Optimal Matched Filter Research Articles

An Information Geometric Viewpoint on the Detection of Range Distributed Targets

The paper adopts the information geometry, to put forward a new viewpoint on the detection of range distributed targets embedded in Gaussian noise with unknown covariance. The original hypothesis test problem is formulated as the discrimination between distributions of the measurements and the noise. The Siegel distance, which is exactly the well-known geodesic distance between images of the original distributions via embedding into a higher-dimensional manifold, is given as an intrinsic measure on the difference between multivariate normal distributions. Without the assumption of uncorrelated measurements, we propose a set of geometric distance detectors, which is designed based on the Siegel distance and different from the generalized likelihood ratio algorithm or other common criterions in statistics. As special cases, the classical optimal matched filter, Rao test, and Wald test, which have been proven to have the CFAR property, belong to the set. Moreover, it is also accessible to an intuitively geometric analysis about how strongly the data contradict the null hypothesis.

PRACTICAL METHODS FOR CONTINUOUS GRAVITATIONAL WAVE DETECTION USING PULSAR TIMING DATA

Gravitational Waves (GWs) are tiny ripples in the fabric of space-time predicted by Einstein's General Relativity. Pulsar timing arrays (PTAs) are well poised to detect low frequency ($10^{-9}$ -- $10^{-7}$ Hz) GWs in the near future. There has been a significant amount of research into the detection of a stochastic background of GWs from supermassive black hole binaries (SMBHBs). Recent work has shown that single continuous sources standing out above the background may be detectable by PTAs operating at a sensitivity sufficient to detect the stochastic background. The most likely sources of continuous GWs in the pulsar timing frequency band are extremely massive and/or nearby SMBHBs. In this paper we present detection strategies including various forms of matched filtering and power spectral summing. We determine the efficacy and computational cost of such strategies. It is shown that it is computationally infeasible to use an optimal matched filter including the poorly constrained pulsar distances with a grid based method. We show that an Earth-term-matched filter constructed using only the correlated signal terms is both computationally viable and highly sensitive to GW signals. This technique is only a factor of two less sensitive than the computationally unrealizable optimal matched filter and a factor of two more sensitive than a power spectral summing technique. We further show that a pairwise matched filter, taking the pulsar distances into account is comparable to the optimal matched filter for the single template case and comparable to the Earth-term-matched filter for many search templates. Finally, using simulated data optimal quality, we place a theoretical minimum detectable strain amplitude of $h>2\times 10^{-15}$ from continuous GWs at frequencies on the order $\sim1/T_{\rm obs}$.

Matched filter analysis of burst waveform injections

Hardware injections provide us with a crucial tool for proving that we understand the response and performance of the LIGO detectors. Since we have complete knowledge of the injected waveform and detailed measurements of the detector response function, we are able to predict and confirm the instrument response. During the S5 science run of LIGO, various burst-type waveforms are being injected. We have analyzed the first seven months of these injections, using optimal matched filters derived from the injection waveforms. We have confirmed that most of the responses follow the predictions and have measured the accuracy of the estimated arrival time. In addition, we examined transients identified by the KleineWelle algorithm in auxiliary data channels at the time of hardware injections. Through this study, we could recognize couplings between auxiliary channels and the gravitational wave channels and assess the safety of the use of auxiliary channels as vetoes for gravitation wave candidates.

AUTOMATED UNNATURAL PATTERN RECOGNITION ON CONTROL CHARTS USING CORRELATION ANALYSIS TECHNIQUES

Pattern recognition techniques are currently pursued to identify unnatural patterns on quality control charts. This approach has been shown to enhance the ability to utilize the information of the chart more effectively than conventional run rules. This paper presents analysis and development of a pattern recognition system for identifying unnatural patterns on quality control charts. The system is based on correlation analysis, where a set of optimal matched filters are generated. To illustrate the design methodology and operation of the system, a set of commonly encountered patterns is utilized, such as the trend, the systematic, and the cyclic patterns. A training algorithm that minimizes the probabilities of Type I and Type II errors i presented. To evaluate the system performance, a testing algorithm as well as a set of newly-defined performance measures are introduced. The obtained results, based on extensive simulation runs, have proved the effectiveness of correlation analysis for control chart pattern recognition. © 1997 Elsevier Science Ltd

Unnatural pattern recognition on control charts using correlation analysis techniques

This paper presents analysis and development of a pattern recognition system for identifying unnatural patterns on quality control charts. The system is based on correlation analysis, where a set of optimal matched filters are generated. To illustrate the design methodology and operation of the system, a set of commonly encountered patterns is utilized, such as the trend, the systematic, and the cyclic patterns. A training algorithm that minimizes the probabilities of Type I and Type II errors is presented. To evaluate the system performance, a testing algorithm as well as a set of newly-defined performance measures are introduced. The obtained results have shown the effectiveness of correlation analysis for control chart pattern recognition.

Optimal correlation filters for images with signal-dependent noise

We address the design of optimal correlation filters for pattern detection and recognition in the presence of signal-dependent image noise sources. The particular examples considered are film-grain noise and speckle. Two basic approaches are investigated: (1) deriving the optimal matched filters for the signal-dependent noise models and comparing their performances with those derived for traditional signal-independent noise models and (2) first nonlinearly transforming the signal-dependent noise to signal-independent noise followed by the use of a classical filter matched to the transformed signal. We present both theoretical and computer simulation results that demonstrate the generally superior performance of the second approach in terms of the correlation peak signal-to-noise ratio.

Matched Recursive Digital Filters

Matched filters having maximal signal-to-noise ratio are designed mostly in form of nonrecursive (FIR) digital filters. In this paper it is shown how recursive optimal matched filters can be designed. In this approach the impulse response of an optimal matched FIR filter is first designed and then approximated by a recursive digital filter such that the filter degree is strongly reduced compared to the nonrecursive filter. Several examples demonstrate the efficiency of the method and provide experimental results

Complex ternary matched filters yielding high signal-to-noise ratios

Complex ternary matched filters (CTMFs) can be implemented optically using detour phase and a single ternary spatial light modulator or a Mach-Zehnder arrangement and two ternary signal light modulators. In this paper, we present the design of CTMFs that yield high signal-tonoise ratios (SNRs) and show with the help of simulation examples that their performance (in the sense of SNRs) is close to that of optimal matched filters.

Optimal polarizations for achieving maximum contrast in radar images

There is considerable interest in determining the optimal polarizations that maximize contrast between two scattering classes in polarimetric radar images. In this paper a systematic approach is presented for obtaining the optimal polarimetric matched filter, i.e., that filter which produces maximum contrast between two scattering classes. The maximization procedure involves solving an eigenvalue problem where the eigenvector corresponding to the maximum contrast ratio is optimal polarimetric matched filter. To exhibit the physical significance of this filter, it is transformed into its associated transmitting and receiving polarization states, written in terms of horizontal and vertical vector components. For the special case where the transmitting polarization is fixed, the receiving polarization which maximizes the contrast ratio is also obtained. Polarimetric filtering is then applied to synthetic aperture radar images obtained from the Jet Propulsion Laboratory. It is shown, both numerically and through the use of radar imagery, that maximum image contrast can be realized when data is processed with the optimal polarimetric matched filter.

Penalties of Sample-and-Sum and Weighted Partial Decision Detectors in Gaussian Noise

The deterioration in performance, measured in the probability of error sense, of sample-and-sum and weighted partial decision detectors are analyzed for arbitrary signal-to-noise ratios. These suboptimal detectors have more modest computational requirements than the optimal digital matched filter making them amenable to simple digital implementations. The effects on the penalties of the signaling waveform employed, the number of samples processed, and the signal-to-noise ratio are considered in detail. Included are the penalties for the optimum weighted partial decision detector. The optimum weighted partial decision detector is the optimum detector, in the minimum probability of error sense, for hard-limited samples. The penalty of the optimum weighted partial decision detector relative to the digital matched filter detector represents the fundamental loss in signal detectability due to hard-limiting in a sampled system.

A comparison of modulation schemes for binary data transmission

The relationships between bit error probability and transmitter power are presented on a common basis for various binary and m-ary modulation schemes operating with the same system data rate. it is assumed that the channel is disturbed by additive white gaussian noise of fixed power spectral density and that optimal matched filter reception is used. the results presented allow a comparison of the efficiencies of the systems in the use of transmitter power to provide a specified bit error probability. the theoretical bandwidth requirements of each system have been considered. sometimes the system designer is constrained to the use of an existing channel of fixed bandwidth and signal/noise ratio. the choice of modulation system under these conditions has also been indicated.