NovAtel Inc. New Positioning Filter: Phase Smoothing in the Position Domain (2002)

During the early days of GPS navigation, Ron Hatch at Magnavox designed a filter that combined delta phase measurements and pseudoranges into a single noise reduced measurement. While reducing the noise on the measurement used in the navigation solution, the reduction of the effect of multipath was not as much as was hoped because of the biased nature of the multipath signal on the pseudorange. At the same time, the time constant in the filter had to be limited because the ionospheric phase advance was a different sign than the pseudorange ionospheric group delay error. Finally, the effectiveness of the phase smoothing technique was limited because in a kinematic environment, frequent signal outages occur and every time this happened all of the smoothed pseudorange information was lost and the accuracy of the pseudorange reverted back to its nominal unsmoothed level. In a differential system position, precision can be improved through the use of the phase ambiguity, which allows the receiver to treat the carrier measurement as a range with ever better precision. This can eventually provide a receiver with a position accuracy at the centimetre level, provided the differential base station is close enough to the receiver. If satellites tracking is interrupted, the position precision in particular directions (depending on the locations of the satellites) can be maintained via the ambiguities of the satellites the system continues to track. In a non-differential system, delta phase measurements in conjunction with a velocity model can be used to help estimate average velocity that can help maintain position accuracy when the constellation drops below 4 satellites, and to help reduce the effect of pseudorange errors when the number of satellites is 4 or more. But the delta phase measurement only measures average velocity, so some assumptions about the system dynamics has to be made and this adds the requirement of additional system noise in the positioning filter which reduces its accuracy. This paper describes a method for combining the delta phase measurement in a filter which includes the current and the previous position. With both the current and previous position in the filter, a position difference can be formed which is directly observable by the phase difference measured between the previous and current time epochs. The previous and current position difference is completely observable by four phase differences or partially observable if less than three satellites are continuously available. The advantage of this method over phase smoothing is that in order for the filter to make use of the delta phase measurement, it only needs to be available since the previous time epoch, rather than over the last 50 seconds or so. Provided that some selection of 4 satellites are available over every epoch, the position accuracy of the system can be maintained and improved. This is in contrast to the phase smoothing technique in which the same four satellites must be continuously tracked in order for the position accuracy to be maintained and improved by the same amount. The advantage of this method over a differential process is that it does not need any base station infrastructure and is simpler than typical RTK algorithms. The accuracy of the system is at the 1 to 2 metre level when the geometry is good and at the 5 to 10 metre level in urban canyons. In the same urban canyon environment, a pseudorange only solution using a least squares technique, the accuracy often degrades to the 100 metre level, so this approach shows a vast improvement over conventional methods. Over the past year, NovAtel Inc. has developed a new filter which uses delta phase measurements as inputs to a filter that maintains both the current and previous position to drastically improve the positioning accuracy in areas where the sky is partially or intermittently obscured. In this paper the positioning algorithm is described and test results showing the positioning improvement over conventional least squares is presented. Results from both inner city (old growth forest) residential neighbourhoods and urban canyons are shown.