Demonstration system for using shipboard-relative GPS

GPS World, April, 2005 by Kathleen Boseley, Jim Waid

The flight ends at 0,0. The ship trajectory is a simple flat path at 20 knots heading due east. The ends of the two trajectories coincide to simulate the landing of the aircraft onto the deck of the ship.

We completed multiple simulation runs that included the following: a fault-free run; runs with cycle slips of 0.5, 1, 2 and 5 cycles; and runs with added carrier phase noise of N(0, 1/8l). Error models for the inertial sensors are simulated based on the typical performance of the Honeywell navigation grade inertial sensors used in the H-764 ACE specified as a 0.8 nmi/hour circular error probable (CEP).

Results

The fault-free case provided a baseline for comparison with the cases that reflect fault modes. Fault-free does not mean without error; it is simply a case where the normal "expected" errors are present without any of the failures as defined from the FMEA. Figure 4 and Figure 5 present the horizontal and vertical relative position error for the fixed wide-lane solution along with the horizontal and vertical protection levels (HPLH0 and VPLH0). For all data samples, the protection levels bound the error and fall well below the alert limits for autolanding, the most stringent of the Sea Based JPALS requirements.

Additional runs were completed in which extra noise was introduced on the L1 carrier phase measurement of a single satellite. The noise was simulated as zero mean white noise with a standard deviation of 2.4 centimeters (1/8 L1 wavelength). The noise was introduced at time 1730. The relative wide-lane fixed position error and protection levels are shown in Figure 6 for the case that demonstrated the least effect and Figure 7 for the case where the noise was most evident. Note that the blue line is the relative position error and the other lines are the protection levels for both the H0 (nearly straight teal and violet lines) and H1 (large variance green and red lines) hypotheses. (H0 refers to the fault-free conditions and H1 refers to a single failure situation.) The relative position protection level is the maximum of the H0 and all the possible failure modes. For all the cases completed (noise on each visible satellite), the protection level bounded the relative position error in all axes.

The next series of runs consisted of normal fault-free conditions until 20 seconds prior to the end of the run. Cycle slip detection is accomplished by forming a test statistic that compares the predicted double difference measurement with the actual double difference measurements. The relative solution Kalman filter maintains an estimate of the double difference measurements during its processing cycle.

The estimated values are then compared with the measured values at the time of the next available GPS measurements. The difference between the predicted and the measured is evaluated as a means for detecting cycle slips. This technique is described in detail in the article by C. Altmayer cited in the Further Readings. The threshold is set based on the expected fault-free behavior of the Kalman filter and the desired false alarm rate defined in the Sea Based JPALS requirements (9.6X10-4/hour)