What is UKF (unscented Kalman filter)

The Unscented Kalman Filter (UKF) is an advanced state estimation technique used in various applications where traditional Kalman Filters (EKFs) might struggle with non-linear systems. Here's a detailed explanation of UKF:

Kalman Filter Limitations:

• The standard Kalman Filter (KF) is a powerful tool for state estimation in linear systems. It provides an optimal (minimum mean squared error) estimate of the system's state by combining noisy sensor measurements with a model of the system's dynamics.
• However, the EKF's linearization process can introduce errors when applied to non-linear systems. This can lead to inaccurate state estimates and filter divergence.

UKF's Approach:

The UKF addresses the limitations of the EKF by employing a deterministic sampling approach called the Unscented Transform (UT) for state and noise propagation. Here's the core concept:

1. Sigma Points: The UKF utilizes a set of deterministically chosen sample points (called sigma points) around the estimated mean and covariance of the state. These sigma points capture the statistical information about the state distribution.
2. Propagation through Non-linear System: Each sigma point is propagated through the system's non-linear model. This provides a transformed set of points representing the state distribution after the non-linear transformation.
3. Mean and Covariance Estimation: The means and covariances of the transformed sigma points are then calculated. These represent the estimated state and its covariance after considering the non-linearity.
4. Measurement Prediction and Update: Similar to the EKF, the UKF predicts the expected measurement based on the estimated state and incorporates actual sensor measurements to update the state estimate and its covariance.

Benefits of UKF:

• Improved Accuracy for Non-linear Systems: By avoiding linearization, the UKF can provide more accurate state estimates compared to the EKF in non-linear scenarios.
• Handles Non-Gaussian Noise: The UKF can handle non-Gaussian noise distributions more effectively than the EKF.

Implementation Details:

• The specific number and selection of sigma points depend on the system's dimensionality. Common choices are using a minimal set (2n + 1, where n is the state dimension) or incorporating additional points for better accuracy.
• The weights assigned to each sigma point during mean and covariance calculation play a crucial role in the UKF's performance.

Applications of UKF:

• Robot Localization and Navigation: UKF is widely used in robotics for state estimation tasks like robot pose estimation (position and orientation) due to its ability to handle non-linear sensor measurements and robot dynamics.
• Autonomous Vehicles: Similar to robot navigation, UKF can be used in autonomous vehicles to estimate the vehicle's state (position, velocity, etc.) by incorporating sensor data from GPS, LiDAR, and other sensors.
• Signal Processing: UKF can be applied in various signal processing tasks where non-linear filtering or state estimation is required, such as target tracking in radar systems.

Comparison with EKF:

In Conclusion:

The UKF is a valuable tool for state estimation in non-linear systems, offering improved accuracy compared to the EKF. While it comes with slightly higher computational complexity, the UKF's ability to handle non-linearities effectively makes it a preferred choice for various applications in robotics, autonomous vehicles, signal processing, and other domains requiring accurate state estimation in non-linear scenarios.