Noise-induced Bias Research Articles

The effect of noise on adaptive envelope-constrained filters

The performance of the envelope-constrained filters designed by the newly developed adaptive algorithms may deteriorate when the input signal is contaminated by noise. The average window with a growing window size, and the exponentially weighted average window are presented. It is shown that the noise-induced bias in the augmented cost function will be reduced because applying such an averaging scheme helps increase values of the signal-to-noise ratio at the filter input channel. With this, the noise effect on the adaptive envelope-constrained filters can be depressed. Simulation results are given to illustrate the improved performance of the adaptive envelope-constrained filters designed in conjunction with the average window.

Unbiased LMS filtering in the presence of white measurement noise with unknown power

This paper presents a new modified least mean squares (LMS) adaptive filtering algorithm for autoregressive (AR) modeling in the presence of white measurement noise with unknown power. In the proposed algorithm, a first-order filter is used to filter the noise-corrupted signal. In this way, the AR model is augmented to have a known pole which can, based on asymptotic analysis, be used to extract and eliminate the noise-induced bias in the standard LMS filtering result, and thus the unbiased parameter estimation can be achieved.

Parametric identification of noisy closed-loop linear systems

The problem of identification of closed-loop linear systems via the direct approach is studied in a general setting. The process noise acting on the plant, the input measurement noise and the output measurement noise may be coloured and they may be arbitrarily correlated with each other. A parameter estimation method is proposed by using the bias correction principle. The kernel of this method is that the noise covariance vector, which determines the noise-induced bias in the standard least-squares estimator, is obtained in an efficient manner. It is shown that the strength of the proposed direct identification method is that it can derive accurate parameter estimates from noisy closed-loop data irrespective of noise dynamics.

Unbiased parameter estimation of linear systems with colored noises

We report a study of the problem of consistent parameter estimation in the general case where the measurement noise is unknown and correlated not only with the system output but also with the system input. A new method is presented for eliminating the noise-induced biases in the least-squares (LS) estimates. In the proposed method, two filters are introduced to filter the system input and output signals, respectively, so that an augmented system with some known zeros and poles is obtained. By shifting the space of the parameters to be estimated and using the known zeros and poles of the parameters to be estimated and using the known zeros and poles, a sufficient number of linear constraints are constructed to determine the noise-induced biases. After eliminating the biases in the ordinary LS estimates, consistent estimates of the parameters are obtained. Analysis shows that the results of the proposed method are independent of the noise model used.

Linear least squares compartmental-model-independent parameter identification in PET.

A simplified approach involving linear-regression straight-line parameter fitting of dynamic scan data is developed for both specific and nonspecific models. Where compartmental-model topologies apply, the measured activity may be expressed in terms of: its integrals, plasma activity and plasma integrals--all in a linear expression with macroparameters as coefficients. Multiple linear regression, as in spreadsheet software, determines parameters for best data fits. Positron emission tomography (PET)-acquired gray-matter images in a dynamic scan are analyzed: both by this method and by traditional iterative nonlinear least squares. Both patient and simulated data were used. Regression and traditional methods are in expected agreement. Monte-Carlo simulations evaluate parameter standard deviations, due to data noise, and much smaller noise-induced biases. Unique straight-line graphical displays permit visualizing data influences on various macroparameters as changes in slopes. Advantages of regression fitting are: simplicity, speed, ease of implementation in spreadsheet software, avoiding risks of convergence failures or false solutions in iterative least squares, and providing various visualizations of the uptake process by straight line graphical displays. Multiparameter model-independent analyses on lesser understood systems is also made possible.

More on noise-induced bias in magnitude determinations

Unavoidable measurement noise may introduce a bias when transforming observed fluxes to magnitudes. The problem of determining the bias is formulated in terms of the magnitude difference between a programme star and a comparison star. A mathematical expression is derived for the probability distribution function of the quantity b = 11m -11m * (11m and 11m * being respectively the observed and true magnitude differences). This is used to find a polynomial equation for the bias 6 (the mode of the distribution function). It is shown that for small flux errors (noise-to­ signal ratio ~ 0.05) the solution is given with excellent accuracy by 6 = 1.086(nz -n1), where n 1 and nz are the squared noise-to-signal ratios of respectively the programme and comparison stars. Values of 16 I larger than about a millimag are not expected in practice.

Noise-induced bias in decibel determinations

It is demonstrated that measurements of power levels expressed in units of decibels are prone to noise-induced bias as a result of the logarithmic nature of the decibel scale. Estimates of the effect of the bias on the mean of a repeated set of values and on the mode value are given, indicating that allowance for noise-induced bias is important in the reporting of measurements made with low values of signal-to-noise ratio of the order < 10.

Target-strength measurements of walleye pollock (Theragra chalcogramma) and Pacific whiting (Merluccius productus)

The importance of knowledge about the target-strength (TS) characteristics of the surveyed fish population to the accuracy of acoustic assessments using echo integration is well known. The most commonly used TS to length (L) relationship for walleye pollock is based on swimbladder morphology measurements and in situ TS measurements TS (in dB)=20 log L−66.0 for fish length in centimeters. For Pacific whiting, TS measurements have not been made over an adequate range of fish lengths to determine the appropriate relationship for use in scaling echo-integration surveys. However, results presented in this paper and elsewhere suggest a smaller TS (about 2 dB for a given length) for 40-60 cm fish. Measurements of the TS of walleye pollock and Pacific whiting were made with a SIMRAD EK500 in the present study. The appropriateness of the currently used TS to length relationship for echo integration scaling is discussed for pollock. The application of a TS to length relationship for Pacific whiting is considered. An attempt to use a system with a transducer lowered through the water column to reduce noise-induced bias is described.

Noise-induced bias in magnitude determinations

Noise-induced bias in magnitude determinations

Noise, biased probability and serial reaction.

Recent studies have shown that moderate intensity noise does influence performance although most studies showing effects of this level of noise have used verbal materials. An experiment showed that moderate intensity noise (85 dBC) also influences attentional selectivity in a serial reaction task which involved the processing of sensory information. Noise decreased response times to signals with high probabilities of occurrence but increased latencies for signals which occurred less frequently. Although attentional selectivity in noise depended on signal probability, it was not influenced by the spatial location of the signal. When a mode of responding is adopted in noise, subjects are often rather inflexible and continue to use this strategy even though it is inappropriate. This was demonstrated in the present study because the noise-induced bias continued even when the signal probabilities were returned to normal. Previous studies using higher noise intensities have shown that noise often increases the number of errors or gaps. The moderate intensity noise used in the present study did not have this effect.

Tracking-Loop Bias Due to Costas Loop Arm Filter Imbalance

An expression is derived which shows that when the bandpass filter preceding a Costas loop is not symmetric and the arm filters are not balanced, a static phase error, which becomes larger as the SNR decreases, can occur due to noise. Conversely, if either condition does not apply, then no noise-induced phase error bias will exist. It is shown, for a modified Costas loop in which one arm filter is removed, that the static phase error may be significant.