, | 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 | and, respectively. |
and | and, respectively. |
| The estimation error vectors in m. |
| The system’s model function. |
and | 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. |
and: | The estimate and its measurement for the sigma point, respectively. |