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Data Fusion via Kalman Filter 125

(a) Estimation error
4
Q=10
y (m) 2

0
0 50 100 150
4
Q=1
y (m) 2

0
0 50 100 150
4
Q=
0.1
y (m) 2
0
0 50 100 150
4
Q=0.01
y (m) 2

0
0 50 100 150
4
Q=0.001
y (m) 2

0
0 50 100 150
Time, t (sec)

FIGURE 3.2 EKF-based GPS solutions for Examples 3.3 and 3.4. (a) Estimation error
for a stationary receiver using the PVA model and EKF with different settings of the
“covariance” parameter Q. (b) Actual (solid line) and estimated trajectory (dots) for a
moving receiver using the PVA model, EKF estimation, and different settings of the
“covariance” parameter Q.

This example shows the possible benefit of using the EKF to combine
measurements over time to attain improved accuracy. The performance that
is achieved will depend on the EKF parameter settings relative to the actual
dynamic situation of the receiver. If the process noise covariance matrix Q k is
too large, then the past information encapsulated in the prior estimate of the
state will be largely ignored in the computation by the EKF of the posterior state
estimate. If the matrix Q k is too small, then the estimated state may significantly
lag the actual state. This is further illustrated in the next example.

Example 3.4 In this example, the receiver is attached to a moving platform.
The platform trajectory is illustrated by the solid curve in each subgraph of

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c003” — 2006/3/31 — 16:42 — page 125 — #27