Performance of Stand-Alone GPS - Understanding GPS: Principles and Applications - page 332

1.0

0.8

σ S
σ L

σ S
σ L

=0

values of 0, 0.25, 0.5 and 1.0

0.6

0.4

σ S
σ L

=1

0.2

0.0

2.5

1.0 2.0

0.0 0.5 1.5

k

Figure 7.7 Cumulative distribution of radial error for various values of σ S / σ L for a two-dimensional
Gaussian random variable.

Table 7.5 Approximate Formulas for the
Magnitude of the Horizontal Error
Approximation Formula* Probability Range

CEP 50 ≈ 0.75 HDOP 0.43-0.54

UERE

CEP 80 ≈ 1.28 HDOP 0.80-0.81

UERE

CEP 90 ≈ 1.6 HDOP 0.89-0.92

UERE

0.95-0.98

CEP 95 ≈ 2.0 HDOP

UERE

* CEP xx is defined as the radius of the circle that when centered at
the error-free location includes xx% of the error distribution.
Hence, CEP 50 = CEP.

CEP

12 ≈⋅

075 . HDOP ⋅ σ UERE =××= 075 . 1 14 . 11 . m

50

CEP ≈⋅ . HD OP ⋅ σ

σ

= 12875 . × 1 × 14 . = 18 . m (7.66)

80 UERE

CEP ≈⋅ 20 . HDOP ⋅ = 20 . ×× 114 28 . = . m

95 UERE

For applications where three-dimensional error distributions are of interest, one
final commonly used metric is spherical error probable (SEP), which is defined as the
radius of a sphere centered at the true position that contains 50% of the measured
positions.

7.3.3 Weighted Least Squares (WLS)
Oftentimes, the UEREs among the visible satellites are not well described as being
independent and identically distributed. In such circumstances, the least-squares