Position, Navigation, and Timing Technologies in the 21st Century. Группа авторов. Читать онлайн. Newlib. NEWLIB.NET

Автор: Группа авторов
Издательство: John Wiley & Sons Limited
Серия:
Жанр произведения: Физика
Год издания: 0
isbn: 9781119458517
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40.8a and 40.8b gives

equation

      where images is the combined measurement error, a Gaussian with zero mean and variance images+images.

      where

      (40.9c)equation

      In the above formulation, a constant nominal period Tfield is used. However, a practical radio transmitter is subject to a certain frequency error. Experimental data in Figure 40.20(f) show such a clock drift. While omitted for short data sets, the frequency error can be accounted for in the time‐differencing formulation (Eq. 40.8c) by introducing a slow‐varying drift term per transmitter to be then estimated jointly.

      In the present setting of dead reckoning from a known location, the initial stationary TOA measurements can be accumulated into a “deterministic” reference. The time difference with respect to such a reference at a fixed time point as in Eq. (40.8) is akin to applying a well‐calibrated bias to all subsequent measurements, which can then be treated as approximately “uncorrelated.” This initial measurement error, if not calibrated out to an insignificant level, would make subsequent time‐difference measurements time‐correlated. Because it is constant, albeit random, it can be viewed as an unknown bias and modeled as an extra state to the positioning Kalman filter.

      Strictly speaking, no matter how well a parameter is calibrated, the subsequent measurements can be time‐correlated via the residual calibration errors. Furthermore, time differencing can also be applied continuously to consecutive measurements, that is, between t+1 and t, rather than between t and t0 = 0 as in Eq. (40.8). Consecutive time differences between times (t+1 and t) and (t and t−1) are correlated through the common epoch t. The standard Kalman filter cannot be applied to consecutive time‐difference measurements because the measurements are correlated. In [92], a fixed‐lag smoother was used where the previous position is introduced as an extra state. With both the current and previous positions in the filter, the position difference becomes directly observable by the time differences of carrier phase measured at the current and previous epochs [92]. A similar formulation can be used for SOOP when processing consecutive time differences of phase and/or range measurements.

      In the field test environment depicted in Figure 40.17, a radio receiver with seven synchronous channels is installed in a minivan together with a battery‐powered data recording system. One channel is assigned to GPS L1, which serves as the reference; one channel to a CDMA cell tower in the PCS band; and the other five channels to five DTV stations. One DTV station (605 MHz) is on Monument Peak in the south, four DTV stations (563, 617, 623, and 647 MHz) are on Sutro Tower in the north, and one CDMA cell tower (1933.75 MHz) is also in the north. Since we were driving from the south to north, the range to the DTV station on Monument Peak was increasing while the ranges to the other six sources in the north were decreasing.

      Figure 40.23(c) shows the relative ranges during motion. Due to fast fading, the range measurements are noisier in motion than during stationary (about four times larger). As discussed above, the range to the DTV channel at 605 MHz on Monument Peak (in the south) is opposite to the other ranges (in the north), with a maximum peak‐to‐peak variation of 70 m but mostly of 20 m. The DTV channel at 647 MHz shows a sharp change of 120 m after moving and toward the end. The other three DTV channels on Sutro Tower show similar behaviors. The largest separation in range is about 50 m, which is consistent with their distances calculated from their coordinates. It is remarkable to note that the CDMA range also fits nicely with the DTV ranges.

Graphs depict the radio dead-reckoning with mixed signals of opportunity.

      Figure 40.23(e) shows the LS solution (green) after averaging with an equivalent interval of 1 s to be compatible with the GPS solution at 1 Hz. Large deviations in the middle of trajectory are likely caused by the range measurements of the DTV channel at 605 MHz. After a threshold testing (±15 m) applied to the relative range predictions to remove measurement