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The Kalman filter algorithm can be applied as a recursive estimator of the state of a dynamic system described by a linear difference equation. Given discrete measurements linearly related to the state of the system, but corrupted by white Gaussian noise, the Kalman filter estimate of the system is statistically optimal with respect to a quadratic function of the estimate error. The first objective of this paper is to give deep enough insight into the mathematics of the Kalman filter algorithm to be able to choose the correct type of algorithm and to set all the parameters correctly in a basic application. This description also includes several examples of different approaches to derive and to explain the Kalman filter algorithm. In addition to the mathematical description of the Kalman filter algorithm this paper also provides an implementation written in MATLAB. The objective of this part is to correctly replicate the target tracker used in the surveillance radar PS-90. The result of the implementation is evaluated using a simulated target programmed to have an aircraft-like behaviour and done without access to the actual source code of the tracker in the PS-90 radar

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Local active noise control systems aim to create zones of quiet at specific locations within a sound field. The created zones of quiet generally tend to be small, especially for higher frequencies, and are usually centred at the error sensors. For an observer to experience significant reductions in the noise, the error sensors therefore have to be placed relatively close to an observer’s ears, which is not always feasible or convenient. Virtual sensing methods have been proposed to overcome these problems that have limited the scope of successful local active noise control applications. These methods require non-intrusive sensors that are placed remotely from the desired locations of maximum attenuation. These non-intrusive sensors are used to provide an estimate of the sound pressures at these locations, which can then be minimised by a local active noise control system. This effectively moves the zones of quiet away from the physical locations of the transducers to the desired locations of maximum attenuation, such as a person’s ears. A number of virtual sensing algorithms have been proposed previously. The difference between these algorithms is the structure that is assumed to compute an estimate of the virtual error signals. The question now arises as to whether there is an optimal structure that can be used to solve the virtual sensing problem, which amounts to a linear estimation problem. It is well-known that the Kalman filter provides an optimal structure for solving such problems. An optimal solution to the virtual sensing problem is therefore derived in this thesis using Kalman filtering theory. The proposed algorithm is implemented on an acoustic duct arrangement to demonstrate its effectiveness. The presented experimental results indicate that the zone of quiet was effectively moved away from the physical sensor towards the desired location of maximum attenuation. The previously proposed virtual sensing algorithms have been developed with the aim to create zones of quiet at virtual locations that are assumed spatially fixed within the sound field. Because an observer is very likely to move their head, the desiredlocations of the zones of quiet are generally moving through the sound field rather than being spatially fixed. For effective control, a local active noise control system incorporating a virtual sensing method thus has to be able to create moving zones of quiet that track the observer’s ears. A moving virtual sensing method is therefore developed in this thesis that can be used to estimate the error signals at virtual locations that are moving through the sound field. It is shown that an optimal solution to the moving virtual sensing problem can be derived using Kalman filtering theory. A practical implementation of the developed algorithm is combined with an adaptive feedforward control algorithm and implemented on an acoustic duct arrangement. The presented experimental results illustrate that a narrowband moving zone of quiet that tracks the desired location of maximum attenuation has successfully been created. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1291123 / Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 2007.

Thesis (M.A. Sc.)--University of Toronto, 2004. / Adviser: C.J. Damaren.

Thesis (M.S.)--Ohio University, March, 1984. / Title from PDF t.p.

Thesis (Ph. D.)--University of Hong Kong, 2008. / Includes bibliographical references (leaf 181-195) Also available in print.