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40.3 Pseudorange Measurements from Broadcasting Signals
ОглавлениеAs described in Section 40.2, TOA measurements from DTV signals (e.g. ATSC 8VSB, DVB‐T, and DTMB) are made relative to the receiver’s local timeline, which may differ from that of a transmitter by clock errors such as bias and drift. The TOA measurements can be taken at a fixed rate (periodic) or at a variable rate whenever a particular event such as the start of a field sync or an OFDM symbol occurs (aperiodic to the receiver). Besides TOA, TOT measurements are required to form pseudoranges from TOA measurements. Note that DTV transmitters can be synchronous as in a SFN or asynchronous, when each transmitter maintains its own clock loosely coupled to a common timeline like UTC.
To derive the pseudorange equations, we first establish the relationship between the timelines at the transmitter (labeled as TX time) and receiver (labeled as RX time) as shown in Figure 40.16. The event of interest for our ranging purpose is the leading edge of the ATSC 8VSB’s field sync segments (or of the useful part of OFDM symbols) represented by up‐pointing arrows in Figure 40.16.
The time at which this leading edge leaves the transmitter antenna is the TOT. The successive times of transmit are related by
where n = 0, 1, 2, … is the number of fields, and Tfield is the nominal period of a field, which is about 24.2 ms (at a field rate of 41.32 Hz) for ATSC‐8VSB signals.
Assume that the receiver’s time ticks at a sampling rate of, say, 10 MHz. The TOA of the leading edge of the field sync segments is estimated by determining the location of the correlation peaks as detailed in Section 40.2.1. Referring to the RX time, we estimate the TOA by counting the samples between successive correlation peaks (denoted by Pn) and the first peak relative to the first sample (denoted by P0).
The first sample is set to be zero for the receiver clock, which differs from the transmitter time by an offset, denoted by t0. As a result, the TOA can be expressed in terms of the correlation peak locations as
(40.2)
where t0 is different for each transmitter using an independent clock.
If we calculate the pseudorange for and at each time of arrival TOAn, the measurements will not be on a uniform scale due to the random nature of the TOA caused by relative movement and noise. Hence, they are called aperiodic pseudoranges, denoted by APRn, and given by
The time of measurement for the aperiodic pseudoranges is the same as the TOA. But aperiodic pseudoranges are not available regularly on a uniform time scale. In order to integrate these pseudoranges with other sensor measurements, interpolation may be required. Alternatively, we can form periodic pseudoranges [23].
In addition to the initial clock offset t0, the clocks may drift in frequency, leading to Tfield and Ns (the number of samples per field) off their nominal values. For the stationary transmitter and receiver, there is no Doppler frequency shift. The changes in symbol rate and sampling rate are due to the clock frequency instability, and the combined effect is observed at the receiver.
Figure 40.16 Relationship of timelines at transmitter and receiver and aperiodic pseudoranges.
For asynchronous transmitters, each pseudorange equation contains at least an unknown of its own related to the transmitter (i.e. the initial clock offset t0). No instantaneous position fixing is possible with such pseudorange measurements for a stand‐alone solution unless additional information such as TOT and LOT is encoded on broadcasting signals (add‐on services). Nevertheless, there are different positioning mechanisms that can be employed to deal with the unknowns in pseudoranges, including differential ranging, relative ranging, and self‐calibration, among others.
Differential ranging involves a reference receiver at a known location that provides an estimate of the TOT or TOA of the same event via a data link to a user in order to cancel out the common TOT at the user receiver, leading to spatial difference of pseudoranges [7, 19, 20]. Relative ranging accumulates changes in range to a transmitter from a starting location [25]. As long as the signal tracking is maintained, the displacement from the starting point can be estimated from the temporal differences of pseudoranges to several transmitters in a process known as radio dead reckoning [23, 24, 82]. If the transmitter locations are known and the receiver starts from a known initial location, the method of self‐calibration can be used to estimate the unknown TOT [17].
As an example, consider the case of self‐calibration with an aperiodic pseudorange (Eq. 40.3). We first form the range between a known transmitter and our receiver at the initial known location as APRn, and count the samples between successive correlation peaks Pn. Since we do not know t0 and Tfield (except its nominal value), we can reformulate Eq. 40.3 as
(40.4)
Assume that the receiver is stationary (or its location known if it is moving). We collect N+1 measurements of APRn = APR and Pn and obtain the following matrix equation:
The least squares solution applied to Eq. 40.5 gives
(40.6a)
(40.6b)
Note that due to the transmitter clock frequency instability, the actual field period may differ from the nominal one, which is thus estimated as part of the calibration process. In Eqs. 40.5 and 40.6c, the scaling by the number of measurements N is to ensure numerical stability of the solution when N becomes very large. Similar equations can be formulated for periodic pseudoranges [23].
Two field test examples with ATSC‐8VSB [23, 29] and one example with DVB‐T [9] are presented next. The test environment with ATSC‐8VSB signals is in the San Francisco Bay area shown on Google Earth in Figure 40.17. The test site is in Foster City; DTV transmitters are located around the Bay at Sutro Tower, Mount San Bruno, Monument Peak, and Mount Allison, respectively; and one CDMA cell tower is along SR92 near the San Mateo Bridge across the Bay. The first test example with ATSC‐8VSB shows the effect of fast fading on mobile ranging, and the second test shows the effect of clock errors on the range bias and their possible calibration.
Mobile Test 1: Slow and Fast Fading. Severe Rayleigh fading occurs for mobile users in urban environments [42, 83], creating “holes” in data streams, which cannot be easily corrected by conventional coding schemes. Only 1 out of 313 segments per data field (about 24 ms) contains pseudorandom (PN) codes that can be used for timing and ranging. Such a low‐duty cycle (0.3%) requires specially designed correlators and code tracking loops for mobile users, particularly when low‐quality clocks are used in both transmitters and receivers. Although subject to Rayleigh fading, tracking of the PN codes is less devastating for DTV‐based ranging than for DTV viewing. In the latter case, interruption prevents continuous reception of ATSC‐8VSB signals, and the picture quality becomes unacceptable to mobile users. In ranging, however, agile acquisition and reacquisition schemes can coast through the “holes” with instantaneous recovery after complete signal losses.
A mobile test was designed and conducted to help better understand mobile fading and its effect on our software DTV receiver. On the roof and sides of a minivan, we placed seven magnetic‐mounted antennas and connected to seven radio channels (Ch1–Ch7) of our data acquisition system. As shown in Figures 40.18(a) and (b), a small patch antenna, marked “1,” is connected to Ch1 for GPS. A whip antenna, marked “2,” is connected to Ch2. The remaining five antennas, marked “3” through “7,” are identical and are connected to Ch3 through Ch7, respectively. Ant3 is placed in the middle section on the right‐hand side (the passenger side), while Ant4 is placed horizontally above the right rear wheel. Ant5 repeats the placement of Ant3 but on the left‐hand side (the driver side). Ant6 is similar to Ant4, but placed far to the left. Ant7 is in the middle on the back.
Figure 40.17 Test environment with ATSC‐8VSB signals on Google Earth.
Figure 40.18 Test setting for study of mobile fading.
The mobile test lasted about 70 s, in which all channels were tuned to the station centered at 653 MHz. In this run, the van was initially stationary for 10 s and then moved for 10 s. It next stopped for 10 s and moved for 10 s. It repeated the stop and move sequence for 10 s each before finally stopping for the last 10 s.
Figures 40.19(a)–(g) show the correlation peak, peak to average ratio, code delay error, carrier phase error, TOA error, and pseudorange as a function of the field number for all six DTV antennas (from left to right, Ant2 and Ant3 on the top, 4 and 5 in the middle, and 6 and 7 on the bottom of each subplot in Figure 40.19), respectively. It is clear from the figures that the signal strength at stop has less variations than in motion, but the peak value during the stops is not necessarily larger. There are peaks and dips during motion. When transitioning from stationary to moving and back to stationary, the signal level could be either high or low, depending on the particular location where the transition took place. The swing of signal strength during motion is due to fading.
Figure 40.19 Fading study with six antennas in a stop‐move‐stop sequence.
The performance ranking among the six DTV antennas is 4 > 3 > 2 > 5 > 6 > 7. That is, the horizontally placed antenna on the side above the right rear wheel outperformed the rest. It happens that the DTV station at 653 MHz uses a horizontally polarized antenna and the signal comes from the right, which is in direct sight of Ant4 with matched polarization.
Mobile Test 2: Clock Errors and Calibration. Six radio channels are assigned to six DTV stations for simultaneous data collection: Ch1 @ 551 MHz (data not shown) and Ch2 @ 635 MHz on San Bruno Mountain, Ch3 @ 563 MHz and Ch4 @ 617 MHz on Sutro Tower, Ch5 @ 605 MHz on Monument Peak, and Ch6 @ 683 MHz on Mt. Allison. A passive UHF whip antenna, magnetically mounted on the roof of a minivan, is split to drive the six radio channels for data acquisition. During the test, the van was stationary for about 40 s and was driven up to about 20 miles per hour for the remaining 50 s.
As shown in Figures 14.20(a)–(e), prior to field number 2000, the minivan was stationary. The reference ranges stayed constant. Except for some small variations (oscillatory), the calibrated ranges were rather close to the reference values, indicating that the calibration algorithms were able to find the offset between the clocks of the receiver and DTV stations.
The transmitters in San Bruno and Sutro Tower are in the north (San Francisco), whereas those in Monument Peak and Allison are in the south (Freemont). Since the minivan was traveling from north to south, it was expected that the pseudoranges to the northern stations would increase (see Figures 14.20(a) and (b)), while those to the southern stations would decrease (see Figure 40.20(c)). However, this is not obvious for the two stations in Figures 14.20(d) and (e) that exhibit large variations.
In Figure 40.20(d), the linearly calibrated pseudorange shows a parabolic shape, meaning that the range rate is not constant but under a certain range acceleration. Taking the difference between two successive TOAs for Ch2 provides measurements of the field length, as shown in Figure 40.20(f). Ideally, the nominal field length is 241971.9818 samples. However, it is clear from Figure 40.20(f) that the field length for Ch2 not only differs from the nominal value (a bias in frequency, meaning a clock drift) but also varies over time. A line is fit to the data as the red curve in Figure 40.20(f). Removing this slope from the original data leads to the second‐order calibrated pseudoranges as shown in Figure 40.20(g), which now has no visible drift any more. Since this station is in the north while the minivan was going from north to south, the range increases after field number 2000.
Figure 40.20(e) is an example of oscillatory behavior in pseudoranges (smaller oscillations are observed in Figures 40.20(a) and (b) as well). Before field number 2000, there are about two cycles with an upward trend and seemly increasing amplitude. Although a polynomial can fit nicely to the measurements, it cannot be extrapolated beyond the fitting interval; that is, it cannot predict the remaining data. Alternatively, a constant amplitude sine wave is fit to the first 1940 data points, which misfits the first cycle due to the omission of the linearly increasing amplitude, but the second cycle has a better fitting. Removing it from the data leads to the calibrated pseudoranges as shown in Figure 40.20(h), where the blue‐colored curve is the original one and the green‐colored curve is the calibrated one. After the nonlinear calibration, the errors during the stationary period are within 20 m. Obviously, a better fit could have been achieved if the change in amplitude was taken into account. Since Ch6 was in the south and the minivan was moving from the north to south, the range decreased as it was moving toward the transmitter.
This example with a small number of DTV transmitters reveals a vast difference in the quality of transmitter clocks. The observed clock errors include (i) clock timing bias, (ii) clock frequency drift, (iii) slow change in clock drift (parabolic), (iv) fast change in clock drift (oscillation), and (v) a combination thereof. Oscillatory clock errors were also observed in GSM signals and attributed to local intermittent clock adjustment [31]. Higher‐order calibration can be applied to estimate both quadratic and sinusoidal clock error components [27]. Figure 40.20(i) shows a histogram of the clock drift rate generated from a survey of 159 ATSC channels [84]. It shows a mean clock drift rate of −0.8 ppm and a standard deviation of 3.6 ppm. Some worst cases include −17.8 ppm and 23.9 ppm, to name a pair. The transmitter clocks generating the signals on Ch2 and Ch6 exhibit a relatively high drift rate, making them undesirable for PNT use.
Mobile Test 3: Delay Spread and NLOS. Tests of ranging algorithms with DVB‐T signals as described in Section 40.2.2 were conducted in suburban and urban environments in Toulouse, France [9]. In the urban runs, one DTV transmitter precisely synchronized to GPS time (±30 ns) operated at a frequency of 762.16667 MHz in the 8K mode (8 MHz bandwidth) with a cyclic prefix ratio of 1/8 and 64‐QAM for data symbol modulation. In the test, the DTV receiver also used GPS time as its reference. Therefore, the measured pseudorange was virtually clock error‐free. Since the DTV transmitter was not phase‐locked on to the GPS time, a phase offset between the transmitter time and GPS time was determined prior to deriving the absolute pseudorange measurements. It was done empirically by making a delay measurement in an open location with direct sight to the transmitter [9].
Figure 40.20 Range calibration and clock error estimation (Subplot (i) taken from [84]).
Source: Reproduced with permission of Stanford University.
Two TV antennas (separated by 1 m) are mounted on the roof of a car, which is driven at a speed between 0 to 50 km/h for 5 min including three stationary segments from 0–10 s, 70–110 s, and 285–300 s as shown in Figure 40.21(a). The evolution of the absolute value of the correlation function over time is shown in Figure 40.21(b), where the horizontal axis is the time, the vertical axis is the delay, and the correlation strength is color‐coded, with the dark red representing the strongest return (0 dB) and the dark blue representing the weakest return (−30 dB). Clearly, the correlation peak is spread out, an indication of the presence of multipath signals, some of which have rather long delays. There is a short horizontal segment with weak return (due to stopping from 70 to 110 s) where the direct signal may be blocked or attenuated to a level comparable to multipath.
Figure 40.21 Results of field tests for ranging with DVB‐T signals [8].
Source: Reproduced with permission of Inside GNSS Media LLC.
Figure 40.21(c) shows the pseudoranges estimated from DVB‐T signals received by the two antennas (blue from the first antenna and red from the second) compared to the reference pseudorange (back) computed from the GPS‐based car position (real‐time kinematic or RTK) and the known transmitter location. The pseudorange errors are mostly positive (i.e. pseudorange in excess of the true value), a clear indication of NLOS errors. The blue curve from the first antenna shows larger bias and spikes than the second, particularly during the static periods (around 100 s and at the end). The errors are very different (up to 150 m) even though they are so close (separated only by 1 m), again a clear sign of location‐dependent multipath errors.
In Figure 40.21(d), the table lists the mean and standard deviation of 35 m and 25 m for the first antenna and 30 m and 20 m for the second, respectively. Advanced measurements processing, which can remove the NLOS signals [9], significantly improves the accuracy, leading to a mean and standard deviation of 4 m and 10 m, respectively.
