<s>
In	O
statistics	O
and	O
signal	O
processing	O
,	O
the	O
orthogonality	B-General_Concept
principle	I-General_Concept
is	O
a	O
necessary	O
and	O
sufficient	O
condition	O
for	O
the	O
optimality	O
of	O
a	O
Bayesian	B-General_Concept
estimator	I-General_Concept
.	O
</s>
<s>
Loosely	O
stated	O
,	O
the	O
orthogonality	B-General_Concept
principle	I-General_Concept
says	O
that	O
the	O
error	O
vector	O
of	O
the	O
optimal	O
estimator	O
(	O
in	O
a	O
mean	B-Algorithm
square	I-Algorithm
error	I-Algorithm
sense	O
)	O
is	O
orthogonal	O
to	O
any	O
possible	O
estimator	O
.	O
</s>
<s>
The	O
orthogonality	B-General_Concept
principle	I-General_Concept
is	O
most	O
commonly	O
stated	O
for	O
linear	O
estimators	O
,	O
but	O
more	O
general	O
formulations	O
are	O
possible	O
.	O
</s>
<s>
Since	O
the	O
principle	O
is	O
a	O
necessary	O
and	O
sufficient	O
condition	O
for	O
optimality	O
,	O
it	O
can	O
be	O
used	O
to	O
find	O
the	O
minimum	B-General_Concept
mean	I-General_Concept
square	I-General_Concept
error	I-General_Concept
estimator	O
.	O
</s>
<s>
The	O
orthogonality	B-General_Concept
principle	I-General_Concept
is	O
most	O
commonly	O
used	O
in	O
the	O
setting	O
of	O
linear	O
estimation	O
.	O
</s>
<s>
In	O
this	O
context	O
,	O
let	O
x	O
be	O
an	O
unknown	O
random	B-General_Concept
vector	I-General_Concept
which	O
is	O
to	O
be	O
estimated	O
based	O
on	O
the	O
observation	O
vector	O
y	O
.	O
</s>
<s>
More	O
accurately	O
,	O
one	O
would	O
like	O
to	O
minimize	O
the	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
(	O
MSE	O
)	O
between	O
and	O
.	O
</s>
<s>
Other	O
settings	O
which	O
can	O
be	O
formulated	O
in	O
this	O
way	O
include	O
the	O
subspace	O
of	O
causal	B-Algorithm
linear	O
filters	O
and	O
the	O
subspace	O
of	O
all	O
(	O
possibly	O
nonlinear	O
)	O
estimators	O
.	O
</s>
<s>
The	O
following	O
is	O
one	O
way	O
to	O
find	O
the	O
minimum	B-General_Concept
mean	I-General_Concept
square	I-General_Concept
error	I-General_Concept
estimator	O
by	O
using	O
the	O
orthogonality	B-General_Concept
principle	I-General_Concept
.	O
</s>
<s>
thus	O
providing	O
an	O
expression	O
for	O
the	O
coefficients	O
of	O
the	O
minimum	B-General_Concept
mean	I-General_Concept
square	I-General_Concept
error	I-General_Concept
estimator	O
.	O
</s>
