Global Positioning System Reference
In-Depth Information
2.5 Kalman filtering
KF is the most commonly used technique for INS/GPS integration (Farrell & Barth,
1998)(Grewal et al., 2007). fig 1 shows a top-level view of the KF-based system used in this
chapter for outdoor mobile robot localization.
As mentioned previously, a loosely-coupled
integration scheme is adopted in this chapter.
Fig. 1. An overview of the KF-based system used for outdoor mobile robot localization.
2.5.1 Error state vector
Since KF requires linearized models it estimates the error state not the navigation states
themselves. The errors in the navigation states estimated by the filter are then used to correct
the mechanization output and provide corrected navigation states. Leveraging the benefits
of wheel encoders during GPS outages the KF presented in this section uses an error vector
containing eleven states.
The linearized error-state system model used by the KF in this work is in the form:
δ
˙
x
= F δ
x
+ G
W
(
t
)
(18)
The error state vector in Equation 18 consists of position errors (for latitude, longitude and
altitude), velocity errors (along East, North and vertical Up), yaw error and inertial sensor
stochastic drift for the single gyroscope and three accelerometers:
= δ
f z T
˙
˙
˙
h
V e
V n
V u
˙
f x
f y
δ
x
φδ
λδ
δ
δ
δ
δ
ψδ
ω z
˙
δ
δ
δ
(19)
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