ANC convergence factor estimation as a function of frequency
A method of operating an audio system in a vehicle includes providing m number of microphones disposed within a passenger compartment of the vehicle. The microphones produce a plurality of microphone signals. Within the passenger compartment of the vehicle, k number of loudspeakers are provided. A plurality of convergence factors μ for use in performing active noise control are estimated. The estimating includes calculating an Eigen value λ(ω) of an autocorrelation matrix of a passenger compartment transfer function as λ k ( ω ) = A k ( ω ) 2 2 , wherein A k (ω) is the frequency response of the passenger compartment transfer function. A frequency ω min of a local minimum of λ(ω) is determined. A largest stable value for μMax(ω min ) is found by experimentation, wherein a rotational speed of an engine of the vehicle, expressed in revolutions per minute, f rpm =2πω min . A calibration factor is calculated as L=λ(ω min )μMax(ω min ). All values of μMax(ω) are estimated as μMax ( ω ) = L λ ( ω ) . A plurality of active noise controlled audio signals are transmitted to the loudspeaker. The active noise controlled audio signals are dependent upon the microphone signals and the estimated convergence factors.
1. A method of operating an audio system in a vehicle, the method comprising:
providing m number of microphones disposed within a passenger compartment of the vehicle, the microphones being configured to produce a plurality of microphone signals;
providing k number of loudspeakers disposed within a passenger compartment of the vehicle;
estimating a plurality of convergence factors μ for use in performing active noise control, the estimating including:
calculating an Eigen value λ(ω) of an autocorrelation matrix of a passenger compartment transfer function as
λ
k
(
ω
)
=
A
k
(
ω
)
2
2
,
wherein A k (ω) is the frequency response of the passenger compartment transfer function;
determining a frequency ω min of a local minimum of λ(ω);
finding a largest stable value for μMax(ω min ) by experimentation, wherein a rotational speed of an engine of the vehicle, expressed in revolutions per minute, f rpm =2πω min ;
calculating a calibration factor as L=λ(ω min )μMax(ω min );
estimating all values of μMax(ω) as
μMax
(
ω
)
=
L
λ
(
ω
)
;
and
transmitting a plurality of active noise controlled audio signals to the loudspeakers, the active noise controlled audio signals being dependent upon the microphone signals and the estimated convergence factors.
2. The method of claim 1 wherein m=1 and k=1.
3. The method of claim 1 wherein m>1 and k>1.
4. The method of claim 1 wherein the values of μMax(ω) are estimated over a range of frequencies with a resolution of about 1 Hz.
5. The method of claim 1 wherein the autocorrelation matrix R is:
R
k
(
ω
)
=
[
A
k
(
ω
)
2
2
0
0
A
k
(
ω
)
2
2
]
.
6. The method of claim 1 wherein a range of stability of μ for each speaker and frequency is 0<μ k (ω)<1/λ k (ω).
7. The method of claim 1 wherein the active noise controlled audio signals are produced by a narrow band filtered X LMS adaptive active noise control system.
8. A method of operating an audio system in a vehicle, the method comprising:
providing a plurality of microphones associated with a passenger compartment of the vehicle, the microphones being configured to produce a plurality of microphone signals;
providing a plurality of loudspeakers associated with the passenger compartment of the vehicle;
estimating a plurality of convergence factors for use in performing active noise control, the estimating including:
calculating an Eigen value of an autocorrelation matrix of a passenger compartment transfer function, the Eigen value being a function of a rotational speed of an engine of the vehicle;
determining an engine rotational speed associated with a local minimum of the Eigen value;
finding by experimentation a largest stable value for one of the convergence factors at a minimum engine speed;
calculating a calibration factor dependent upon the largest stable value for one of the convergence factors at a minimum engine speed; and
estimating all values of the convergence factor within a range of engine speeds, the estimating being dependent upon the calibration factor and the Eigen values within the range of engine speeds; and
transmitting a plurality of active noise controlled audio signals to the loudspeaker, the active noise controlled audio signals being dependent upon the microphone signals and the estimated convergence factor values.
9. The method of claim 8 wherein the Eigen value is
λ
k
(
ω
)
=
A
k
(
ω
)
2
2
,
wherein A k (ω) is a frequency response of the passenger compartment transfer function.
10. The method of claim 9 wherein the calibration factor is calculated as L=λ(ω min )μMax(ω min ), wherein μ is the convergence factor.
11. The method of claim 9 wherein the estimating all values of the convergence factor includes estimating all values of μMax(ω) as
μ
Max
(
ω
)
=
L
λ
(
ω
)
.
12. The method of claim 11 wherein the values of μMax(ω) are estimated over a range of frequencies with a resolution of less than 10 Hz.
13. The method of claim 8 wherein the autocorrelation matrix is:
R
k
(
ω
)
=
[
A
k
(
ω
)
2
2
0
0
A
k
(
ω
)
2
2
]
wherein A k (ω) is a frequency response of the passenger compartment transfer function.
14. The method of claim 8 wherein a range of stability of the convergence factor μ for each speaker and frequency is 0<μ k (ω)<1/λ k (ω), wherein λ k (ω) is the Eigen value.
15. A method of operating an audio system in a vehicle, the method comprising:
providing at least one microphone associated with a passenger compartment of the vehicle, the microphone being configured to produce a plurality of microphone signals;
providing at least one loudspeaker associated with the passenger compartment of the vehicle;
estimating a plurality of convergence factors for use in performing active noise control, the estimating including:
calculating an Eigen value of an autocorrelation matrix of a passenger compartment transfer function;
calculating a calibration factor dependent upon a largest stable value for one of the convergence factors at a minimum engine speed; and
estimating all values of the one convergence factor within a range of engine speeds, the estimating being dependent upon the calibration factor and a plurality of Eigen values within the range of engine speeds; and
transmitting a plurality of active noise controlled audio signals to the loudspeaker, the active noise controlled audio signals being dependent upon the microphone signals and the estimated convergence factor values.
16. The method of claim 15 wherein the Eigen value is a function of a rotational speed of an engine of the vehicle.
17. The method of claim 15 further comprising determining an engine rotational speed associated with a local minimum of the Eigen value.
18. The method of claim 17 further comprising finding by experimentation the largest stable value for one of the convergence factors at a minimum engine speed.
19. The method of claim 15 wherein the Eigen value is
λ
k
(
ω
)
=
A
k
(
ω
)
2
2
,
wherein A k (ω) is a frequency response of the passenger compartment transfer function.
20. The method of claim 19 wherein the calibration factor is calculated as L=λ(ω min )μMax(ω min ), wherein μ is the convergence factor, wherein the estimating all values of the one convergence factor includes estimating all values of μMax(ω) as
μ
Max
(
ω
)
=
L
λ
(
ω
)
,
wherein the values of μMax(ω) are estimated over a range of frequencies with a resolution of less than 100 Hz.