Introduction to linear and nonlinear programming

A receding horizon Kalman FIR filter is presented that combines the Kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown. The suggested filter is a FIR filter form which has many good inherent properties. It can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state. The suggested filter can be represented in either an iterative form or a standard FIR form. It is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition. The validity of the suggested filter is illustrated by numerical examples.

A receding horizon Kalman FIR filter for discrete time-invariant systems

We present a new approach to the least-squares design of stable infinite impulse response (IIR) digital filters. The design is accomplished by using an iterative scheme in which the denominator polynomial obtained from the preceding iteration is treated as a part of the weighting function, and each iteration is carried out by solving a standard quadratic programming problem that yields a stable rational function. When the iteration converges, a stable and truly least-squares solution is obtained. The method is then extended to address the least-squares design of stable IIR two-dimensional (2-D) filters. Examples are included to illustrate the proposed design techniques.

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A weighted least-squares method for the design of stable 1-D and 2-D IIR digital filters

A receding horizon Kalman finite-impulse response (FIR) filter is suggested for continuous-time systems, combining the Kalman filter with the receding horizon strategy. In the suggested filter, the horizon initial state is assumed to be unknown. It can always be obtained irrespective of unknown information on the horizon initial state. The filter may be the first stochastic FIR form for continuous-time systems that may have many good inherent properties. The suggested filter can be represented in an iterative form and also in a standard FIR form. The suggested filter turns out to be a remarkable deadbeat observer. The validity of the suggested filter is illustrated by numerical examples.

A receding horizon Kalman FIR filter for linear continuous-time systems

http://ntur.lib.ntu.edu.tw/bitstream/246246/142508/1/101.pdf

An iterative method for the design of variable fractional-order FIR differintegrators

A closed-form least-squares solution to the design problem of two-dimensional real zero-phase finite-impulse-response (FIR) filters with quadrantally symmetric or antisymmetric frequency response is obtained. An in-depth study of the matrices involved in the development of the design technique reveals a number of useful properties. It is shown that these properties lead to an optimal analytical solution for the filter coefficients, making it unnecessary to use the time-consuming methods of optimization, matrix inversion, and iteration. Because of the reduced order of the matrices involved, their specific characteristics, and the analytical approach, the computational complexity is greatly reduced. Simplicity and efficiency of the design technique is illustrated through examples. The results in terms of error in frequency response compare favorably with those obtained by using other techniques. It is shown that the design time using the proposed technique is significantly smaller than that required by the I/sub p/-optimization technique or weighted least-squares technique using Harris' ascent algorithm or modified Lawson's algorithm. >

An analytical least square solution to the design problem of two-dimensional FIR filters with quadrantally symmetric or antisymmetric frequency response

J.-D. Wang

Papers

An analytical least square solution to the design problem of two-dimensional FIR filters with quadrantally symmetric or antisymmetric frequency response