### Copyright (C) 1996 John W. Eaton
###
### This file is part of Octave.
###
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### under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2, or (at your option)
### any later version.
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### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with Octave; see the file COPYING.  If not, write to the Free
### Software Foundation, 59 Temple Place - Suite 330, Boston, MA
### 02111-1307, USA.

## Usage: [k, p, e] = lqe (A, G, C, SigW, SigV {,Z})
##
## Linear quadratic estimator (Kalman filter) design for the 
## continuous time system
##
##   dx/dt = A x + B u + G w
##       y = C x + D u + v
##
## where w, v are zero-mean gaussian noise processes with respective
## intensities SigW = cov (w, w) and SigV = cov (v, v).
##
## Z (if specified) is cov(w,v); otherwise cov(w,v) = 0.
##
## Observer structure is dz/dt = A z + B u + k( y - C z - D u).
##
## Returns:
##
##   k = observer gain, (A - K C) is stable
##   p = solution of algebraic Riccati equation
##   e = closed loop poles of (A - K C)

function [k, p, e] = lqe (a, g, c, sigw, sigv, zz)

  ## Written by A. S. Hodel (scotte@eng.auburn.edu) August, 1993.

  if (nargin != 5 && nargin != 6)
    error ("lqe: invalid number of arguments");
  endif

  ## The problem is dual to the regulator design, so transform to lqr
  ## call.

  if (nargin == 5)
    [k, p, e] = lqr (a', c', g*sigw*g', sigv);
  else
    [k, p, e] = lqr (a', c', g*sigw*g', sigv, g*zz);
  endif

  k = k';

endfunction