The Wiener Third-Order-Statistics-Based Compensator of the Non-Gaussian Noise

This paper introduces a novel technique for parameter estimation of an autoregressive (AR) all-pole process under non-Gaussian noise environment using third order cumulants of the observed sequence. The proposed AR parameters estimation technique is based on formulating a particular structured matrix with entries of third order cumulants of the observed output sequence only. This matrix almost possesses a full rank structure. The observed sequence may be contaminated with additive Gaussian noise (white or colored), whose power spectral density is unknown. The system is driven by a zero-mean independent and identically distributed (i.i.d) non-Gaussian sequence. Simulation results confirm the good numerical conditioning of the algorithm and the improvement in performance with respect to well-known methods even when the observed signal is heavily contaminated with Gaussian noise.

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Estimation and detection in non-Gaussian noise using higher order statistics

IEEE Transactions on Signal Processing ◽

10.1109/78.324738 ◽

1994 ◽

Vol 42 (10) ◽

pp. 2729-2741 ◽

Cited By ~ 56

Author(s):

B.M. Sadler ◽

G.B. Giannakis ◽

Keh-Shin Lii

Keyword(s):

Order Statistics ◽

Gaussian Noise ◽

Higher Order ◽

Higher Order Statistics ◽

Non Gaussian

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Principal domains of the trispectrum, signal bandwidth, and implications for deconvolution

Geophysics ◽

10.1190/1.1444792 ◽

2000 ◽

Vol 65 (3) ◽

pp. 958-969 ◽

Cited By ~ 4

Author(s):

Lisa A. Pflug

Keyword(s):

Order Statistics ◽

Fourth Order ◽

Gaussian Noise ◽

Second Order ◽

Second Order Statistics ◽

Mathematical Properties ◽

Existence Conditions ◽

Non Gaussian ◽

The Individual ◽

The Relationship

Fourth‐order statistics can be useful in many signal processing applications, offering advantages over or supplementing second‐order statistical techniques. One reason is that fourth‐order statistics can discriminate between non‐Gaussian signals and Gaussian noise. Another is that fourth‐order statistics contain phase information, whereas second‐order statistics do not. In the continuing development of the mathematical properties of fourth‐order statistics, several researchers have derived existence conditions and definitions for the unaliased and aliased principal domains of the discrete trispectrum, which is significantly more complex than the power or energy spectrum. The consistencies and inconsistencies of these results are presented and resolved in this paper. The most flexible definitions give four individual principal domains for the discrete trispectrum: two unaliased and two aliased. The most useful combinations are those that combine the two unaliased domains together and the two aliased domains together, which can be done easily from the four individual domains. The relationship between the individual trispectral domains and signal bandwidth is important when using the fourth‐order statistic for applications because they have particular properties that can be detrimental to some deconvolution algorithms. The reasons for this, as well as the validity of proposed solutions to this problem, are explained by the trispectral structure and its origins.

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