doapar1.m

阵列信号处理的工具箱

function  [doaHat, sHat, Q, doaHatAllIt, sigma2] = doapar1(method, sigIn, doaStart, focusDist, rangeIx, cpiIx, in7, in8, in9)

%DOAPAR1 Parametric estimation of DOA with different methods.
%
%--------
%Synopsis:
%  [doaHat,...]=doapar1(method,sigIn,doaStart,focusDist,rangeIx,cpiIx,...)
%
%Description:
%  Parametric estimation of DOA (Direction of Arrival) with different methods.
%
%Output and Input:
%  doaHat (DoaParamT): The estimated doa.
%  method (StringT): Estimation method. See below for sections about each
%    method.
%    = 'dml': Deterministic Maximum Likelihood.
%    = 'sml': Stochasic Maximum Likelihood.
%    = 'wsf': Weighted Subspace Fitting.
%    = 'ssf': Subspace Fitting.
%    = 'rmusic': Root Music.
%    = 'esprit': LS-Esprit.
%    = 'ptmf': Parametric Target Model Fitting.
%  sigIn (RxRadarSigT or RxCorrMatT): The input antenna signal or a
%    spatial correlation matrix. (For PTMF only RxRadarSigT is possible).
%  focusDist (RealScalarT): Focusing distance, e.g. 'Inf' for far field.
%    Not used yet.
%  rangeIx (IntScalarT): Index of range bin. Only used when "sigIn" is
%    of type RxRadarSigT. Default = 1.
%  cpiIx (IntScalarT): Index for CPI. Only used when "sigIn" is
%    of type RxRadarSigT. Default = 1.
%
%--------
%DML (Deterministic Maximum Likelihood).
%Synopsis:
% doaHat = doapar1('dml', sigIn, doaStart)
% doaHat = doapar1('dml', sigIn, doaStart, [], rangeIx, [])
% doaHat = doapar1('dml', sigIn, doaStart, [], rangeIx, cpiIx)
% doaHat = doapar1('dml', sigIn, doaStart, focusDist, rangeIx, cpiIx)
% [doaHat, sHat, dummy1, dummy2, sigma2] = doapar1('dml', sigIn, doaStart,
%   focusDist, rangeIx, cpiIx)
%
%Output and Input:
%  sHat (CxMatrixT): The complex envelope of the estimated source signals,
%    a complex matrix of size (noSrc x T), where noSrc is the number of
%    sources and T is the number of snapshots. Not tested.
%  sigma2 (RealScalarT): Estimated noise variance. Not tested.
%  sigIn (RxRadarSigT or RxCorrMatT): The input antenna signal or a
%    correlation matrix of it.
%  doaStart (Vector of DoaT): Start values of DOA:s. These should be
%    close to the real values.
%
%Description:
%  Returns maximum likelihood estimates for the DOA:s for a deterministic
%  signal model, see [2].
%  This method needs Matlab Optimization Toolbox.
%
%Algoritm:
%  An optimization problem is solved using the function "leastsq" in the
%  Optimization Toolbox [6,7]. For details see the code in the function doapar1
%  and in the function "dmlfun" and reference [2] and [11] p. 111-112.
%
%--------
%SML (Stochasic Maximum Likelihood).
%Synopsis:
% doaHat = doapar1('sml', sigIn, doaStart)
% doaHat = doapar1('sml', sigIn, doaStart, [], rangeIx, [])
% doaHat = doapar1('sml', sigIn, doaStart, [], rangeIx, cpiIx)
% doaHat = doapar1('sml', sigIn, doaStart, focusDist, rangeIx, cpiIx)
% [doaHat, Rss, dummy1, dummy2, sigma2] = doapar1('sml', sigIn, doaStart,
%   focusDist, rangeIx, cpiIx)
%
%Output and Input:
%  Rss (RxMatrixT): Estimated source signal correlation matrix.
%  sigma2 (RealScalarT): Estimated noise variance. Not tested.
%  sigIn (RxRadarSigT or RxCorrMatT): The input antenna signal or a
%    correlation matrix of it.
%  doaStart (Vector of DoaT): Start values of DOA:s. These should be
%    close to the real values.
%
%Description:
%  Returns maximum likelihood estimates for the DOA:s for a stochastic
%  signal model, see [2].
%  This method needs Matlab Optimization Toolbox.
%
%Algoritm:
%  An optimization problem is solved using the function "fminu" in the
%  Optimization Toolbox [6,7]. For details see the code in the function doapar1
%  and in the function "smlfun" and reference [2].
%
%--------
%WSF (Weighted Subspace Fitting).
%Synopsis:
% doaHat = doapar1('wsf', sigIn, doaStart)
% doaHat = doapar1('wsf', sigIn, doaStart, [], rangeIx, [])
% doaHat = doapar1('wsf', sigIn, doaStart, [], rangeIx, cpiIx)
% doaHat = doapar1('wsf', sigIn, doaStart, focusDist, rangeIx, cpiIx)
%
%Output and Input:
%  sigIn (RxRadarSigT or RxCorrMatT): The input antenna signal or a
%    correlation matrix of it.
%  doaStart (Vector of DoaT): Start values of DOA:s. These should be
%    close to the real values.
%
%Description:
%  See reference [4] (This is probably the same description as in [2]).
%  This method needs Matlab Optimization Toolbox.
%
%Algoritm:
%  An optimization problem is solved using the function "leastsq" in the
%  Optimization Toolbox [6,7]. For details see the code in the function doapar1
%  and in the function "wsffun" and reference [2].
%
%--------
%SSF (Subspace Fitting).
%Synopsis:
% doaHat = doapar1('ssf', sigIn, doaStart)
% doaHat = doapar1('ssf', sigIn, doaStart, [], rangeIx, [])
% doaHat = doapar1('ssf', sigIn, doaStart, [], rangeIx, cpiIx)
% doaHat = doapar1('ssf', sigIn, doaStart, focusDist, rangeIx, cpiIx)
%
%Output and Input:
%  sigIn (RxRadarSigT or RxCorrMatT): The input antenna signal or a
%    correlation matrix of it.
%  doaStart (Vector of DoaT): Start values of DOA:s. These should be
%    close to the real values.
%
%Description:
%  See reference [4] (This is probably the same description as in [2]).
%  This method needs Matlab Optimization Toolbox.
%
%Algoritm:
%  An optimization problem is solved using the function "leastsq" in the
%  Optimization Toolbox [6,7]. For details see the code in the function doapar1
%  and in the function "ssffun" and reference [2].
%
%--------
%ROOT MUSIC.
%Synopsis:
% doaHat = doapar1('rmusic', sigIn, noSrc)
% doaHat = doapar1('rmusic', sigIn, noSrc, [], rangeIx, [])
% doaHat = doapar1('rmusic', sigIn, noSrc, [], rangeIx, cpiIx)
% doaHat = doapar1('rmusic', sigIn, noSrc, focusDist, rangeIx, cpiIx)
%
%Output and Input:
%  sigIn (RxRadarSigT or RxCorrMatT): The input antenna signal or a
%    correlation matrix of it.
%  noSrc (IntScalarT): The number of sources.
%
%Description:
%  Gets a RootMUSIC pseudo DOA. For a description, see reference [2].
%  This method can only be used for ULA:s ([2] p. 80-81).
%  Note, that Root Music and LS-Esprit do not calculate the steering
%  matrix and does not call the function spastemat. All necessary calibration
%  compensation must therefore be done beforehand on the signals.
%
%Algoritm:
%
%--------
%LS-ESPRIT.
%Synopsis:
% doaHat = doapar1('esprit', sigIn, noSrc)
% doaHat = doapar1('esprit', sigIn, noSrc, [], rangeIx, [])
% doaHat = doapar1('esprit', sigIn, noSrc, [], rangeIx, cpiIx)
% doaHat = doapar1('esprit', sigIn, noSrc, focusDist, rangeIx, cpiIx)
%
%Output and Input:
%  sigIn (RxRadarSigT or RxCorrMatT): The input antenna signal or a
%    correlation matrix of it.
%  noSrc (IntScalarT): The number of sources.
%
%Description:
%  For a description, see reference [2].
%  This method can only be used for ULA:s ([2] p. 80-81).
%  Can only be used for ULA:s ([2] p. 80-81).
%  Note, that Root Music and LS-Esprit do not calculate the steering
%  matrix and does not call the function spastemat. All necessary calibration
%  compensation must therefore be done beforehand on the signals.
%
%Algoritm:
%
%--------
%PTMF (Parametric Target Model Fitting)
%Synopsis:
%  doaHat = doapar1('ptmf', sigIn, doaStart, [], [], [], stepLength)
%  doaHat = doapar1('ptmf', sigIn, doaStart, [], rangeIx, [], stepLength)
%  doaHat = doapar1('ptmf', sigIn, doaStart,[], rangeIx, cpiIx, stepLength)
%  [doaHat, sHat, Q, doaHatAllIt] = doapar1('ptmf', sigIn, doaStart,
%    focusDist, rangeIx, cpiIx, stepLength)
%
%Description:
%  Estimates the DOA with PTMF (Parametric Target Model Fitting) and
%  stochastic approximation. This is probably the same optimization problem
%  as with the 'dml' method but a different optimization method is used!?!
%
%Output and Input:
%  sHat (CxMatrixT): The complex envelope of the estimated source signals,
%    a complex matrix of size (noSrc x T), where noSrc is the number of
%    sources and T is the number of snapshots.
%  Q (RealVectorT.'): The error function (the squared modulus of the error,
%    see []) for all iterations. Size (1 x T), where T is the number of
%    snapshots.
%  doaHatAllIt (RealMatrixT): Estimated theta angle for all iterations.
%    The size is (noSrc x T), where noSrc is the number of sources and T
%    is the number of snapshots.
%  sigIn (RxRadarSigT): The input antenna signal.
%  doaStart (Vector of DoaT) :Start values of DOA:s. These should be
%    close to the real values.
%  stepLength (RealScalarT): Step length, e.g. 0.01. It is a balance between
%    stability an rapid convergence.
%
%Algoritm:
%  The algorithm is based on the one in [] by U. Nickel but there are
%  some changes:
%  * The notation is somewhat changed (to come closer to []).
%  * The step length 'stepLength' is fix and not a function of time.
%  * There is no limitation of the change in theta to 1/10 of the beamwidth.
%  * The change in theta is normalized with the power of the antenna signals.
%  * The pseudo invers is used instead of the "normal equations" due to better
%    numerical properties.
%
%Known Bugs:
%  A possible bug is that the derivative of the steering matrix is complex
%  conjugated.
%  Now a complex conjugation of the signals is done. This is maybe an
%  indication of a bug somewhere.
%
%--------
%Notations:
%  Data type names are shown in parentheses and they start with a capital
%  letter and end with a capital T. Data type definitions can be found in [1]
%  or by "help dbtdata".
%  [D] = This parameter can be omitted and then a default value is used.
%  When the [D]-input parameter is not the last used in the call, it must be
%  given the value [], i.e. an empty matrix.
%  ... = There can be more parameters. They are explained under respective
%  metod or choice.
%
%Examples:
%
%Software Quality:
%  (About what is done to ascertain software quality. What tests are done.)
%  The methods 'dml', 'sml', 'wsf', 'ssf', 'rmusic' and 'esprit' were used
%  in the work done by A. Heydarkhan [8].
%  The method 'ptmf' was used in the work done by M. Borgstr鰉 and
%  S. Bj鰎klund [9].
%
%Known Bugs:
%  The last input parameters "ranges", "theta0" and "poserr" (DBT release 1.6)
%  of the function spastemat are not used.
%  The wavelength is acquired from the antenna definition. This is not
%  logical but works as the wavelength happens to be stored there.
%
%References:
%  [1]: Bj鰎klund S.:"DBT, A MATLAB Toolbox for Radar Signal Processing.
%    Reference Guide", FOA-D--9x-00xxx-408--SE, To be published.
%  [2]: Krim H., Viberg M.:"Two Decades of Array Signal Processing Research",
%    IEEE Signal Processing Magazine, July 1996, pp. 67-94.
%  [3]: Roy R., Kailath T.:"ESPRIT-Estimation of Signal Parameters via
%    Rotational Invariance Techniques", IEEE Transaction on Acoustics,
%    Speech and Signal Processing, Vol. 37, No. 7, p. 984-995, July 1989.
%  [4]: Viberg M.:"Sensor Array Signal Processing, Lecture notes", Chalmers
%    University of Technology, From courses held at Chalmers the spring 1996
%    and at FOA the autumn 1996.
%  [5]: Carlstedt O.: "Superuppl鰏ning vid radarspaning i st鰎d signalmilj