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Kalman Filtering Tutorial - Biorobotics Lab

1 Understanding and ApplyingKalman FilteringLindsay KleemanDepartment of Electrical and Computer Systems EngineeringMonash University, Clayton2 a basic understanding of Kalman Filtering and assumptionsbehind its (but cannot avoid) mathematical treatment to broaden some practicalities and examples of C++ software is a Kalman filter and What Can It Do?A Kalman filter is an optimal estimator - ie infers parameters of interest fromindirect, inaccurate and uncertain observations. It is recursive so that newmeasurements can be processed as they arrive. (cf batch processing where alldata must be present).Optimal in what sense?If all noise is Gaussian, the Kalman filter minimises the mean square error ofthe estimated if the noise is NOT Gaussian?Given only the mean and standard deviation of noise, the Kalman filter is thebest linear estimator.

The process of finding the “best estimate” from noisy data amounts to “filtering out” the noise. However a Kalman filter also doesn’t just clean up the data measurements, but also projects these measurements onto the state estimate.

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