Common Values Used With Gnss; Table 1-1: Common Accuracy Measures Used With Gps - C-Nav IALA Hardware Reference Manual

C-Nav Hardware Reference Guide
The following table describes some of the statistical formulas and measures commonly used for
GNSS positional accuracy measurement:

Table 1-1: Common Accuracy Measures Used with GPS

Measurement Statistical
Dimension Measure
Root Mean
1D
Square
Probable
1D
Error
Error
2D
Ellipse
Circular
2D Error
Probable
Twice
Distance
2D
Root Mean
Square
Error
3D
Ellipsoid
Spherical
3D Error
Probable
*(Mikhail, 1976) †(Langley, 1991) **(National Geodetic Survey, 1986)

Common Values Used with GNSS

•
Speed of light ..... c = 299792458 meters per second
•
L1 frequency ...... f
•
L2 frequency ...... f
• Wavelength ....... λ = c/f (meters per second)
• L1 wavelength .... λ
• L2 wavelength .... λ
Abbreviation Probability Approximation
rms
PE
N/A
CEP
2drms
N/A
SEP
= 1575420000 Hz
L1
= 1227600000 Hz
L2
= 0.190293672798 meters
L1
= 0.244210213425 meters
L2
11
68.3%*
0.674 σ**
50%*
Defined by σ
39.4%*
& correlation
Radius:
50%*
0.589 (σ
Radius: 2σ
Varies, 95.4
σ = √ σ
†
– 98.2%
Defined by:
σ , σ
19.9%*
x
correlations
Radius:
0.513 (σ
50%*
Related
Expressions
MSE – mean
square error
σ
(the square of
the rms)
N/A
, σ
x y
N/A
CPE – also
called circular
+ σ
)*
x y
probable error
nd
2 , less
common
†
definition: 2
+ σ
2 2
dimensional
x y
rms (circle's
radius 1 σ)
, σ
& N/A
y z
SEP – also
called
+ σ
+
x y
spherical
σ
)*
z
probably error