The conventional ESPRIT method is accompanied by the problem of very long signal processing time. The radar device of the invention includes a signal vector-forming unit for forming signal vectors based on waves reflected from an object and received by using a plurality of receiving antennas; a submatrix-forming unit for forming submatrices based on the signal vectors; a regular matrix operation unit for calculating a regular matrix from the submatrices; an eigenvalue decomposition unit for calculating an eigenvalue of the regular matrix; and an angle calculation unit for calculating an angle at where the object is present from the eigenvalue.
1. A radar device comprising:
a signal vector-forming unit configured to form signal vectors having elements of a number of N based on waves reflected from an object and received by using a plurality of receiving antennas of the number of N;
a submatrix-forming unit configured to (i) calculate N×N covariance matrices based on the signal vectors having the elements of the number of N, (ii) extract N×(N−1) submatrices from the N×N covariance matrices, and (iii) form two of (N−1)th-dimensional submatrices R 1 and R 2 from the N×(N−1) submatrices;
a regular matrix operation unit configured to calculate a regular matrix Ψ as Ψ=R 1 −1 *R 2 from the two of (N−1)th-dimensional submatrices R 1 and R 2 ;
an eigenvalue decomposition unit configured to calculate an eigenvalue exp(jΦ k ) (k=1 to N−1) of the regular matrix Ψ; and
an angle calculation unit configured to calculate an angle θ k , at where the object is present from phase θ k =2*π*(d/λ)*sin(θ k ) of the eigenvalue exp(jφ k ), where d is a distance between antennas of a uniform linear array reception antenna, and λ is a wavelength of a center frequency of signals formed by an oscillator.
2. A radar device comprising:
a signal vector-forming unit configured to form signal vectors of a number of k(k=1 to N−1) having elements of a number of N based on waves reflected from an object and received by using receiving antennas of the number of N;
a submatrix-forming unit configured to form column vectors by arranging longitudinally each component of the signal vectors of the number of k having elements of the number of N and arranging the signal vectors of the number of k in row direction, and calculating two of M(M<N)th-dimensional submatrices R 1 and R 2 from the column vectors;
a regular matrix operation unit configured to calculate a regular matrix Ψ as Ψ=R 1 −1 *R 2 from the two of M(M<N)th-dimensional submatrices R 1 and R 2 ;
an eigenvalue decomposition unit configured to calculate an eigenvalue exp(jΦ k )(k=1 to M(N<N) of the regular matrix Ψ; and
an angle calculation unit configured to calculate an angle θ k at where the object is present from phase Φ k =2*π*(d/λ)*sin(θ k ) of the eigenvalue exp(jθ k ), where d is the distance between antennas of the uniform linear array reception antenna, and λ is the wavelength of a center frequency of signals formed by an oscillator.
3. The radar device according to claim 1 , further comprising:
an evaluation function-forming unit configured to form an evaluation function ε(α) using the submatrices R 1 and R 2 as
ε(α)=∥ R 1 −αR 2 ∥ 2 =∥( J 1 A ) R xx ( I 3 −αΦ H )( J 1 A ) H +σ 2 ( I 3 −αK 3 )∥ 2
where
J
1
=
[
1
0
0
0
0
1
0
0
0
0
1
0
]
A
=
[
1
1
1
exp
(
jϕ
1
)
exp
(
jϕ
2
)
exp
(
jϕ
3
)
exp
(
j
2
ϕ
1
)
exp
(
j
2
ϕ
2
)
exp
(
j
2
ϕ
3
)
exp
(
j
3
ϕ
1
)
exp
(
j
3
ϕ
2
)
exp
(
j
3
ϕ
3
)
]
:
array response matrix
Rxx: a covariant matrix of a vector x including received signals x k (k=1 to 3) of a k-th incoming wave as a component,
I
3
=
[
1
0
0
0
1
0
0
0
1
]
Φ
=
[
exp
(
jϕ
1
)
0
0
0
exp
(
jϕ
2
)
0
0
0
exp
(
jϕ
3
)
]
σ: (a mean noise power) 1/2
K
3
=
[
0
1
0
0
0
1
0
0
0
]
;
and
a minimum value calculation unit configured to calculate a minimum value of the evaluation function, wherein
the angle calculation unit calculates φ from α=exp(jφ) where the evaluation function becomes the minimum value, and calculates an angle θ at where the object is present from the calculated φ=2*π*(d/λ)*sin(θ).
4. The radar device according to claim 1 , wherein the radar further comprises an angle reliability evaluation unit configured to evaluate the reliability of the calculated angle.
5. The radar device according to claim 2 , wherein the radar further comprises an angle reliability evaluation unit configured to evaluate the reliability of the calculated angle.