Page 257 - Introduction to Autonomous Mobile Robots

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∂ α ti ∂ α ti ∂ α ti Chapter 5
,
,
,
----------- ----------- -----------
∇ h = x ˆ ∂ y ˆ ∂ ∂ θ ˆ = 0 0 – 1 (5.65)
i
r ∂ r ∂ r ∂ – cos W α – sin W α 0
,
,
,
,
,
ti
ti
ti
--------- --------- --------- ti ti
x ˆ ∂ y ˆ ∂ ∂ θ ˆ
The measurement prediction results in predicted lines represented in the robot coordi-
nate frame (figure 5.32). They are uncertain, because the prediction of robot position is
uncertain.
4. Matching. For matching, we must find correspondence (or a pairing) between predicted
and observed features (figure 5.33). In our case we take the Mahalanobis distance

r

line i
r i

-π α i 0 π

Figure 5.32
Measurement predictions: Based on the map and the estimated robot position the targets (visible
lines) are predicted. They are represented in the model space similar to the observations.