Inverse, and transpose, respectively.

The i row of.

, , and

Link-i's length (m), twist (rad), and offset (m), and joint- -i angle (rad), respectively.


and, respectively.


and, respectively.

The estimation error vectors in m.

The system’s model function.


Prismatic joint-1 motor force (N) and Revolute joint-i motor torque (N. M), respectively.

Gravity acceleration (m/s2).

The sensor’s model function.

Subscripts used to identify elements.

The identity matrix with dimensions of.

Time step value.

The a priori value at time k.

The a posteriori value at time k.

The correction gain of the filter.

Inertia matrix.

Masses of links 1, 2, 3 and 4 respectively (kg).

Number of measurements and states, respectively.

The state's error covariance matrix.

The output’s error covariance matrix.

The error covariance matrix.

The number of the sigma points.

The process noise covariance matrix.

The measurements noise covariance matrix.

The summation operator.

Sampling time, and is equal to 0.001 sec.

Joints force and torques vector.

Viscous friction vector.

The measurement and system noise, respectively.

The assigned weight.

The state vector.

The output vector.


The estimate and its measurement for the sigma point, respectively.