an equivalent loop bandwidth of 5.6 millihertz. Provided that the tracking channel can maintain code and Doppler lock (e.g., via aiding from other channels for vector tracking), then we will show that a carrier tracking sensitivity of well below zero decibelhertz is possible. In forests, the canopy attenuates the GNSS signals and causes diffuse scattering. Tree trunks cause the signals to creep around them, causing an extra delay. Whereas standard receivers generally cannot track the signal without cycle slips inside forests, difference correlator tracking is stable and potentially allows use of the carrier phase for precise positioning even for satellites tracked at low elevation angles. Difference correlators also partly allow for indoor carrier phase positioning. Phase delays caused by the penetration of building materials determine the accuracy limit. This article proposes a method to identify time windows with approximately constant delays. L1 C/A and L2CM indoor data show periods of, for example, 16 minutes, where propagation delays remain within a few centimeters variation. Using this method, we can compute an indoor position using carrier phases only (no code pseudoranges) with an accuracy of one meter. The difference correlator concept may also find applications for attitude systems with multiple antennas or for possible use on board spacecraft, which receive GNSS signals at very low power levels. Difference Correlator Concept Applying longer filter times reduces the noise and eliminates multipath contributions. A simpler version of difference correlators was introduced in Chapter 10 of T. Pany’s book, Navigation Signal Processing for GNSS Software Receivers (see the Additional Resources section at the end of this article), and will be summarized here. Forming Differences. At the correlator level forming differences is a little tricky, because various (equivalent) ways to define the carrier phase inside the receiver are available and because the timing relationship of the data is important. The following discussion describes the methods of singledifference forming and doubledifference forming as well as how undifferenced observations are then rederived from these formed differences. SingleDifference Observations. Generally the classical receiver singledifference carrier phase observation is defined through an equation such as the following: Δφ^{k}(t^{k}) = φ^{k,rov}(t^{k}) — φ^{k,refk}(t) (1) where, φ^{k,rov} is the rover carrier phase to satellite k [radians] The carrier phases are read from a RINEX file or a similar source (e.g., RTCM). The epoch t^{k} generally refers to the receiver timescale. Note, the timescales do not match exactly, but those timing errors between receiver clocks can be tolerated if satellite position calculation properly accounts for these differences. Singledifference Correlator. Forming correlator differences requires a slightly different approach. First, the tracking channel outputs a carrier phase reading based on the internal numerically controlled oscillator (NCO), which is not necessarily under the control of a PLL. Typically, we use a frequencylocked loop (FLL) or vector tracking methodology for this purpose. In general, the internal tracking is not locked to the received carrier phase (due to poor signal conditions), and the prompt correlator contains the difference between the received and internal carrier phase. Estimating the received rover phase follows expression such as: exp{iφ^{k,rov}(t)} =a(t)exp{iφ^{k,NCO}(t)} P^{k,rov}(t) (2) where, a(t) is the inverse signal amplitude (not relevant here), Therefore, a receiver singledifference correlator is written as ΔP^{k}(t^{k}) = exp{iφ^{k,NCO} (t^{k})} P^{k,rov}(t^{k})exp{iφ^{k,ref} (t^{k})}d(t^{k}_{sent}) (3) where, d is the broadcast navigation data bit (if any) and To wipe off data bits we retrieve the broadcast data bit from the reference station corresponding to the sent time for the correlator value P^{k,rov}. We assume that the internal receiver time t^{k} is steered towards the true GPS time within plus or minus one millisecond and that the same applies for the reference receiver. Then we simply take t^{k} (which is a rover time) and use it as a reference station time to extract the reference station carrier phase. Using Equation (5), this process is later reversed, thereby compensating for any timing error in the range. Applying a filter F (see next section) to batches of singledifference correlator values allows the phase of the filtered correlator values to be unwrapped, thus: ΔQ^{k}(t)=F{ΔP^{k}(t)} = ΔQ^{k}(t)exp{iΔη^{k}(t)} (4) where, ΔQ^{k} is the filtered singledifference correlator Finally, adding the unwrapped phase to the reference station phase yields the new improved undifferenced rover carrier phase, which is then written into the RINEX file or used otherwise: φ^{k,rov}(t) = Δη^{k}(t) + φ^{k,ref}(t) (5) The computation of (3) requires the evaluation of the reference station carrier phase at the rate of the correlator values (e.g., 50 hertz). The phase itself is typically available with a lower rate (e.g., 1 hertz). Therefore, a suitable interpolation procedure must be used. . . . Undoing Double Differencing. GNSS data format standards like RINEX are only defined for undifferenced observations. Retrieving singledifference (and finally undifferenced) observations from the doubledifference phase is not straightforward because the receiver clock error has been completely eliminated during the doubledifference process. The following paragraphs propose two methods with which to reintroduce the receiver clock error. For any positioning processing, this error has to be taken into account again and then, respectively, removed. The only important thing is that a relationship remains intact between the carrier and range clock within the receiver. . . .
Block Diagram Currently, the difference correlator scheme applies only for carrier tracking. Rover code and Doppler observations are produced using standard tracking loops with vector DLL (VDLL) or vector FLL (VFLL). The implemented difference correlator scheme is generally realtime capable, but at this time reference station data is read in via a RINEX file. For realtime operation, RTCM could be used. . . .
Batch Processing Correlator Batch Filters. The batch filter was introduced earlier in equations (4) and (7). Here, we now offer a detailed description. . . . Cost Minimization Filter. The cost minimization filter first fits a quadratic phase model to the batch of correlator values. . . . Sensitivity. Assuming that the reference satellite and the reference station data have virtually no noise, we can approximate the variance of a doubledifference correlator… . . .
Field Trials: Signal Processing Results Canopy Test. For the canopy test, a geodeticquality rover antenna was placed on a tripod inside a forest … The experiment took place on December 1, 2011, tracking satellites over the course of half an hour. A large part of the deciduous forest where the test took place had already dropped most of its leaves. Nevertheless, the forest is quite dense and frequent “shadowing” (signal obstructions) due to trunks and branches was expected. With an antenna splitter, the signal was fed into the RF front end of the multiGNSS software receiver to record the GPS L1 signal samples and into a commercial geodetic receiver used for comparison. The reference station was located 2.477 kilometers away from the observatory Graz/Lustbühel, Austria. Signal Processing Results. Code and Doppler vector tracking based on 20 millisecond–long coherent integrations was used to track all visible satellites at the rover. The estimated signal power at the rover varied from 5 to 51 decibelhertz ... Values below 1015 decibelhertz occur for the lowelevationangle satellites. . . .
Indoor Test . . . Data Processing. We postprocessed the gathered data in the usual way . . . Results. A typical good result of the carrier tracking performance is that of PRN25 with PRN12 used as the reference satellite. Both signals penetrate the ceiling to reach the indoor antenna … the L1 and L2 carrier phase estimates are highly consistent and reflect the geometric motion of the satellite. Doppler (slope) and phase estimates are also consistent, and the signal processing did not detect any cycle slips. The only difficult period occurred around the time interval 3450–3600 seconds on L2CM. During this time, fading on L2 occurred, as can been seen in the righthand part of Figure 13. However, the spectrum of the doubledifference correlator still shows a clearly visible peak, and we argue that the estimates are not corrupted by excessive noise, as reflected in the snapshot of the doubledifference correlator spectrum … . . .
Use in Indoor Positioning Knowing that the pseudorange quality is not sufficient, we decided to base the positioning mainly on the carrier phases. The pseudoranges must be downweighted drastically so that the baseline computation is effectively identical to a phaseonly differential positioning. Phaseonly computations are well known to rely heavily on satellite geometry changes for position determination and require therefore longer measuring intervals. Under open sky scenarios this has been the traditional method of precise differential positioning for several decades now. The open question for us was, do the indoor observations still have enough contribution from the lineofsight signal (to the satellite geometry itself) or is the whole dataset so contaminated by multipath reflections as to prevent any reasonable positioning result? The carrier phase observations were processed using a proprietary software. We used all carrier phase observations available. The carrier phases on L2 were only available for PRN12, PRN25, PRN29, and PRN31. These satellites enabled us to track the L2C code. However, more satellites supported L1 carrier phase tracking. The complete carrier phase information set from satellites above an elevation mask of 15 degrees has been used in our baseline computations. . . .
Conclusions Depending on the intended use, satellite or receiver singledifference correlators can be used or doubledifference correlators. For static differential positioning, the use of doubledifference correlators seems to be the method of choice, allowing coherent integration times of several dozens of seconds. Our indoor test (with a batch length of 30 seconds) verifies this high tracking sensitivity. With the rover antenna on one of the reference points located in an IFEN conference room, we can continuously track the carrier phase of all satellites on L1 C/A and L2CM. The phase and Doppler estimates based on the individual batches are highly consistent in the sense that the phase difference between the two batches relates well to the estimated Doppler. Estimates from timely adjacent batches are uncorrelated. Indoor signals are wellknown for strong multipath and fading effects. The presence of biases especially introduces challenges for position determination based on observation data tracked indoors. Despite the fact that some of the carrier phase observations were collected indoors, these are not pure sampled arbitrary reflections of the original signals. The indoor carrier phase observations are continuous and allow the application of sophisticated differential carrier processing. The position deviations to the truth of around two meters (vertical) and, respectively, less than one meter (horizontal) are exceptionally good for the environment chosen. The forest trials lead us to a similar conclusion. The observations are continuous and might be used with sophisticated differential carrier processing, but the handling of propagation delays is critical. Our analysis has only just started and will continue to address this as well as other issues. Other applications in which the signal is only attenuated and biases are not introduced (e.g., strong interference, or a large distance to the GNSS satellites as might occur for a GNSS space receiver) also seem to be well suited for employing the difference correlator — and promise an easier data evaluation. For the complete story, including figures, graphs, and images, please download the PDF of the article, above. Acknowledgement Additional Resources ManufacturersThe new carriertracking algorithm tested in the research described in this article is from IFEN GmbH, Poing, Germany. The processing software used in forest and indoor trials was from inPosition gmbh, Heerbrugg, Switzerland. The GNSS software receivers used in the tests were the SXNSR from IFEN GmbH. The indoor test used a Zephyr 2 antenna from Trimble, Sunnyvale, California, USA, the forest tests an Ashtech geodetic L1/L2 701975 antenna.Copyright © 2018 Gibbons Media & Research LLC, all rights reserved. 
