% -*- texinfo -*-
% @deftypefn {Function File} {[@var{l}, @var{m}, @var{p}, @var{e}] =} dlqe (@var{a}, @var{g}, @var{c}, @var{sigw}, @var{sigv}, @var{z})
% Construct the linear quadratic estimator (Kalman filter) for the
% discrete time system
% @iftex
% @tex
% $$
% x_{k+1} = A x_k + B u_k + G w_k
% $$
% $$
% y_k = C x_k + D u_k + v_k
% $$
% @end tex
% @end iftex
% @ifinfo
%
% @example
% x[k+1] = A x[k] + B u[k] + G w[k]
% y[k] = C x[k] + D u[k] + v[k]
% @end example
%
% @end ifinfo
% where @var{w}, @var{v} are zero-mean gaussian noise processes with
% respective intensities @code{@var{sigw} = cov (@var{w}, @var{w})} and
% @code{@var{sigv} = cov (@var{v}, @var{v})}.
%
% If specified, @var{z} is @code{cov (@var{w}, @var{v})}. Otherwise
% @code{cov (@var{w}, @var{v}) = 0}.
%
% The observer structure is
% @iftex
% @tex
% $$
% z_{k|k} = z_{k|k-1} + l (y_k - C z_{k|k-1} - D u_k)
% $$
% $$
% z_{k+1|k} = A z_{k|k} + B u_k
% $$
% @end tex
% @end iftex
% @ifinfo
%
% @example
% z[k|k] = z[k|k-1] + L (y[k] - C z[k|k-1] - D u[k])
% z[k+1|k] = A z[k|k] + B u[k]
% @end example
% @end ifinfo
%
% @noindent
% The following values are returned:
%
% @table @var
% @item l
% The observer gain,
% @iftex
% @tex
% $(A - ALC)$.
% @end tex
% @end iftex
% @ifinfo
% (@var{a} - @var{a}@var{l}@var{c}).
% @end ifinfo
% is stable.
%
% @item m
% The Riccati equation solution.
%
% @item p
% The estimate error covariance after the measurement update.
%
% @item e
% The closed loop poles of
% @iftex
% @tex
% $(A - ALC)$.
% @end tex
% @end iftex
% @ifinfo
% (@var{a} - @var{a}@var{l}@var{c}).
% @end ifinfo
% @end table
% @end deftypefn