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**Motion Model**

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We are using an Ackerman Model:

_{}

Now,
if we translate our model to the gps and laser point, let us call this point_{}.

_{}

The
velocity _{} is
measured with an encoder locate in the back left wheel. This velocity is
translated to the center of the axle with the following equation:

_{}

For our vehicle:

_{}

Finally the discrete model in global coordinates can be approximated with the following set of equations:

_{}

**Figure 1**: *Vehicle
kinematics*

**Observation Model**

** **

Observation model for range and bearing sensor:

_{}

**Figure 2**: *Vehicle
and Laser sensor*

** **

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**A.1
Motion Model Jacobians:**

_{}

**A.2
Observation Model Jacobians:**

_{}

For the Slam case, where the state vector is the vehicle posse and beacons position:

_{}

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__Ute Dimensions:__

**2 Sensors**

**2.1 Sensors available
in the Ute**

** **

Dead Reckoning:

Velocity Encoder and Steering angle

Inertial Measument Unit: 3 accel / 3 gyros / 2 inclinometers ( Watson Unit )

External Sensors:

GPS

Laser

Vision

** **

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