1. Pseudoranges to Four Satellites

2. Definition of Pseudorange

3. Pseudorange with Propagation Errors

4. Topocentric Position

5. Approches to Solution
Solution must be determined iteratively, given a satellite ephemeris and approximate position of the receiver
Assume an average value for the travel time. Satellite position is interpolated for the epoch and topocentric position computed. Travel time recomputed by dividing by c. Iterate until specified convergence is achieved.
Second method requires pseudoranges and the receiver position is iterated on by calculating the amount of earth rotation during the transmission time. Again must iterate until specified convergence is achieved.

6. Navigation Solution
Nominal pseudoranges

7. Dilution of Precision Factors
Commonly used to describe the effect of geometry of satellite constellation on the accuracy of the position estimate at some epoch
DOP factors are simple functions of the diagonal elements of the covariance matrix of the final adjusted parameters
s = so DOP
Where so denotes the standard deviation of the observed pseudoranges and s is the standard deviation of the horizontal or vertical position

8. DOP Definitions and Expressions
VDOP: vertical dilution of precision
HDOP: horizontal dilution of precision
PDOP: positional dilution of precision
TDOP: time dilution of precision
GDOP: geometric dilution of precision

9. Undifferenced Carrier Phase Observable

10. Carrier phase related to topocentric range
Station clock error enters in two ways: large term, fdtk, and the
smaller term, which is a function of topocentric range rate,
For a dtk of 1 nsec, the term fdtk contributes 1.5 cycles, which is
About 150 times the expected carrier phase measurement accuracy!
Satellite clock errors affect the phase observable through the
Large term fdtP as well as the smaller frequency offset term.

11. Single Difference Solution
Solution remains sensitive to both RCVR and SV clock errors
Slant Range
Two stations observe the same SV at the same epoch

12. Double Difference Solution
Solution NO LONGER sensitive to RCVR and SV clock errors.
Best solution arises when integer ambiguity is fixed.
Pseudoranges
Two stations observe the same two SVs at the same epoch

13. Triple Difference Solution
Often computed in pre-processing to get approximate positions for
double-difference solutions and to map phase breaks, which show up
as outliers in the computed phase residuals. t1 t0 t1 t0
Two stations observe the same two SVs at two consecutive epochs

14. Common-mode Cancellations

15. Doppler Observation and Geometry
Physics is the same as the carrier phase approach but mathematical treatment is different. Doppler processing relies on the integrated Doppler observation, encompassing two epochs. Carrier phase formulation introduces the ambiguity term, which when fixed adds strength to the solution.