Dynamic Positioning for Dummies - Kalman Filter & Error Computation (4)

Summary

In this lecture, Dylan Paganini explains the role of Kalman filtering in dynamic positioning systems, focusing on its application for error computation and vessel position estimation. He highlights how Kalman filters combine model estimates and measured data to improve accuracy by adjusting the weight of the measurements and estimates. The presentation also covers how changes in the Kalman gain can affect system stability and performance, especially in dynamic environments like heavy lifts or Arctic operations. Additionally, he introduces an advanced error force estimator for handling rapidly changing unmeasured forces, improving the vessel's response to external conditions.

Takeaways

• 😀 Kalman filtering is used to improve vessel position and heading accuracy by combining model estimates with measured data.
• 😀 The Kalman filter works by comparing the estimated position and heading with the measured data, calculating a residual error, and then using the Kalman gain to adjust the estimate.
• 😀 The Kalman gain determines how much weight should be given to the measurement versus the model's estimate based on their respective errors.
• 😀 If the Kalman gain is high (close to 1), the system trusts the measurements more, while a low gain (close to 0) prioritizes the model estimates.
• 😀 The system uses dead reckoning (based on model estimates) when there are no position measurements, but this will gradually become less accurate over time.
• 😀 Error in the measurement and model estimates needs to be calculated to adjust the Kalman gain and improve position accuracy.
• 😀 A low-pass filter is used to process the measured forces, like sea current and waves, which are not directly measured but affect the vessel's position.
• 😀 The Kalman filter does not consider set points directly; it focuses only on the measured and estimated positions and heading for adjustments.
• 😀 In special cases with rapidly changing external forces (like in Arctic operations or heavy lifts), the Kalman filter's gain can be adjusted to improve performance.
• 😀 Increasing the Kalman gain can make the system more responsive to rapid changes but could lead to instability, so adjustments should be carefully controlled.
• 😀 A new error force estimator, using a linear approach for residual force calculations, allows for more stable and rapid responses in dynamic conditions without affecting the system's stability.

Q & A

What is the purpose of using a Kalman filter in dynamic positioning systems?

The Kalman filter is used to estimate a vessel's position and heading by comparing measured data with the best model predictions. It helps account for errors in the model, unmeasured forces, and other uncertainties in the system, improving the accuracy of the vessel's positioning.

How does the Kalman filter update the vessel's position estimate?

The Kalman filter updates the vessel's position estimate by incorporating a 'current gain' that determines how much trust to place on the measured data versus the model's estimate. The formula used is the previous estimate plus the Kalman gain multiplied by the residual (the difference between measured and estimated positions).

What role does the Kalman gain play in the filtering process?

The Kalman gain determines how much influence the measurement data will have on the new estimate. A higher Kalman gain gives more weight to the measurements, while a lower Kalman gain gives more weight to the model's estimate. This helps adjust the system’s response to different levels of measurement accuracy and model reliability.

How is the Kalman gain calculated?

The Kalman gain is calculated as the ratio of the errors in the estimate to the sum of the errors in the estimate and the errors in the measurement. This ratio determines how much trust the filter should place on the measurement data compared to the model estimate.

What happens when the Kalman gain approaches 1?

When the Kalman gain approaches 1, it means that the measurement data is highly accurate and the model estimate is unstable. In such cases, the system will place more weight on the measurements, potentially making the estimates more responsive but also more susceptible to any noise in the measurements.

What is 'dead reckoning' in the context of dynamic positioning systems?

Dead reckoning occurs when all position reference systems are lost, and the system continues to estimate the vessel's position based solely on the model. While initially accurate, the position estimate gradually deteriorates over time due to the lack of real-time measurement updates.

How does the low-pass filter affect the Kalman filter in dynamic positioning?

The low-pass filter is used to smooth out rapid changes in external forces (such as waves or sea currents) by applying a time constant to the data. It helps reduce the impact of noise and instability on the vessel's position estimates, though it introduces some delay in the system's response to these forces.

What is the significance of the 'residual force' in dynamic positioning systems?

The residual force represents the difference between the model's prediction and the actual forces acting on the vessel. It is calculated by taking into account unmeasured forces like waves or current, and it influences the vessel's movement, contributing to the overall error in the positioning system.

How does the error force estimator improve dynamic positioning during special operations?

The error force estimator directly calculates residual forces as additional forces, improving the system’s response to rapidly changing, unmeasured forces. This estimator allows for a more stable and quicker response in scenarios such as heavy lifting or operations in extreme conditions like Arctic waters.

Why do manufacturers limit the Kalman gain adjustment in dynamic positioning systems?

Manufacturers limit the adjustment of the Kalman gain to prevent instability in the system. If the Kalman gain were set too low, the system would rely too much on the model and ignore measurements. Conversely, if set too high, the system could become overly sensitive to noisy measurements, leading to erratic behavior.