Non-Gaussian detection
AssigneeThe Charles Stark Draper Laboratory, Inc.
InventorMukund N. Desai
Life of this patent
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Abstract
A system and method for detection of a particular signal of interest within a set of measurements. The particular signal of interest is detected in the presence of arbitrary noise and interferents. The system and method are capable of detecting the presence of the particular signal of interest in the presence of non-Gaussian noise and unknown interference. The system and method also are capable of detecting the presence of the particular signal of interest in the presence of interferents that lie in a different subspace from the signal of interest, but nevertheless corrupt the measurements.
Claims37
A method for determining the presence of a signal of interest within a set of measurement data, the method comprising the steps of:
- extracting data representative of a first signal having characteristics associated with the signal of interest from the measurement data;
- extracting data representative of one or more second signals having characteristics dissimilar to the signal of interest;
- and
- processing the data representative of the first signal with the data representative of the one or more second signals to determine the likelihood of whether the signal of interest is present in the measurement data.
A system for determining the presence of a signal of interest within a set of measurement data, the system comprising:
- a processor for extracting data representative of a first signal having characteristics associated with the signal of interest, extracting data representative of one or more signals having characteristics dissimilar to the signal of interest, and processing the data representative of the first signal with the data representative of the one or more second signals to determine the likelihood of whether the signal of interest is present in the measurement data.
A detector for determining the presence of a signal of interest within a set of measurement data, the detector comprising a likelihood ratio of the general form:
- 69 λ ( x ) = x ′ ( P S - P U ) x 2 σ 2 ;
- wherein x is a vector of measurement data;
- x′ is a transpose of x;
- S is a matrix whose columns span a signal space;
- Ps is a projection operator that projects a vector along signal space;
- U is a matrix whose columns span an interferent space;
- Pu is a projection operator that projects a vector along unknown interferent space;
- and
- σ is a standard deviation of noise.
A detector for determining the presence of a signal of interest within a set of measurement data, the detector comprising a likelihood ratio of the general form:
- 70 λ ( x ) = [LeftBracketingBar] s ′ x [RightBracketingBar] [LeftDoubleBracketingBar] s [RightDoubleBracketingBar] q [RightDoubleBracketingBar] x - s θ ^ p [RightDoubleBracketingBar] p ;
- wherein x is a vector of measurement data;
- {circumflex over (θ)}p is a maximum likelihood estimate of θ;
- s is a vector that spans a signal space;
- θ is a gain vector associated with s;
- p is a shape parameter of a probability density function of noise;
- and
- 71 q is equal to p p - 1 .
A detector for determining the presence of a signal of interest within a set of measurement data, the detector comprising a likelihood ratio of the general form:
- 72 Λ ( x ) = [LeftDoubleBracketingBar] x = U ψ ^ p [RightDoubleBracketingBar] p [LeftDoubleBracketingBar] s - S θ ^ p [RightDoubleBracketingBar] p ;
- wherein x is a vector of measurement data;
- {circumflex over (θ)}p is a maximum likelihood estimate of θ;
- S is a matrix whose columns span the signal space;
- θ is a gain vector associated with S;
- U is a matrix whose columns span an interferent space;
- {circumflex over (ψ)}p is a maximum likelihood estimate of ψ
- ψ is a gain vector associated with U;
- and
- p is a shape parameter of a probability density function of noise.
A detector for determining the presence of a signal of interest within a set of measurement data, the detector comprising a likelihood ratio of the general form:
- 73 λ ( x ) = - ( 1 ω 1 [LeftDoubleBracketingBar] x - s θ ^ p [RightDoubleBracketingBar] p ) p + ( [LeftBracketingBar] s ′ x [RightBracketingBar] [LeftDoubleBracketingBar] ω 0 s [RightDoubleBracketingBar] q ) p ;
- wherein x is a vector of measurement data;
- {circumflex over (θ)}p is a maximum likelihood estimate of θ;
- s is a vector that spans the signal space;
- θ is a gain vector associated with s;
- ω0 is a width factor associated with known noise;
- ω1 is a width factor associated with unknown noise;
- p is a shape parameter of a probability density function of noise;
- and
- 74 q is equal to p p - 1 .
A detector for determining the presence of a signal of interest within a set of measurement data, the detector comprising a likelihood ratio of the general form:
- 75 Λ ( x ) = - ( 1 ω 1 [LeftDoubleBracketingBar] x - s θ ^ p [RightDoubleBracketingBar] p ) p + ( 1 ω 0 [LeftDoubleBracketingBar] x - U ψ ^ p [RightDoubleBracketingBar] p ) p ;
- wherein x is a vector of measurement data;
- {circumflex over (θ)}p is a maximum likelihood estimate of θ;
- S is a matrix whose columns span the signal space;
- θ is a gain vector associated with S;
- U is a matrix whose columns span an interferent space;
- {circumflex over (ψ)}p is a maximum likelihood estimate of ψ
- ψ is a gain vector associated with U;
- ω0 is a width factor associated with known noise;
- ω1 is a width factor associated with unknown noise;
- and
- p is a shape parameter of a probability density function of noise.
A detector for determining the presence of a signal of interest within a set of measurement data, the detector comprising a likelihood ratio of the general form:
- 76 Λ ( x ) = [LeftDoubleBracketingBar] x [RightDoubleBracketingBar] p [LeftDoubleBracketingBar] x - S θ ^ p [RightDoubleBracketingBar] p ;
- wherein x is a vector of measurement data;
- {circumflex over (θ)}p is a maximum likelihood estimate of θ;
- S is a matrix whose columns span a signal space;
- θ is a gain vector associated with S;
- and
- p is a shape parameter of a probability density function of noise.
A detector for determining the presence of a signal of interest within a set of measurement data, the detector comprising a likelihood ratio of the general form:
- 77 Λ ( x ) = - ( 1 ω 1 [LeftDoubleBracketingBar] x - S θ ^ p [RightDoubleBracketingBar] p ) p + ( 1 ω 0 [LeftDoubleBracketingBar] x [RightDoubleBracketingBar] p ) p ;
- wherein x is a vector of measurement data;
- {circumflex over (θ)}p is a maximum likelihood estimate of θ;
- S is a matrix whose columns span the signal space;
- θ is a gain vector associated with S;
- ω0 is a width factor associated with known noise;
- ω1 is a width factor associated with unknown noise;
- and
- p is a shape parameter of a probability density function of noise.
Dependencies are inferred from the claim text.