This paper presents an optimal discrete time reduced order Kalman ̄lter. The reduced order ̄lter is used to estimate a linear combination of a subset of the state vector. Most previous approaches to reduced order ̄ltering rely on a reduction of the model order. However, this paper takes the full model order into account. The reduced order ̄lter is obtained by minimizing the trace of the estimat...

The use of a paraunitary lter bank for image processing requires a special treatment at image boundaries to ensure perfect reconstruction and orthogonality of these regions. Using time-varying boundary lter banks, we will discuss a procedure that explores all degrees of freedom of the border lters in a method essentially independent of signal extensions, allowing us to design optimal boundary l...

It has been observed empirically that each coe cient in a Parks-McClellan lter converges to a steady state value as the lter length increases. This suggests the possibility of obtaining lters that are near optimal while "re-using" lter coe cients from shorter lters in the design of longer lters. In the context of approximate processing this then allows a ltering operation to be done in stages. ...

A comparison of the performance of three diierent Natural Algorithms applied to the task of IIR system identiication is presented. In all cases, stability of the adaptive lter is guaranteed through the choice of a lattice lter structure and appropriate coding of the lattice lter reeection coeecient space. We show that whilst simulated annealing-based adaptive algorithms perform well, algorithms...

If a continuous-time nonlinear system with continuous measurements is subjected to process and measurement noise, the evolution of the probability density function associated with the state is given by the solution to a nonlinear stochastic partial diierential equation called the Kushner equation. If the Kushner equation can be solved then various lters based on diierent optimality criteria cou...

In recent years particle …lters have been applied to a variety of state estimation problems. A particle …lter is a sequential Monte Carlo Bayesian estimator of the posterior density of the state using weighted particles. The e¢ ciency and accuracy of the …lter depend mostly on the number of particles used in the estimation and on the propagation function used to re-allocate weights to these par...

This paper presents a Gaussian-mixture implementation of the PHD lter for tracking extended targets. The exact lter requires processing of all possible measurement set partitions, which is generally infeasible to implement. A method is proposed for limiting the number of considered partitions and possible alternatives are discussed. The implementation is used on simulated data and in experiment...

We brieey describe technical aspects and speciications of the new UKST H interference lter which is probably the largest of its kind available in astronomy. Preliminary exposures show that the lter gives excellent imaging with high overall transmission and uniformity at H wavelengths. This is achieved over a circular area of about 305 mm diameter or about 5.7 degrees (the so called`clear apertu...

1 A lter for edge detection In graylevel images boundaries are often associated to step-like discontinuities. In its simplest form the problem of nding boundaries in 1D images may therefore be thought of as the problem of nding step-discontinuities in a signal. The naive approach to this problem is to use a diierentiator and a threshold in series. The derivative of the signal ought to present l...