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.
40.4 Practical Issues and Search for Solutions
Using ATSC‐8VSB signals as an example, this section first analyzes the effect of transmitter‐receiver geometry on positioning accuracy in Section 40.4.1 to highlight the needs for mixed SOOP. Mobile test results for radio dead reckoning with mixed SOOP are presented in Section 40.4.2. A number of practical issues are discussed in Section 40.4.3 as part of future research.
40.4.1 Analysis of Geometry Effect on Positioning Performance
Range‐based positioning accuracy is determined by ranging errors on the one hand and by the ranging geometry on the other hand. For the 2D case, the circular probably error
