Method and apparatus for determining dominant sound source directions in a higher order Ambisonics representation of a sound field
In Higher Order Ambisonics, a problem is the tracking of time variant directions of dominant sound sources. The following processing is carried out: from a current time frame of HOA coefficients, estimating a directional power distribution of dominant sound sources, from said directional power distribution and from an a-priori probability function for dominant sound source directions, computing an a-posteriori probability function for said dominant sound source directions, depending on said a-posteriori probability function and on dominant sound source directions for the previous time frame, searching and assigning dominant sound source directions for said current time frame of said HOA coefficients.
1. A method for determining dominant sound source directions in a Higher Order Ambisonics representation denoted HOA of a sound field, said method comprising:
from a current time frame of HOA coefficients, estimating a directional power distribution with respect to dominant sound sources;
from said directional power distribution and from an a-priori probability function for dominant sound source directions, computing an a-posteriori probability function for said dominant sound source directions;
depending on said a-posteriori probability function and on dominant sound source directions for the previous time frame of said HOA coefficients, searching and assigning dominant sound source directions for said current time frame of said HOA coefficients,
wherein said a-priori probability function is computed from a set of estimated sound source movement angles and from said dominant sound source directions for the previous time frame of said HOA coefficients, and wherein said set of estimated sound source movement angles is computed from said dominant sound source directions for the previous time frame of said HOA coefficients and from dominant sound source directions for the penultimate time frame of said HOA coefficients.
2. The method according to claim 1 , further comprising:
computing said a-posterior probability function according to the Bayesian rule, wherein said a-priori probability function predicts, depending on the knowledge at said previous time frame of said HOA coefficients, the probability that any of the dominant sound sources is located at any test direction at said current time frame of HOA coefficients.
3. The method according to claim 1 , further comprising:
calculating said a-priori probability function according to
P PRIO (l,Ω q )=1−Π d=1 D [1−P {circumflex over (Ω)} DOM,d (l) PRIO,SINGLE (Ω d )] and determining the probability of any one of D sound sources being located at direction Ω q in said current time frame l of HOA coefficients,
wherein
P
Ω
~
DOM
,
d
(
l
)
PRIO
,
SINGLE
(
Ω
q
)
=
(
κ
d
(
l
-
1
)
Q
·
sinh
(
κ
d
(
l
-
1
)
)
·
exp
{
κ
d
(
l
-
1
)
·
cos
(
θ
q
,
d
)
}
if
κ
d
(
l
-
1
)
≠
0
1
Q
if
κ
d
(
l
-
1
)
=
0.
,
{circumflex over (Ω)} DOM,d (l) denotes a discrete random variable indicating the direction of the d-th source at the l-th time frame and has values Ω q , q=1, . . . Q,
κ d (l−1) is a concentration parameter determining the shape of a von Mises-Fisher distribution around the mean direction,
θ q, d denotes the angle distance between an estimated direction
{circumflex over (Ω)} DOM,d (l−1) and a test direction.
4. The method according to claim 2 , further comprising:
computing said a-posterior probability function according to:
P
POST
(
l
,
Ω
q
)
=
P
PRIO
(
l
,
Ω
q
)
·
σ
2
(
l
,
Ω
q
)
∑
q
=
1
Q
P
PRIO
(
l
,
Ω
q
)
·
σ
2
(
l
,
Ω
q
)
,
wherein σ 2 (l) is said directional power distribution.
5. The method according to claim 1 , further comprising
carrying out said assigning of dominant sound source directions for said current time frame l of said HOA coefficients by:
following determining of all current dominant sound source directions {circumflex over (Ω)} CURRDOM,d (l), d=1, . . . D, assigning these directions to the dominant sound source directions {circumflex over (Ω)} DOM,d (l−1), d=1, . . . , D from the previous frame, wherein the assignment function :{1, . . . D}→{1, . . . , D} is determined such that the sum of angles
∑
d
=
1
D
<
(
Ω
^
CURRDOM
,
d
(
l
)
,
Ω
^
DOM
,
f
𝒜
,
1
(
d
)
(
l
-
1
)
)
between assigned directions is minimised;
obtaining said dominant sound source directions by
Ω
^
DOM
,
(
d
)
(
l
)
:=
Ω
^
CURRDOM
,
f
𝒜
,
l
-
1
(
d
)
(
l
)
for
d
=
1
,
…
,
D
,
where (•) denotes the inverse assignment function.
6. The method according to claim 3 , further comprising:
setting for an initialisation of said concentration parameter for the first two time frames (l=1, l=2) of said HOA coefficients said concentration parameter to zero by κ d (0)=κ d (1)=0 for all d=1, . . . , D.
7. The method according to claim 1 , further comprising:
choosing arbitrarily for an initialisation, for a non-available previous time frame of said HOA coefficients, the direction estimates of said dominant sound source directions.
8. An apparatus for determining dominant sound source directions in a Higher Order Ambisonics representation denoted HOA of a sound field, said apparatus comprising a processor configured to:
estimating from a current time frame of HOA coefficients a directional power distribution with respect to dominant sound sources;
computing from said directional power distribution and from an a-priori probability function for dominant sound source directions an a-posteriori probability function for said dominant sound source directions;
searching and assigning, depending on said a-posteriori probability function and on dominant sound source directions for the previous time frame of said HOA coefficients, dominant sound source directions for said current time frame of said HOA coefficients;
computing said a-priori probability function from a set of estimated sound source movement angles and from said dominant sound source directions for the previous time frame of said HOA coefficients;
computing said set of estimated sound source movement angles from said dominant sound source directions for the previous time frame of said HOA coefficients and from dominant sound source directions for the penultimate time frame of said HOA coefficients.
9. The apparatus according to claim 8 , wherein said a-posterior probability function is computed according to the Bayesian rule, and wherein said a-priori probability function predicts, depending on the knowledge at said previous time frame of said HOA coefficients, the probability that any of the dominant sound sources is located at any test direction at said current time frame of HOA coefficients.
10. The apparatus according to claim 8 , wherein said a-priori probability function is calculated according to
P PRIO (l,Ω q )=1−Π d=1 D [1−P {tilde over (Ω)} DOM,d (l) PRIO,SINGLE (Ω q )] and determines the probability of any one of D sound sources being located at direction Ω q in said current time frame l of HOA coefficients,
and wherein
P
Ω
~
DOM
,
d
(
l
)
PRIO
,
SINGLE
(
Ω
q
)
=
(
κ
d
(
l
-
1
)
Q
·
sinh
(
κ
d
(
l
-
1
)
)
·
exp
{
κ
d
(
l
-
1
)
·
cos
(
θ
q
,
d
)
}
if
κ
d
(
l
-
1
)
≠
0
1
Q
if
κ
d
(
l
-
1
)
=
0.
,
{tilde over (Ω)} DOM,d (l) denotes a discrete random variable indicating the direction of the d-th source at the l-th time frame and has values Ω q , q=1, . . . , Q,
κ d (l−1) is a concentration parameter determining the shape of a von Mises-Fisher distribution around the mean direction,
θ q,d denotes the angle distance between an estimated direction
{circumflex over (Ω)} DOM,d (l−1) and a test direction.
11. The apparatus according to claim 9 , wherein said a-posterior probability function is computed according to:
P
POST
(
l
,
Ω
q
)
=
P
PRIO
(
l
,
Ω
q
)
·
σ
2
(
l
,
Ω
q
)
∑
q
=
1
Q
P
PRIO
(
l
,
Ω
q
)
·
σ
2
(
l
,
Ω
q
)
,
wherein σ 2 (l) is said directional power distribution.
12. The apparatus according to claim 8 , wherein said assigning of dominant sound source directions for said current time frame of said HOA coefficients is carried out by:
following determining of all current dominant sound source directions {circumflex over (Ω)} CURRDOM,d (l), d=1, . . . , D, assigning these directions to the dominant sound source directions Ω DOM,d (l−1), d=1, . . . , D from the previous frame, wherein the assignment function :{1, . . . , D}→{1, . . . , D} is determined such that the sum of angles
∑
d
=
1
D
<
(
Ω
^
CURRDOM
,
d
(
l
)
,
Ω
^
DOM
,
f
𝒜
,
1
(
d
)
(
l
-
1
)
)
between assigned directions is minimised;
obtaining said dominant sound source directions by
Ω
^
DOM
,
(
d
)
(
l
)
:=
Ω
^
CURRDOM
,
f
𝒜
,
l
-
1
(
d
)
(
l
)
for
d
=
1
,
…
,
D
,
where (•) denotes the inverse assignment function.
13. The apparatus according to claim 10 , wherein for an initialisation of said concentration parameter for the first two time frames of said HOA coefficients said concentration parameter is set to zero by κ d (0)=κ d (1)=0 for all d=1, . . . , D.
14. The apparatus according to claim 8 wherein, for an initialisation, for a non-available previous time frame of said HOA coefficients the direction estimates of said dominant sound source directions are chosen arbitrarily.