Two-sided Linear Prediction Research Articles

Generalized two-sided linear prediction approach for land mine detection

Ground penetrating radar (GPR) is a widely used sensor for land mine detection. However, GPR signal return is very susceptible to ground bounce and reflection of clutter objects, which makes the detection a difficult problem to date. In this paper, we propose to utilize two-sided linear prediction (LP) to model the background interference and then employ the residue energy to generate the test statistic. It is demonstrated from real GPR data that the proposed scheme is able to significantly suppress the interference due to ground reflection and is superior to the adaptive ground bounce removal and one-sided LP methods.

Time–frequency analysis and instantaneous frequency estimation using two-sided linear prediction

This paper presents a new time–frequency distribution which uses a time-dependent two-sided linear predictor model. The current sample is estimated as a weighted sum of the past and future values. The two-sided linear prediction approach yields a smaller prediction error than that obtained by using the usual one-sided linear predictor model. To estimate the time-dependent coefficients of the two-sided linear predictor, these are expanded as a linear combination of a set of time functions basis which leads to an ensemble of equations of the type of Yule-Walker equations. The nonstationary power spectrum estimate is used as a time–frequency distribution to characterize the signal jointly in the time domain and the frequency domain. We show that two-sided prediction-based time–frequency distribution can discriminate two close components in the time–frequency plane that neither Choi-Williams distribution nor one-sided prediction-based time–frequency distribution are capable of resolving. Also, the proposed time–frequency distribution is used to estimate the instantaneous frequency. Examples show that the proposed approach outperforms the usual technique based on the nonstationary autoregressive model.

Similarities and differences between one-sided and two-sided linear prediction

Provides a comparison between one-sided linear prediction (OSP) and two-sided linear prediction (TSP) with respect to prediction error, relationships to AR modeling and to two-sided AR modeling, and the application to time series interpolation, linear-phase filter design, and spectral estimation. Although some of these results have appeared previously in scattered references, the authors present a unified framework for deriving all of these results, as well as new, additional results. New contributions of the paper include: (i) proof that TSP produces smaller, nonwhite residuals than OSP, extending previous results; (ii) specification of the frequency-domain error criterion minimized by TSP, and comparison with the analogous OSP criterion; (iii) demonstration that TSP and two-sided AR modeling are different problems, unlike OSP; (iv) interpretation of performance of TSP interference-rejection filters. >

Two-sided linear prediction and reconstruction of a stationary time series

The problem of two-sided linear prediction and reconstruction of a stationary process y on a finite interval is solved.

Blind deconvolution of symmetric noncausal impulse responses using two-sided linear prediction

Considers the problem of estimating the time-symmetric, noncausal impulse response of a linear time-invariant system from measurements of the response of the system to an unknown input signal, which is assumed to be a realization of a white random process. The symmetric impulse response is modeled by a two-sided AR or ARMA system model. The two-sided AR coefficients are estimated using a two-step procedure. First, an estimate of an unconstrained parameter vector is computed by solving a close-to-Toeplitz-plus-Hankel system of equations using previously developed fast algorithms. Then, the polynomial square root of the result is obtained by solving a constrained least-squares problem which has a simple solution. Unlike previous methods, this approach requires no iterative procedure. However, it may lead to an unstable model in some extreme cases. Simulation results illustrate the performance of the proposed methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fast algorithms for close-to-Toeplitz-plus-Hankel systems and two-sided linear prediction

The low-displacement-rank definition of close-to-Toeplitz (CT) matrices is extended to close-to-Toeplitz-plus-Hankel (CTPH) matrices. Fast algorithms for solving CTPH systems of equations are presented. A matrix is defined as CTPH if the sum of a CT matrix and a second CT matrix postmultiplied by an exchange matrix; an equivalent definition in terms of UV rank is also given. This definition is motivated by the application of the algorithms to two-sided linear prediction (TSP). Autocorrelation and covariance forms of TSP analogous to those for one-sided linear prediction (OSP) are defined. The covariance form of TSP is solved using the CTPH fast algorithms, just as the covariance form of OSP is solved using CT fast algorithms. Numerical examples show that TSP produces smaller residuals than OSP and resolves sharp spectral peaks better than OSP, and that covariance TSP produces smaller residuals than autocorrelation TSP.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Digital whitening of band-limited white noise in the presense of colored noise

Four all zero whitening filters, one-sided and two-sided Wiener and linear prediction filters, are compared on the basis of reduction of input noise power, when the sum of a band-limited white noise and the colored noise is the input to a unity gain whitening filter. The colored noise is assumed to be one of the three types: equally spaced, equal power multiple tones, a periodic pulsetrain of random strength, and a random process having a first-order Butterworth spectrum. Based upon this comparison, the two-sided Wiener filter is shown to reduce the greatest noise power, independent of the type of the colored noise.

On suppression of a sinusoidal signal in broad-band noise

In an estimator-subtractor configuration of the generalized adaptive line enhancer (ALE), a sinusoidal signal (in broad-band noise) is estimated by the two-sided and one-sided Wiener and linear prediction filters. For a fixed number of input samples, the estimation error in Wiener and prediction filters is shown to be minimum, when both future and past samples, not necessarily equal in numbers, are utilized in the present estimate of the signal. The error in the estimate of the signal by the two-sided Wiener filter is also shown to be equal to that by the optimized form of the well-known ALE.