MATLAB/Simulink implementation of Kalman filters and its non-linear variants

• Kalman Filter is an optimal state observer
• Also called Linear Quadratic Estimation (LQE)
• Works for linear systems
• Takes into account statistical noise
• Combines estimated and measured readings from different sources using joint probability distribution to estimate an optimal reading

Process noise (wk): Noise due to inexact nature of modelled physical equations, such as deviations due to air pressure. Needs to be tuned. Measurement noise (vk): Noise characteristic to the sensor's working. Needs to be obtained from sensor calibration.

• Both wk and vk can be assumed to be mutually uncorrelated white Gaussian noise processes.

• The state-space equations of the system are:

• In control theory, a state observer or state estimator is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system.

• In essence, Kalman filter has two steps: Predict and Update

Linear model

Non-linear model

Kalman filter

Extended kalman filter

Unscented kalman filter

• Tuning of kalman filter parameters and initial state assumptions
• Normalized error visualization
• Implementation of particle filter for non-gaussian system
• Model a real system and compare results with actual hardware testing

• Battery pack state of charge estimation using ESC cell model
• Sensorless motor drive control and state estimation
• Automotive navigation systems and sensor fusion
• Image processing and noise removal

• https://in.mathworks.com/help/control/ug/extended-and-unscented-kalman-filter-algorithms-for-online-state-estimation.html
• https://groups.seas.harvard.edu/courses/cs281/papers/unscented.pdf
• https://in.mathworks.com/help/control/ug/nonlinear-state-estimation-using-unscented-kalman-filter.html
• https://academic.csuohio.edu/simond/pubs/ESDNonlinear.pdf
• https://ieeexplore.ieee.org/document/7530343
• https://ieeexplore.ieee.org/document/7734116