Showing papers on "Kernel adaptive filter published in 1986"

Numerical aspects of different Kalman filter implementations

Abstract: A theoretical analysis is made of the error propagation due to numerical roundoff for four different Kalman filter implementations: the conventional Kalman filter, the square root covariance filter, the square root information filter, and the Chandrasekhar square root filter. An experimental analysis is performed to validate the new insights gained by the theoretical analysis.

Exact finite-dimensional nonlinear filters

Abstract: A new nonlinear filter is derived for continuous-time processes with discrete-time measurements. The filter is exact, and it can be implemented in real time with a computational complexity that is comparable to the Kalman filter. This new filter includes both the Kalman filter and the discrete-time version of the Benes filter as special cases. Moreover, the new theory can handle a large class of nonlinear estimation problems that cannot be solved using the Kalman or discrete-time Benes filters. A simple approximation technique is suggested for practical applications in which the dynamics do not satisfy the required conditions exactly. This approximation is analogous to the so-called "extended Kalman filter" [10], and it represents a generalization of the standard linearization method.

Synthesis and analysis of state-space active filters using intermediate transfer functions

Abstract: This paper is concerned with the realization of a given arbitrary filter transfer function as a network of resistively interconnected integrators. These state-space realizations are synthesized using a new technique called intermediate function (IF) synthesis. The technique is based on the selection of a set of functions to serve as either the transfer functions from the filter input to the integrator outputs or the transfer functions from the integrator inputs to the filter output. Relationships between the filter sensitivity and dynamic range and the intermediate functions are derived. A number of results are also given to aid in the selection of a set of IF's that yields structures with optimum performance.

Optimal Edge Detector Design I: Parameter Selection and Noise Effects

Abstract: This paper comments on the optimality of the Laplacian of a Gaussian edge detection filter which localizes edges through zero crossings in the filtered image. The arguments of both Marr and Hildreth, and Dickey and Shanmugam are reviewed to establish that the filter is optimal in the sense of maximizing output image energy near edge features. This filter's principal advantage over other edge detectors is that its response is user-adjustable through selection of a single parameter, the Gaussian standard deviation. However, no clear method for the selection of this parameter has been provided. The problem is addressed here by applying the filter to two ideal periodic edge models blurred by a Gaussian distribution point-spread function. The observed response to the edge spacing and blur standard deviation is then translated into a filter parameter design procedure. The problems of optimum filter performance in the presence of additive Gaussian noise are then addressed. The problem of selecting the sampled filter's coefficient word size is dealt with in a companion paper.

Adaptive filter for dual energy radiographic imaging

Abstract: A radiographic scanner (A) generates a high energy image representation which is stored in a high energy image matrix (V) and a low energy image representation which is stored in a low energy image memory (U). A pair of filter functions selecting circuits (C) select a first or soft tissue specific filter function and second or bone specific filter function, respectively. The soft tissue filter function selecting circuit selects and adjusts the soft tissue filter function in accordance with the pixel value of the low energy image representation for each corresponding pair of pixel values. Convolvers (44, 46) convolve pixel values from the high and low energy image representations with the selected and adjusted filter functions. A soft tissue transform function (48) transforms the filtered high and low energy image representations into a soft tissue or other material specific image representation (42). The other filter selecting and adjusting circuit selects and adjusts the bone specific filter functions which are convolved with the high and low energy image representations by convolvers (54, 56). A bone specific transform function (58) transforms the filtered high and low energy image representations into a bone basis image.

Efficient Approximation of Kalman Filter for Target Tracking

Abstract: A Kalman filter in the Cartesian coordinates is described for a maneuvering target when the radar sensor measures range, bearing, and elevation angles in the polar coordinates at high data rates. An approximate gain computation algorithm is developed to determine the filter gains for on-line microprocessor implementation. In this approach, gains are computed for three uncoupled filters and multiplied by a Jacobian transformation determined from the measured target position and orientation. The algorithm is compared with the extended Kalman filter for a typical target trajectory in a naval gun fire control system. The filter gains and the tracking errors for the proposed algorithm are nearly identical to the extended Kalman filter, while the computation requirements are reduced by a factor of four.

Zero-tracking adaptive filters

Abstract: A new type of adaptive filter is proposed which can directly estimate and track its own zeros. The adaptation algorithm adapts the zeros of the filter and hence, indirectly, the filter coefficients. To first order in the adaptation parameter, the new algorithm is equivalent to the usual LMS algorithm, and thus it shares the same convergence properties with the latter. The cases of adaptive prediction, the adaptive Pisarenko method, and adaptive point-source location are discussed in detail.

A self-orthogonalizing efficient block adaptive filter

Abstract: This paper deals with the development of a unique self-orthogonalizing block adaptive filter (SOBAF) algorithm that yields efficient finite impulse response (FIR) adaptive filter structures. Computationally, the SOBAF is shown to be superior to the least mean squares (LMS) algorithm. The consistent convergence performance which it provides lies between that of the LMS and the recursive least squares (RLS) algorithm, but, unlike the LMS, is virtually independent of input statistics. The block nature of the SOBAF exploits the use of efficient circular convolution algorithms such as the FFT, the rectangular transform (RT), the Fermat number transform (FNT), and the fast polynomial transform (FPT). In performance, the SOBAF achieves the mean squared error (MSE) convergence of a self-orthogonalizing structure, that is, the adaptive filter converges under any input conditions, at the same rate as an LMS algorithm would under white input conditions. Furthermore, the selection of the step size for the SOBAF is straightforward as the range and the optimum value of the step size are independent of the input statistics.

Non linear adaptive filters

Abstract: A non-linear adaptive filter is described having a linear filter connected in parallel with a non-linear filter. The linear filter provides fast adaption until it has modelled the linear contribution of each coefficient. Thereafter the non-linear filter continues to adapt until the error signal has been reduced to an acceptable level. In a preferred embodiment a plurality of unit delay devices provide taps to sub-processing units each of which is arranged to be adapted according to a linear algorithm during an initial part of a training period, and to a non-linear algorithm after said initial part. The filter has particular use in echo cancellers for data modems.

Application of an extended Kalman filter for state estimation of a yeast fermentation

Abstract: The development of a Kalman filter for state and parameter estimation of a biotechnical process is discussed Because of the large complexity of biotechnical processes, mathematical models for online estimation are based on extensive simplifications Therefore model errors in the structure and parameters cannot be avoided In such situations, simulations of the process in combination with the estimator are very helpful during the design phase: these permit fast examinations of the different behaviour of linear filters compared to nonlinear algorithms and also investigations of the influence of sampling interval and initial values of state and filter variables on the estimation By the use of such simulations, the suitability of process models with various degrees of simplifications can also be easily tested Based on the simulations, an extended Kalman filter with iteration of the output equations was chosen Besides the states, two parameters of a third order process model are estimated online The filter algorithm was tested during batch processes and worked well after a slight modification The filter behaviour observed in the experiments was very similar to the simulations

Sinusoidal disturbance rejection with application to helicopter flight data estimation

Abstract: This paper is concerned with the problem of eliminating sinusoidal disturbances from data while producing minimal distortion to the underlying data. A particular example of this problem arises in the filtering of helicopter data which are corrupted by sinusoidal disturbances due to rotor motion. It is shown that an optimal solution to the problem can be found using Kalman filtering theory. The properties of the optimal filter are analyzed using recent results on filtering for nonstabilizable systems. These results are then used to motivate a particular near-optimal filter which has enhanced robustness properties relative to the optimal filter. It will also be shown that an identical filter can be derived using recent results on the evaluation of recursive discrete Fourier transforms. This link between time and frequency domain methods leads to a rather complete understanding of the characteristics of the filter. Specific results are presented showing the application of the filter to real helicopter data.

Storm surge prediction using Kalman filtering

Abstract: In this study the theory of Kalman filtering has been employed to develop a new method for predicting water-levels along the Dutch coast. The combination of the standard Kalman filter with a non-linear tidal model of the entire North Sea is, from a computational point of view, not (yet) feasible. Therefore, in this investigation two different approaches have been developed. The first is based on the approximation of the tidal movement in the Dutch coastal area by a one-dimensional model. The two-dimensional effects due to the wind and the Coriolis force are taken into account by introducing some additional, empirical equations. The finite difference scheme and the system noise processes, introduced to describe the uncertainty associated with the model, are chosen such that numerical difficulties are avoided. Water-levels and velocities as well as the uncertain parameters in the model are estimated on-line by the Kalman filter. Since the model is continuously being adapted to the changing conditions, even this simple conceptual model gives satisfactory predictions. However, the time interval over which accurate predictions can be produced is limited because the one-dimensional approximation is only realistic for a smal1 part of the southern North Sea. To increase the prediction interval the second Kalman filter approach that is developed in this investigation is based on a two-dimensional model of the entire North Sea. The extension of the one-dimensional filter to two space dimensions does not give rise to conceptual problems but, as noted before, impose an unacceptably greater computational burden. In order to reduce this burden, the Kalman filter is approximated by a time-invariant one. In this case the time-consuming filter equations do not have to be computed over again as new measurements become available, but need only be solved once. Furthermore, by defining the system noise processes on a coarse grid and by employing a Chandrasekhar-type filter algorithm; a computationally attractive implementation of the filter is obtained. It is shown that the algorithm can be vectorized efficiently and that using a CDC CYBER 205 vector processor it is possible to combine the steady-state filter approach with very large models. Numerical difficulties can be avoided by carefully choosing the finite difference scheme, the boundary treatment and most important, the system noise processes. The filter has been tested extensively using simulated data as well as field data. The results show excellent filter performance, especially if we take into account that the number of measurements available (as yet) has been very limited. With respect to the results of the deterministic model without using tbe water-levels measurements available, the improvement obtained by filtering these measurements is substantial.

Recursive center-frequency adaptive filters for the enhancement of bandpass signals

Abstract: In some signal enhancement and tracking applications, where a priori information regarding the signal bandwidth and spectral shape is available, it is suggested to use a recursive center-frequency adaptive filter instead of a fully adaptive filter. A new adaptive algorithm, namely, the recursive maximum-mean-squares (RMXMS) algorithm, is developed based on the gradient ascent technique for the implementation of these filters. An adaptation mechanism based on the Gauss-Newton algorithm is also presented. This class of filters is found to have several advantages which include faster convergence and lesser computational complexity compared to the fully adaptive filters.

A fast filter for real-time image processing

Abstract: In this paper, a new digital filter structure is developed for the implementation of two-dimensional (2-D) recursive filters for realtime image processing. The proposed structure has a short clock cycle time or a high data throughput rate, independent of the order of the filter. Parallelism and pipelining are the two features of the proposed filter structure that contribute to its high-speed performance. The filter can be implemented without multipliers. Using standard integrated circuits and memories, the new filter is capable of filtering images of size up to 512 {\times} 512 pixels with a TV scan rate of 30 frames/s in real time. The effects of the finite precision arithmetic have been considered. Scaling and overflow problems are studied to give insight into the choice of a proper scaling factor, so that an adequate signal-to-noise ratio at the filter output can be obtained.

Adaptive Kalman filtering

Abstract: The increased power of small computers makes the use of parameter estimation methods attractive. Such methods have a number of uses in analytical chemistry. When valid models are available, many methods work well, but when models used in the estimation are in error, most methods fail. Methods based on the Kalman filter, a linear recursive estimator, may be modified to perform parameter estimation with erroneous models. Modifications to the filter involve allowing the filter to adapt the measurement model to theexperimental data through matching the theoretical and observed covoriance of the filter innovations sequence. The adaptive filtering methods that result have a number of applications in analytical chemistry.

Adaptive filters realized with second order sections

Abstract: Adaptive digital filters are currently used in many communication systems for echo cancellation, channel equalization, and adaptive noise cancellation. Most practical applications presently use adaptive finite impulse response (FIR) digital filters because they are well behaved in terms of convergence and stability properties. This paper presents an adaptive algorithm that operates with a parallel form infinite impulse response (IIR) filter structure for applications in which an FIR filter requires too much computation. The new algorithm is derived mathematically and the results of computer experiments are presented to demonstrate its performance.

Adaptive Filter Techniques for Separation of Luminance and Chrominance in PAL TV Signals

Abstract: Mass storage devices will be introduced in consumer TV products in the near future. After changing over TV signal processing from analog to digital, firstly the use of field and frame stores allows to do a big step towards a better picture quality, even in existing standards.

Adaptive digital filter for determining a transfer equation of an unknown system

Abstract: An adaptive digital filter for identifying a transfer function of a unknown system is employed, for example, for echo cancellation and howling prevention. The transfer function of the adaptive filter can be obtained by the sum of outputs from N paths and forms a system of orthogonal functions having coefficient parameters of four groups of a, b, p and q. The groups p and q are adaptively adjusted in response to an error signal while the groups a and b are previously set based on a measurement effected previously or adaptively adjusted in response to the error signal.

Adaptive television deghosting system

Abstract: An adaptive television deghosting system operates on modulated video signals including a direct signal component and one or more ghost signal components. The system uses synchronously demodulated in-phase and quadrature-phase baseband video signals as the respective real and imaginary input signals to a complex IIR filter. The filter coefficients are developed adaptively from preset initial values using the signals provided by the filter during a training interval. The training interval includes the interval between the leading edge of the vertical sync pulse and the first serration pulse of each field. The filtered training signals are subtracted from a sync-tip reference value to develop a signal which is proportional to the error in the filter coefficient values. The error signal values corresponding to ghost signals are multiplied by the complex conjugate of the training signal values which represent the analogous sampling points of the direct signal. The values produced by this multiplication operation are scaled by an adaptation constant and accumulated to produce the filter coefficients which are used to cancel the ghost signals.

Adaptive filter including signal path compensation

Abstract: Impulse response estimation is improved in an adaptive filter by compensating digital signals incoming to the filter to include a nonlinearity substantially identical to a nonlinearity included in a return signal path to the filter.

New Results in Sridhar Filtering Theory

Abstract: A nonlinear adaptive filter is introduced and applied to the classical problem of detecting a sinusoidal signal, with unknown frequency, in white noise. The filter is basically a new result in what is known as Sridhar filtering theory. In the derivation of the filter, called the “Pontryagin filter”, the Pontryagin minimum principle and the method of invariant imbedding are used. The stability, bias and convergence properties are also studied and presented.

On the time‐varying wiener filter*

Abstract: For a new approach to designing the time-varying Wiener filter, the input is first divided into sections and then the time-varying filter is determined from the entire input and the desired output. The technique differs from the existing one in which the time-invariant filter is determined from each section. Hence, the main difference, between the proposed and the existing technique lies in the arrangement of input data. The proposed technique requires fewer computational operations and performs better than the time-invariant Wiener filter, as illustrated by numerical examples.

Adaptive digital filter for eliminating howling

Abstract: An adaptive digital filter is connected in parallel with a transmission system and includes a plurality of delay circuits, a nonrecursive digital filter having coefficient parameters of the delay circuits so as to approximate the characteristics of the transmission system, and a correction circuit for correcting the coefficient parameters of the nonrecursive digital filter. The adaptive digital filter further includes a first variable attenuator, a second variable attenuator and a comparator. The first variable attenuator receives an input signal for the adaptive digital filter, variably attenuates the input signal in response to a first control signal, and supplies an attenuated input signal to the transmission system and the nonrecursive digital filter. The second variable attenuator receives a difference between the output signals from the nonrecursive digital filter and the transmission system and variably attenuates the difference signal in response to a second control signal. The attenuated difference signal serves as an output of the adaptive digital filter. The comparator compares the level of the input signal with the level of the output signal from the transmission system and drives the first or second attenuator, which receives a lower level signal when the level difference exceeds a predetermined value.

An adaptive delay filter with varibale gains and variable taps

Abstract: In this paper we extend our work on a new type of adaptive filter called an adaptive delay filter. This filter structure includes variable delay taps in addition to the variable gains. The adaptive delay filter is especially applicable to system modelling problems in which the system to be modelled has a sparse impulse response. Using the standard adaptive filter could require very large filters, while an adaptive delay filter could model the sparse impulse response with very few elements in the filter since the delay taps spread out to adapt to the unknown system. Our previous work presented an algorithm for adapting the delay taps while keeping the gains constant. We now present results of combining an algorithm for adapting the delay taps with an algorithm for adapting the gains. An analysis of the corresponding mean squared error surface is included, along with simulation results of the adaptive delay filter's performance in modelling both the delay taps and the gains of an unknown sparse system.

State-space analysis of the adaptive notch filter

Abstract: The adaptive notch filter has a variety of applications in the field of communications including 60-Hz noise cancellation, phase-locked loops, frequency-hop filtering, and channel equalization. We present a simple derivation of the time-invariant state equations for the adaptive notch filter. Unlike previous work, this analysis provides a closed-form solution for the LMS weight vector as a rotated and filtered product of the desired response. This analysis also lends a simple explanation of non-Wiener type adaptive behavior.

A nonlinear digital filter for separating nonstationary waves from stationary waves of the EEG

Abstract: A new nonlinear digital filter which separates nonstationary waves such as spikes from stationary background waves of the EEG is proposed. This filter is composed of a prediction filter and a simple nonlinear function, and separates the nonstationary waves by processing the prediction error with the nonlinear function. This filter aims at real-time analysis of EEG, hence the algorithm of this filter is deliberately kept very simple, and the parameters in it are set adaptively. Some examples of separating spikes from epileptic EEG data are shown.

Noise reduction for an estimated Wiener filter using noise references (Corresp.)

Abstract: A simple approach to the adaptation of a linear filter to cope with spectral uncertainties is presented. Based on the calculation of the total output error power, including the errors of spectral estimation, a criterion is proposed for deciding whether the estimated filter is effective at any given frequency. By forcing the filter response to unity at all ineffective frequencies, an improvement in performance is obtained.

A multi-threshold adaptive filtering for image enhancement

Abstract: There is a compromise between noise removal and texture preservation in image enhancement. It is difficult to do an image enhancement task by using only one simple filter for a real world image which may consist of regions of various local activities. We describe a multi-threshold adaptive filter (MTA filter) for solving this problem in this paper. It uses a generalized gradient function which reflects the local contextual information as a cue to determine the nature of the filtering for each local neighborhood. In this way, several simple filters can be combined to form a more efficient and more flexible context dependent filter. As a result, specific filter is only applied to the region which is suitable for it. Thus, a balanced texture preserving and noise removal effect can be simultaneously achieved.