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espritdoa

Direction of arrival using TLS ESPRIT

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Syntax

ang = espritdoa(R,nsig)
ang = espritdoa(___,Name,Value)

Description

example

ang= espritdoa(R,nsig)estimates the directions of arrival,ang, of a set of plane waves received on a uniform line array (ULA). The estimation employs theTLS ESPRIT, the total least-squares ESPRIT, algorithm. The input arguments are the estimated spatial covariance matrix between sensor elements,R, and the number of arriving signals,nsig. In this syntax, sensor elements are spaced one-half wavelength apart.

example

ang= espritdoa(___,Name,Value)estimates the directions of arrival with additional options specified by one or moreName,Valuepair arguments. This syntax can use any of the input arguments in the previous syntax.

Examples

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Open Live Script

Assume a half-wavelength spaced uniform line array with 10 elements. Three plane waves arrive from the 0°, –25°, and 30° azimuth directions. Elevation angles are 0°. The noise is spatially and temporally white. The SNR for each signal is 5 dB. Find the arrival angles.

N = 10; d = 0.5; elementPos = (0:N-1)*d; angles = [0 -25 30]; Nsig = 3; R = sensorcov(elementPos,angles,db2pow(-5)); doa = espritdoa(R,Nsig)
doa =1×330.0000 -0.0000 -25.0000

Theespritdoafunction returns the correct angles.

Open Live Script

Assume a uniform line array with 10 elements. The element spacing is 0.4 wavelength. Three plane waves arrive from the 0°, –25°, and 30° azimuth directions. Elevation angles are 0°. The noise is spatially and temporally white. The SNR for each signal is 5 dB. Find the arrival angles.

N = 10; d = 0.4; elementPos = (0:N-1)*d; angles = [0 -25 30]; Nsig = 3; R = sensorcov(elementPos,angles,db2pow(-5)); doa = espritdoa(R,Nsig,'ElementSpacing',d)
doa =1×3-25.0000 -0.0000 30.0000

espritdoareturns the correct angles.

Input Arguments

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Spatial covariance matrix, specified as a complex-valued, positive-definite,N-by-Nmatrix. In this matrix,Nrepresents the number of elements in the ULA array. IfRis not Hermitian, a Hermitian matrix is formed by averaging the matrix and its conjugate transpose,(R+R')/2.

Example:[ 4.3162, –0.2777 – 0.2337i; –0.2777 + 0.2337i , 4.3162]

Data Types:double
Complex Number Support:Yes

Number of arriving signals, specified as a positive integer.

Example:3

Data Types:double

Name-Value Pair Arguments

Specify optional comma-separated pairs ofName,Valuearguments.Nameis the argument name andValueis the corresponding value.Name必须出现在引号。您可以指定数name and value pair arguments in any order asName1,Value1,...,NameN,ValueN.

Example:‘ElementSpacing’, 0.45

ULA element spacing, specified as a real-valued, positive scalar. Position units are measured in terms of signal wavelength.

Example:0.4

Data Types:double

Row weights specified as a real-valued positive scalar. These weights are applied to the selection matrices which determine the ESPRIT subarrays. A larger value is generally better but the value must be less than or equal to (Ns–1)/2, whereNs是麻木了er of subarray elements. The number of subarray elements isNs= N–1. The value ofN是麻木了er of ULA elements, as specified by the dimensions of the spatial covariance matrix,R. A detailed discussion of selection matrices and row weighting can be found in Van Trees[1], p. 1178.

Example:5

Data Types:double

Output Arguments

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Directions of arrival angle returned as a real-valued, 1-by-Mvector. The dimensionM是麻木了er of arriving signals specified in the argument,nsig. This angle is the broadside angle. Angle units are degrees and angle values lie between –90° and 90°.

References

[1] Van Trees, H.L.Optimum Array Processing. New York: Wiley-Interscience, 2002.

Extended Capabilities

See Also

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Introduced in R2013a

Phased Array System Toolbox Documentation
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