Global Positioning System Reference
In-Depth Information
T
wheels are essentially rigid.
Therefore the error in forward speed
δ
V
f
contained in
δ
θ
is
expressed as a white noise term using the standard deviation of
δ
V
f
. The standard deviation
is added to the process noise coupling state vector
G
.
2.5.4 Heading error
As mentioned earlier, pitch and roll do not have an error model in this work. This is because
errors in pitch and roll do not accumulate as for the other measurements due to a lack of
integration operations. To obtain an expression for heading error, use the yaw expression from
mechanization for yaw
and linearize it by taking the first order terms in the Taylor series
expansion. An expression for the error in yaw (and consequently azimuth) is determined:
ψ
⎡
⎣
⎤
⎦
δφ
V
e
tan
φ
(
1
δ
h
V
e
csc
φ
tan
φ
−
ω
e
cos
φ
+
˙
ψ
=
δ
(29)
R
+
h
2
R
+
h
R
+
h
)
V
e
δω
z
δ
2.5.5 Measurement model
Section 2.5.1 described the error-state system model for the KF. The KF also needs a
measurement model to be used in the update stage. There are two measurement update
models used in this work. The first is when GPS is available and the second is used when
there is a GPS outage. During GPS availability both GPS position and velocity are used and
the differences between the RISS mechanization position and velocity and those of GPS are
used as a measurement. The measurement model is as follows:
z
GPS
k
GPS
k
v
GPS
k
=
H
x
k
+
(30)
z
GPS
k
Where the measurement state vector
is defined as:
⎡
⎣
⎤
⎦
INS
k
GPS
k
φ
−
φ
INS
k
GPS
k
λ
−
λ
h
INS
k
h
GPS
k
−
z
GPS
k
V
INS
e
k
V
GPS
e
k
=
(31)
−
V
INS
n
k
V
GPS
n
k
−
V
INS
u
k
V
GPS
u
k
−
INS
z
k
GPS
z
k
− ω
ω
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