7B-4-4 
♦ Kalman filter 
♦ Smoothing the code pseudorange with 
carrier phase measurements 
The KF is sensitive to a priori information, 
initial conditions and modeling errors. 
Hence, failure in any step will lead to 
incorrect filtering results. 
The smoothing algorithm makes use of the 
information of the carrier phase, and the 
accuracy of the phase is higher than the 
pseudorange. The smoothing of the code 
pseudorange using carrier phase 
measurements was first investigated by Hatch 
(1982). In this paper, we applied a smoothing 
algorithm proposed by Lachapelle et al. 
(1986). 
Algorithm (smoothing of code pseudorange 
using carrier phase measurements) 
For satellite i, let the DGPS corrected 
pseudorange be denoted as P m j, P m j+\, the 
measured phase as <p., q> J+l and the smoothed 
pseudorange p mj , p m . +1 at epoch j andj+1. 
The following smoothing scheme is obtained 
by 
P ni+> —jPmj-H + f(Pnj +(^. 
(4) 
where A is the wave length. 
It should be noted that the carrier 
phase signal in (4) is sensitive to cycle 
slips. If cycle slips occurs, the 
accuracy of the smoothed pseudorange 
will be affected. The key of the 
equation (4) is to detect cycle slips in 
real time (Hofmanm-Wellenhof et 
al.,1994). There are many ways to 
detect cycle slips, see Schwarz et al. 
(1994), Bastos and Landau (1988), 
Bohenek (1995), and Lipp and Gu 
(1994) for instance. We will not 
discuss this topic here. Once a cycle 
slip occurs, (4) is reset by setting j=l. 
Then a new iteration begin. It turns 
out that the smoothed 
pseudorange P m j+\ when used for 
positioning yields a significant 
improvement in positioning accuracy 
compared to conventional DGPS 
positioning. This is documented by 
experiments in Section 4. 
3. Integration of the DGPS/DR System 
A DGPS system gives very accurate 
positions, but the GPS signals are 
frequently blocked from reaching the