, | 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/s |

| 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. |