Kalman Filter

Posted on September 21, 2023

Neville Dubash headshot

This post was originally published in two parts which have been combined below.

Part 1


The Kalman filter is a powerful algorithm used to estimate the state of a dynamic system from noisy measurements. Developed in the 1960s, it has become a fundamental tool in various fields due to its ability to provide accurate and reliable estimates even in the presence of uncertainty and noise.

At its core, the Kalman filter is based on Bayesian statistics principles and optimal estimation. It combines two sources of information: predictions from a dynamic model and measurements from sensors. The dynamic model describes how the system’s state evolves over time, while the measurements provide noisy observations of the system. By iteratively incorporating new data, the Kalman filter continuously refines its estimates, dynamically balancing the weight given to predictions and measurements based on their respective uncertainties.

The Kalman filter operates in two main steps:

  1. Prediction Step: the filter predicts the state of the system at the next time step based on the current state estimate and the system’s dynamic model. The prediction also includes an estimate of the uncertainty in the state prediction, represented by an error covariance matrix.
  2. Update Step: the filter incorporates the latest measurement into the prediction. It calculates the Kalman gain, which determines how much weight should be given to the measurement relative to the prediction. The Kalman gain depends on the uncertainty in both the prediction and the measurement. A high-gain value implies that the measurement is trusted more, while a low-gain value means the prediction is trusted more. The new state estimate and error covariance matrix are then updated based on the Kalman gain and the measurement residual.

By combining predictions from a dynamic model with measurements from sensors, the filter continuously refines its estimates, dynamically balancing the importance of predictions and measurements based on their respective uncertainties. This makes the Kalman filter an indispensable tool in many fields, enabling accurate and reliable state estimation for a wide range of applications.

Part 2


Enhancing Oil Processing Efficiency with Kalman Filter-based Middlings Interface Detection

The separation process in the oil sands industry involves extracting bitumen from ore that is primarily made up of clay and sand. One of the key vessels in this process is the primary separation cell (PSC) or primary separation vessel (PSV). The separation process involves the mixing of ore with hot water and chemicals, upstream of the PSC/PSV, to create a slurry of “aerated bitumen”, solids, and water. This slurry is fed into the PSC/PSV where, ideally, the aerated bitumen rises to the top and all the solids fall to the bottom.

The efficient operation of the PSC/PSV is critical for optimal production. A significant challenge lies in accurately detecting the middlings interface, which lies below the bitumen (froth) layer. Traditional methods often rely on single sensors, making them susceptible to noise and uncertainties that can impact the accuracy of the interface detection.

The Kalman filter offers a potential solution to address this challenge. By fusing data from multiple sensors, including pressure transmitters, level sensors, density meters, and cameras, the Kalman filter can obtain a more accurate and robust estimation of the middlings interface position. This sensor fusion approach leverages the strengths of each sensor, compensating for their individual limitations and ensuring accurate and reliable estimates.

The Kalman filter’s ability to handle noise and uncertainties is particularly valuable in real-world applications. The filter takes into account the known characteristics of sensor noise and the system dynamics. As new sensor measurements become available, the Kalman filter updates its internal state estimate and error covariance matrix in real-time, allowing the system to adapt promptly to changes in the process.

Using the Kalman filter for sensor fusion provides a cutting-edge solution that can increase bitumen froth quality; its ability to accurately estimate the interface level in real-time empowers the oil sand industry to make data-driven decisions, enhancing productivity and profitability.


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