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US 9,562,968 B2Granted
Sensor system and method for determining target location using sparsity-based processing
AssigneeSaab Sensis Corporation
InventorRyan Haoyun Wu
Life of this patent
Estimating the term…
Abstract
A system and method for an arrayed sensor to resolve ambiguity in received signals, improve direction of arrival accuracy and estimate a location of one or more targets in an environment including signal interference.
Claims12
A sensor system for estimating a location of a target using a sparse representation framework comprising:
- a plurality of receiving elements for receiving energy signals including an energy signal-of-interest, other transmitted energy signals and coherent interference;
- and
- at least one receiver comprising at least one processor using the sparse representation framework for processing the received energy signals and using a sparsity solver for estimating the location of the target,
- wherein the at least one processor using a sparse representation framework is configured to:
- receive received energy signals and separate the energy signal-of-interest present in a signal collection window of a plurality of signal collection windows in at least one of a spatial domain, a temporal domain and a frequency domain, so that only the energy signal-of-interest and associated coherent interference are present in the signal collection window, wherein the energy signal-of-interest is a single signal-of-interest transmitted by the target and includes associated coherent interference;
- convert the energy signal-of-interest and associated coherent interference present in each signal collection window from an energy signal in a time domain to an energy signal in a frequency domain;
- divide the energy signal in the frequency domain in each signal collection window with a reference signal which is not equal to 0;
- arrange a search grid around an area defined by an angle θ and a delay τ on an at least 2-D grid where a frequency domain measurement ratio term for angle θ is represented as follows:
- r
- n
- ,
- m
- =
- ∑
- k
- =
- 1
- K
-
-
- ∑
- l
- =
- 1
- L
-
-
- α
- k
- ,
- l
-
- ⅇ
- -
- j
-
-
- 2
-
-
- π
-
-
- f
- m
-
- (
- τ
- k
- -
- Δ
-
-
- t
- n
- ,
- l
- )
-
- ∑
- k
- =
- 1
- K
-
-
- ∑
- l
- =
- 1
- L
-
-
- α
- k
- ,
- l
-
- ⅇ
- -
- j
-
-
- 2
-
-
- π
-
-
- f
- m
-
- (
- τ
- k
- -
- Δ
-
-
- t
- n
-
-
- 0
- ,
- l
- )
-
- where:
- rn,m is the spectrum ratio measurement corresponding to the n-th element and the m-th frequency, fm;
- k=1 . . . K is the search indices corresponding to the delay search grid τk=τ1 . . . τK;
- l=1 . . . L is the search indices corresponding to the angle search grid θk=θ1 . . . θK;
- αk,l is the unknown amplitude to be solved corresponding to the k-th delay search point and the l-th angle search point;
- Δtn,i=(nd sin θl)/C is the relative delay of the signal received at the n-th element corresponding to the l-th angle search point;
- Δtn0,i=(n0d sin θl)/C is the relative delay of the signal received at the reference element corresponding to the l-th angle on the angle search grid;
- d is the spacing between elements;
- C is the speed of light;
- and
- j represents the square root of −1;
- form matrix vector equations using a signal model matrix;
- calculate all possible values for term (τk-Δtn,1) based on the search space defined by values of angle θ and values of delay τ, sort the calculated values for the term (τk-Δtn,1) from small to large and denote the sorted calculated values for the term (τk-Δtn,1) from small to large as follows:
- {εn,1,εn,2 . . . εn,V}
- where:
- V=KL and the corresponding amplitudes are denoted as
- {β1, β2, . . . , βV}, which belong to the set of amplitudes α, and
- the terms corresponding to (τk-Δtn0,1) are now denoted as {εn0,1, εn0,2, . . . εn0,V}, and are arranged based on the sorting sequence of the calculated values for (τk-Δtn,1) and are not necessarily in an ascending order;
- rearrange the spectrum ratio equation using the new notations to obtain the following homogeneous spectrum ratio equation in matrix vector form;
- [
- φ
- 11
- …
- φ
- V
-
-
- 1
- ⋮
- ⋱
- ⋮
- φ
- 1
-
-
- M
- …
- φ
- VM
- ]
- ︸
- φ
-
- [
- β
- 1
- ⋮
- β
- V
- ]
- ︸
- β
- =
- [
- 0
- ⋮
- 0
- ]
- where:
- φim=(rn,mZm−εn0,i−Zm−εn,i) is the i-th row and m-th column element of φ;
- and
- Z=ej2πfm;
- apply the sparsity solver configured to solve the matrix vector equations to estimate the location of the target, the at least one processor being configured to passively estimate the location of the target, the sparsity solver being configured to solve for β, and estimate a location of the target transmitting the signal-of-interest where the solution of β is spanned by the null space of φ, a correct β is sparse, and β cannot be zero;
- and
- output the estimated location of the target.
170 more elements
A sensor system for estimating a location of a target using a sparse representation framework where at least one interfering transmitter is transmitting an interfering energy signal, comprising:
- at least one transmitter for transmitting an energy signal in at least one direction, the energy signal reflecting off of at least the target;
- a plurality of receiving elements for receiving energy signals including an energy signal-of-interest, the energy signal reflecting off of at least the target, transmitted interfering energy signals and coherent interference;
- and
- at least one receiver comprising at least one processor using the sparse representation framework for processing the received energy signals and using a sparsity solver for estimating the location of the interfering transmitter transmitting the interfering signal passively and a location of the target actively,
- wherein to passively estimate the location of the interfering transmitter transmitting the interfering signal the at least one processor using a sparse representation framework is configured to:
- receive energy signals and separate the interfering energy signal present in a signal collection window of a plurality of signal collection windows in at least one of a spatial domain, a temporal domain and a frequency domain, so that only the interfering energy signal and associated coherent interference are present in the signal collection window;
- convert the interfering energy signal and associated coherent interference present in each signal collection window from an energy signal in a time domain to an energy signal in a frequency domain;
- divide the energy signal in the frequency domain in each signal collection window with a reference signal which is not equal to 0;
- arrange a search grid around an area defined by an angle θ and a delay τ on the at least 2-D grid, where a frequency domain measurement ratio term for angle θ is represented as follows:
- r
- n
- ,
- m
- =
- ∑
- k
- =
- 1
- K
-
-
- ∑
- l
- =
- 1
- L
-
-
- α
- k
- ,
- l
-
- ⅇ
- -
- j
-
-
- 2
-
-
- π
-
-
- f
- m
-
- (
- τ
- k
- -
- Δ
-
-
- t
- n
- ,
- l
- )
-
- ∑
- k
- =
- 1
- K
-
-
- ∑
- l
- =
- 1
- L
-
-
- α
- k
- ,
- l
-
- ⅇ
- -
- j
-
-
- 2
-
-
- π
-
-
- f
- m
-
- (
- τ
- k
- -
- Δ
-
-
- t
- n
-
-
- 0
- ,
- l
- )
-
- where:
- rn,m is the spectrum ratio measurement corresponding to the n-th element and the m-th frequency, fm;
- k=1 . . . K is the search indices corresponding to the delay search grid τk=τ1 . . . τK;
- l=1 . . . L is the search indices corresponding to the angle search grid θk=θ1 . . . θK;
- αk,l is the unknown amplitude to be solved corresponding to the k-th delay search point and the l-th angle search point;
- Δtn,i=(nd sin θl)/C is the relative delay of the signal received at the n-th element corresponding to the l-th angle search point;
- Δtn0,i=(n0d sin θl)/C is the relative delay of the signal received at the reference element corresponding to the l-th angle on the angle search grid;
- d is the spacing between elements;
- C is the speed of light;
- and
- j represents the square root of −1;
- calculate all possible values for term (τk-Δtn,1) based on the search space defined by values of angle θ and values of delay τ, sort the calculated values for the term (τk-Δtn,1) from small to large and denote the sorted calculated values for the term (τk-Δtn,1) from small to large as follows:
- {εn,1,εn,2 . . . εn,V}
- where:
- V=KL and the corresponding amplitudes are denoted as {β1, β2, . . . , βV}, which belong to the set of amplitudes α, and the terms corresponding to (τk-Δtn0,1) are now denoted as {εn0,1, εn0,2 . . . εn0,V}, and are arranged based on the sorting sequence of the calculated values for (τk-Δtn,l) and are not necessarily in an ascending order;
- rearrange the spectrum ratio equation using the new notations to obtain the following homogeneous spectrum ratio equation in matrix vector form;
- [
- φ
- 11
- …
- φ
- V
-
-
- 1
- ⋮
- ⋱
- ⋮
- φ
- 1
-
-
- M
- …
- φ
- VM
- ]
- ︸
- φ
-
- [
- β
- 1
- ⋮
- β
- V
- ]
- ︸
- β
- =
- [
- 0
- ⋮
- 0
- ]
- where:
- φim=(rn,mZm−εn0,i−Zm−εn,i) is the i-th row and m-th column element of φ;
- and
- Z=ej2πfm;
- the sparsity solver is configured to solve for β, and
- estimate a location of the interfering transmitter transmitting the interfering signal where the solution of β is spanned by the null space of φ, a correct β is sparse, and β cannot be zero;
- and
- outputs the estimated location of the target;
- and
- wherein to actively estimate the location of the target the at least one processor using a sparse representation framework is configured to:
- apply spatial nulling to suppress the interfering energy signal transmitted from the estimated location of the target transmitting the interfering energy signal;
- detect the target in an azimuth-elevation-range resolution cell and
- establish a three-dimension (3-D) grid covering an area including the azimuth-elevation-range resolution cell containing the one or more targets;
- reform the target location estimation problem into a linear angle-excess range estimation problem for the target represented in the general form:
- Ax=y
- where:
- x is a solution vector,
- A is a matrix of known functions, and
- y is a vector from observation;
- form a number of measurement equations, the number of measurement equations being equal to N×M, where N is the number of outputs from receiving elements of the sensor array, and M is the number of frequency sampling points available;
- form a matrix based on the N×M measurement equations for the solution vector y and a K×L search space in the 3-D grid;
- form a 3-D image of the K×L search space, where the solution vector x for the target on the 3-D image is sparse when a number of grid points within the K×L search space is larger than a number of grid points P having a value above a noise floor of the K×L search space (KL>>P);
- apply the sparsity solver configured to solve the matrix for the solution vector x to estimate a location of the target, and
- output the estimated location of the target.
185 more elements
Dependencies are inferred from the claim text.