# What's the difference between Pose Measurement and Position Measurement?

I have read a robotic related paper called Estimating SE(3) elements using a dual quaternion based linear Kalman filter, and the author proposed that the equation of position measurement is denoted as:

$$\mathbf{a}=\mathbf{R}\mathbf{b}+\mathbf{t}$$

where $$\mathbf{a}$$ is the sensor measurement, $$\mathbf{R}$$ ∈ SO(3) is the rotation matrix, $$\mathbf{b}$$$$\mathbf{R}^{3}$$is the point to be transformed and $$\mathbf{t}$$$$\mathbf{R}^{3}$$ is the translation vector. In an application such as rigid registration of images, $$\mathbf{a}$$ is the sensed location of points and $$\mathbf{b}$$ is the corresponding point on the CAD model of the object.

The equation of pose measurement is denoted as:

$$\mathbf{AX-XB=0}$$

where $$\mathbf{A,B}$$ are pose-measurements, and the $$\mathbf{X}$$ is the desired transformation to be estimated.

So is there anyone who know what the difference between pose measurement and position measurement?

referring to your equation $$\boldsymbol{a}=\boldsymbol{Rb}+\boldsymbol{t} ,$$ the position measurement would be $$\boldsymbol{t}$$ whilst the orientation measurement would be $$\boldsymbol{R}$$. These quantities can be obtained in different ways, e.g. position could be measured using GPS while orientation could be obtained using an IMU. I hope this helps,