Method for parameterizing a filter for active noise suppression of a hearing instrument

Abstract

The invention describes a method for parameterizing a filter (F) for active noise cancellation (ANC) of a hearing instrument (1), which is to be worn by a user in an ear canal (2), wherein the filter (F) is configured to generate a correction signal (u) for a loudspeaker (L1) of the hearing instrument (1) directed into the ear canal (2) based on an error signal (e) of an in-ear microphone (M1) of the hearing instrument (1), which records a sound (S1) containing a noise (d) in the ear canal (2), which, in operation of the active noise cancellation (ANC) of the hearing instrument (1), generates a correction sound (k) from the correction signal (u) to compensate for the noise (d) in the ear canal (2), and wherein filter coefficients (q) of the filter (F) are determined by means of an optimization problem.In said optimization problem, a sensitivity function dependent on said filter coefficients (q) and / or said filter (F), which describes a transfer of the noise (d) into the error signal (e), is weighted with an objective weighting function (Wd) and optimized, in particular minimized, wherein said optimization, in particular minimization, is carried out subject to at least one constraint on said sensitivity function and / or on a sensitivity function complementary to said sensitivity function, wherein the objective weighting function (Wd) is given by a number of continuously differentiable, in particular analytic, functions and has a bandpass characteristic.

Description

[0001] The invention relates to a method for parameterizing a filter for a particularly non-adaptive active noise suppression of a hearing instrument which is to be worn by a user in an ear canal, wherein the filter is configured to generate a correction signal for a loudspeaker of the hearing instrument directed into the ear canal based on an error signal of an in-ear microphone of the hearing instrument, wherein filter coefficients of the filter are determined by means of an optimization problem.

[0002] Hearing instruments such as headphones, headsets, etc., as well as hearing aids designed to treat a wearer with a hearing impairment, are increasingly being offered active noise cancellation features. These usually suppress ambient noise by emitting a correction signal into the user's ear canal via a hearing instrument loudspeaker. In this case, ambient sound can be picked up, for example, by a microphone directed into the environment in order to identify the background noise present there for generating the correction signal. Alternatively, or depending on the design, in addition to this, a microphone directed into the ear canal can be used to directly record the portion of the background noise that propagates into the ear canal via an acoustic transmission path past the hearing instrument (which usually largely closes off the entrance to the ear canal).

[0003] Of great importance in this context is the algorithm or filter used for active noise reduction, which generates the correction signal to suppress background noise in the ear canal based on the input signal from the microphone in question. The filter can be an adaptive filter, meaning the filter parameters themselves depend on the input signal of the microphone to which the filter is applied. Such an adaptive filter usually allows for a rapid response to changes in the input signal; however, artifacts or overshoots can also occur due to the potentially highly variable filter parameters (and, in some cases, poor convergence).

[0004] On the other hand, the filter can also be static, meaning that the filter parameters are independent of the microphone's input signal, so that the filter essentially statically replicates the aforementioned transmission path of the noise into the ear canal (which is also largely time-independent, except for minimal changes due to jaw movements or similar by the user, which are negligible to a first approximation). Such a static filter avoids the aforementioned problems of convergence of the filter parameters, but the correct model for reproducing the transmission path is now all the more important for the precision of the filter when generating the correction signal.

[0005] The invention is therefore based on the object of specifying a method by means of which a filter for a particularly non-adaptive active noise suppression of a hearing instrument can be parameterized as simply and precisely as possible.

[0006] The stated object is achieved according to the invention by a method for parameterizing a filter for a particularly non-adaptive active noise suppression of a hearing instrument which is to be worn by a user in an ear canal, wherein the filter is configured to generate a correction signal for a loudspeaker of the hearing instrument directed into the ear canal based on an error signal of an in-ear microphone of the hearing instrument which records a sound in the ear canal containing an interference noise, which loudspeaker, when the active noise suppression of the hearing instrument is in operation, generates a correction sound from the correction signal to compensate for the interference noise in the ear canal.

[0007] According to the method, it is provided that filter coefficients of the filter are determined by means of an optimization problem, wherein in said optimization problem a sensitivity function which is dependent on said filter coefficients and / or said filter and which describes a transfer of the interference noise into the error signal is weighted and optimized, in particular minimized, with an objective weighting function, wherein said optimization, in particular minimization, takes place under at least one secondary condition to said sensitivity function and / or to a sensitivity function complementary to said sensitivity function, and wherein the objective weighting function is given by a number of continuously differentiable, in particular analytical functions, and has a bandpass characteristic.

[0008] Advantageous and partly inventive embodiments are the subject of the dependent claims and the following description.

[0009] A hearing instrument generally includes any device that is designed to generate a sound signal from an electrical signal - which can also be provided by an internal signal of the device - and to supply it to the ear of a wearer of this device, i.e. in particular a headphone (e.g. as an "earplug"), a headset, data glasses with a loudspeaker, etc. However, a hearing instrument also includes a hearing aid in the narrower sense, i.e. a device for treating a wearer's hearing impairment, in which an input signal generated from an ambient signal by means of a microphone is processed into an output signal and is amplified in particular in a frequency band-dependent manner, and an output sound signal generated from the output signal by means of a loudspeaker or similar is suitable, in particular in a user-specific manner, to at least partially compensate for the wearer's hearing impairment.

[0010] During intended use, the hearing instrument is worn by a user "at" an ear canal, which specifically means that the hearing instrument is worn on one ear, at least partially closing the ear canal from the outside and / or partially penetrating the external ear canal. Noise that passes the hearing instrument via an acoustic transmission path and enters the ear canal is then compensated for by active noise cancellation using the corrective sound that is emitted by the hearing instrument via its loudspeaker directed into the said ear canal.

[0011] The in-ear microphone is preferably also directed into the ear canal, i.e., if the hearing instrument largely closes the external auditory canal except for the aforementioned acoustic transmission path, this defines an "inside" and an "outside" with regard to the hearing instrument, with the "inside" referring to the largely closed ear canal, and the "outside" referring to the entire, free external space.

[0012] This is based on Figure 1 described. Figure 1 This block diagram shows an active noise suppression system in a hearing instrument 1, which is worn on a person's ear canal 2, thereby largely sealing it. This arrangement defines an "inside" In for the hearing instrument 1, which is defined by the ear canal 2 "beyond" the components of the hearing instrument 1, and an "outside" Out, which is defined by the free space beginning at ear 4.

[0013] The hearing instrument 1 has an in-ear microphone M1 and a loudspeaker L1, both of which are directed inwards (In), i.e., into the ear canal 2, so that an output sound y generated by the loudspeaker L1 propagates towards the eardrum (not shown) at the other end of the ear canal 2, and the in-ear microphone M1 picks up a sound S1 in the ear canal 2, which, among other things, also contains a background noise d that has propagated along an acoustic transmission path H (dashed line) past the hearing instrument 1 from outside (Out) into the ear canal 2. The background noise d can be generated externally (Out) by any type of background noise source as a background noise r, e.g., by an engine of a vehicle or machine, such as traffic noise, fan noise, or machine whirring / humming, etc.

[0014] The acoustic transmission path H from outside (Out) to inside (In) of ear canal 2 (e.g., for the propagation of background noise r into ear canal 2 as background noise d) is also referred to as the primary transmission path. The transmission path from loudspeaker L1 to the in-ear microphone M1 in ear canal 2 itself is referred to as the secondary transmission path G and can, in particular, include resonances of the output sound y in ear canal 2. In this case, an output characteristic (i.e., a frequency response) of loudspeaker L1 is also absorbed into the secondary transmission path G.

[0015] The in-ear microphone M1 now generates an input signal referred to as the error signal e, based on which a correction signal u is generated by an active noise reduction (ANC) (which is shown here as a dashed block outside the hearing instrument 1 solely for reasons of space, but is physically implemented in the hearing instrument 1 on a suitable signal processor or processor unit, etc.). The correction signal u is converted by the loudspeaker L1 into a correction sound k, which is incorporated into the output sound y. An A / D conversion of the error signal e or a D / A conversion of the correction signal u is functionally absorbed in the in-ear microphone M1 or in the loudspeaker L1, respectively.

[0016] For active noise reduction ANC, a filter F is applied to the error signal, which is determined by filter coefficients q (coefficient vector) or can be parameterized via it.

[0017] The filter coefficients qk (entries k of the coefficient vector q ) are determined according to the method by means of an optimization problem in which a sensitivity function S, which describes the transmission of the noise d into the error signal e, is weighted with an objective weighting function W d and then optimized (preferably minimized).

[0018] The sensitivity function thus describes which portion of the noise d (which is caused by the external noise r and its propagation via the primary transmission path H) is included in the error signal e, taking into account that the error signal e itself depends on the correction signal u propagated via the secondary transmission path G.

[0019] If the filter F is described in its dependence on the filter coefficients q as F( q ), it follows from Fig. 1 e = d + G ∗ u = d + F q ∗ G ∗ e , where * denotes a convolution in the time domain (or the discrete time domain). By applying a Z-transformation to equation (i), the already mentioned relation between the error signal e and the noise d in the Z-domain is obtained as E Z = S Z ⋅ D Z = D Z 1 − F q Z ⋅ G Z .

[0020] To set the filter parameters q To obtain the sensitivity function S ( q, e jΩk< ) is weighted with the frequency-dependent objective weighting function W d (e jΩk< ) and minimized: min q ‖ S q e jΩ k W d e jΩ k ‖ 2 2

[0021] The minimization is carried out under a constraint on the sensitivity function S ( q, e jΩk< ) and / or to a complementary sensitivity function T ( q, e jΩk< ) with T ( q, e jΩk< ) = 1 - S ( q, e jΩk< ) for all parameters q and all frequency arguments e jΩk< .

[0022] The objective weighting function W d (e jΩk< ) is chosen in such a way that it is given by a number of continuously differentiable and in particular analytical functions (of the frequency), and also has a bandpass characteristic (the dependence of the frequency is expressed in the following case by e jΩk< or by Ω k, depending on which representation is more advantageous in each case).

[0023] The optimization problem at hand and the associated choice of the objective weighting function allow the filter for generating the correction signal for active noise reduction to be implemented particularly easily, since no direct measurement of the individual is necessary. Rather, the objective weighting function can be determined specifically based on statistical characteristics that can be measured for a manageable number of subjects and then made available to a large number of users.

[0024] The objective weighting function preferably has a lower band limit in a frequency interval from 10 Hz to 100 kHz, particularly preferably from 40 Hz to 80 Hz, and / or an upper band limit in a frequency interval from 200 Hz to 800 kHz, particularly preferably from 400 Hz to 600 Hz, wherein the band limit is in each case given by the frequency at which a frequency response of the objective weighting function has dropped to half, based on the maximum value in dB. Outside of the mentioned frequency ranges, active noise suppression cannot be achieved satisfactorily with the mentioned filter due to a loss of the phase relationship in the ear canal, so that the frequency response of the objective weighting function, on the basis of which the filter is parameterized via the above-mentioned optimization problem, only needs to have significant contributions in the relevant range.

[0025] In particular, the frequency response of the objective weighting function exhibits at least three inflection points. This means that the objective weighting function, which models the frequency response of typical noise, exhibits at least one plateau- or hump-shaped region. The ability to create such a plateau in the objective weighting function allows for the highlighting of a subfrequency band within the actual bandpass range in which the active noise suppression should be particularly effective.

[0026] The objective weighting function preferably comprises a sum of an ascending, smoothed step function and a descending, smoothed step function, where the ascending and descending smoothed step functions are each given by a sigmoid function or an arctangent or arccotangent function. These functions are particularly easy to parameterize and, moreover, particularly stable in numerical methods for implementing the optimization problem (iii).

[0027] The objective weighting function advantageously also includes a Gaussian function and / or a constant term. This provides additional degrees of freedom via the corresponding variables of the Gaussian function, which allows for particularly precise adjustment of the objective weighting function.

[0028] The objective weighting function W d (Ω k ) of the frequency argument Ω k thus advantageously has the following form: W d Ω k = K 0 + a sig 1 1 + e b sig 1 log 10 Ω k Ω sig 1 + a sig 2 1 + e b sig 2 log 10 Ω k Ω sig 2 + a g e − b g log 10 2 Ω k Ω g , where K 0 is a constant term, where the amplitude parameters a sig1 , a sig2 , ag , the frequency parameters Ω sig1 , Ω sig2 , Ω g (preferably with Ω say 1 < Ω say 2 ) and the slope parameters b sig1 , b sig2 , bg are used to parameterize the frequency response, and the products of a sig1 and b sig1 on the one hand and of a sig2 and b sig2 on the other hand have opposite signs. The second and third terms on the right-hand side of equation (iv) each represent sigmoid functions, and the fourth term is a Gaussian function.

[0029] In Figure 2a and 2b the relationships for individual parameters mentioned here are illustrated. Figure 2a(top left) shows the dependence of a sigmoid function on the frequency argument Ω k for different values ​​of b sig . As can be seen, with increasing parameter b sig , the slope becomes steeper and the step shorter. This is comparable to the well-known relationship for Gaussian functions, which become narrower in the exponent (i.e., decreasing variance) and thus more pointed (due to normalization) with increasing parameter bg. Figure 2b (top right) shows the relationship between the signs of a- sig and b sig . An increasing sigmoid function is clearly obtained when the two parameters have different signs, while a decreasing sigmoid function is obtained when the signs of a sig and b sig are identical.

[0030] Conveniently, said filter F (see Figure 1 ) applied to the error signal e the correction signal u, where the filter F is a control filter Q and a secondary filter Ĝwherein the control filter Q is applied to a residual error signal e res , and from this the correction signal u is generated up to a constant factor, wherein the residual error signal e res is generated based on a difference between the error signal e and the feedback signal and the secondary filter Ĝ filtered correction signal u, and where said filter coefficients in the optimization are the coefficients of the control filter Q ( q ) can be determined. The secondary filter is preferred Ĝ is chosen such that it simulates the secondary path G, which leads in the ear canal 2 from the loudspeaker L1 to the in-ear microphone M1.

[0031] This is done by Figure 3 which the filter F after Figure 1 schematically in a block diagram. For the active noise reduction ANC, the filter F ( q ) is applied, which is a control filter Q ( q) and the secondary filter Ĝ The control filter Q ( q ) is applied to the residual error signal e res , resulting in the correction signal u up to a constant factor, which is chosen to be -1 in this case. The residual error signal e res is generated using the control filter Q ( q ) resulting correction signal u' (the factor -1 is only a phase), to which the secondary filter Ĝ is applied. The resulting signal y is subtracted from the error signal e to generate the residual error signal e res.

[0032] Ideally, the secondary path is measured frequency-by-frequency for a large number of test subjects, with the secondary filter being formed frequency-by-frequency based on the respective minimum across all secondary paths at the relevant frequency. This means that measurements only need to be performed for a relatively small number of test subjects (usually in the tens of thousands), and the results can then be used for a large number of users (even in the five- to six-digit range or even higher) in their respective hearing instruments.

[0033] Preferably, the secondary filter Ĝ(e jΩk< ) is formed as a function of the frequency Ω k as the one of all measured secondary paths (G) which has the largest maximum over all considered frequencies, G ^ e jΩ k = arg max G ∈ G d ‖ G e jΩ k ‖ ∞ ⇔ arg max G ∈ G d max Ω k G e jΩ k , k = 0 , … , N Ω − 1 where the amount G d denotes the set of all measured secondary paths, and NΩ is the number of discrete frequencies. This is a particularly robust determination for the secondary filter Ĝ(e jΩk< ).

[0034] Alternatively, for each of the measured secondary paths G m a frequency-wise limit function WG,m (e jΩk< ) can be defined as W G , m e jΩ k = max G ∈ G d ′ G e jΩ k − G m e jΩ k G m e jΩ k , m = 1 , … , M G , where MG is the number of subjects, and the amount G ' d denotes the set of measured secondary paths without the secondary path m, where the secondary filter Ĝ(e jΩk< ) is formed depending on the frequency argument e jΩk< as the frequency-wise minimum over all limit functions, G ^ e jΩ k = arg min G ∈ G d ‖ W G , m e jΩ k ‖ ∞ = arg min G ∈ G d sup Ω k W G , m e jΩ k where the amount G d denotes the set of all measured secondary paths.

[0035] This means in particular: For each frequency e jΩk< and each secondary path G m (i.e. each measured secondary transmission path of a corresponding subject m), the limit function WG,m (e jΩk< ) is first formed as the value for which the absolute value of the fraction in equation (vi) reaches a maximum. This fraction forms for all the other measured secondary paths G, G ∈ G ' d the relative deviation from the secondary path G m . If one has now determined for each subject m and his measured secondary path G m at each frequency e jΩk< the maximum relative deviation of another measured secondary path, these values ​​each form the limit function WG,m (e jΩk< ).

[0036] Now, for each frequency e jΩk<, the minimum value over all limit functions of the individual subjects m is determined, see equation (vi), and the respective secondary path at which the limit function becomes minimal for a frequency e jΩk< is determined as the value of the secondary filter Ĝ(e jΩk< ) at this frequency e jΩk<.

[0037] Conveniently, the sensitivity function S ( q , e jΩk< ) depending on the filter coefficients q of the control filter Q and the frequency e jΩk< and depending on the secondary filter Ĝ(e jΩk< ) formed as S q , e jΩ k = 1 + Q e jΩ k G ^ e jΩ k .

[0038] This can be seen from Figure 3 particularly well recognized.

[0039] The optimization problem is conveniently of the following form: min q ‖ S q e jΩ k W d e jΩ k ‖ 2 2 s . t . ‖ T q e jΩ k W T e jΩ k ‖ ∞ < 1 ‖ S q e jΩ k W S e jΩ k ‖ ∞ < 1

[0040] S denotes sensitivity function, W d the objective weight function, qwhere λ is the vector of filter coefficients, T is the complementary sensitivity function (i.e., T = 1 - S), and Ws and WT are frequency-wise conditions for the sensitivity function and the complementary sensitivity function, respectively. The conditions Ws and WT on S and T are formulated in the supremum norm.

[0041] The sensitivity function S can be used, for example, to set the general amplification of interference. For normalization purposes, the integral over the logarithm of | S (e jΩk< ) | must be limited to << 1 up to a cutoff frequency. This means that there are ranges for | S (e jΩk< ) | which are < 1, and ranges in which | S (e jΩk< ) |> 1. In the latter case, interference is generally amplified ("disturbance amplification"). The specific form of S can then be used to set the frequency ranges up to which the system suppresses interference. These ranges should preferably be tuned to those frequency ranges in which the objective weighting function W d assumes values ​​significantly different from zero.

[0042] Preferably, the condition WT is formed based on an analysis of the variance of a plurality of measured secondary paths, and / or the condition Ws is formed depending on a nominal performance or an upper limit for noise amplification. The nominal performance is particularly given by the case in which the model for the secondary path replicates the actual secondary path.

[0043] The invention further mentions a method for active noise suppression in a hearing instrument, in particular a hearing aid, as well as a hearing instrument which is designed to carry out such a method for active noise suppression.

[0044] For the method for active noise reduction, a sound signal containing a background noise is converted into an error signal by means of an in-ear microphone of the hearing instrument in the ear canal of a user, wherein a correction signal is generated by a filter based on the error signal, wherein the correction signal is converted into a correction sound to compensate for the background noise by a loudspeaker of the hearing instrument directed into the ear canal, and wherein filter coefficients of the filter are parameterized using the corresponding method described above. This includes, in particular, that the filter coefficients q of a control filter Q can be determined by the optimization problem described above, preferably according to equation (iii) and in particular according to equation (vii).

[0045] The hearing instrument according to the invention comprises an in-ear microphone which is configured to record a sound signal in an ear canal of the user when worn as intended by a user, a loudspeaker which is directed into the ear canal when worn as intended by the user, and a signal processing unit, wherein the hearing instrument is configured to carry out the said method for active noise suppression.

[0046] The inventive method for active noise suppression in a hearing instrument and the hearing instrument share the advantages of the inventive method for parameterizing a filter for active noise suppression in a hearing instrument. The advantages mentioned for the latter method can be applied mutatis mutandis to the method for active noise suppression in a hearing instrument and to the hearing instrument.

[0047] The invention also mentions a method for modeling a secondary filter which simulates a secondary path which leads in an ear canal of a user of a hearing instrument from a loudspeaker of the hearing instrument arranged there to an in-ear microphone of the hearing instrument directed into the ear canal, wherein the secondary path is measured frequency by frequency for a plurality of test subjects, and wherein the secondary filter is formed frequency by frequency based on the respective minimum across all secondary paths at the respective frequency.

[0048] Preferably, the secondary filter Ĝ(e jΩk< ) is formed as a function of the frequency argument e jΩk< according to equation (v).

[0049] Embodiments of the invention are explained in more detail with reference to the accompanying drawings, each of which shows schematically: Fig. 1 shows a block diagram of an active noise suppression in a hearing instrument which is worn on a person's ear canal. Fig. 2a shows the dependence of a sigmoid function for various parameters in the exponent over the frequency. Fig. 2b shows the relationship between the signs of the prefactor and the parameter in the exponent of a sigmoid function. Fig. 3 shows a block diagram of a detailed design of the filter of the active noise suppression according to Fig. 1 , and Fig. 4 a modeled objective weighting function for the filter according to Fig. 3 over frequency, and a corresponding measured spectrum.

[0050] Corresponding parts and sizes are provided with the same reference numerals in all figures.

[0051] In Figure 4In the upper image, an objective weighting function W d is shown above the frequency, as it is to be used for the above-mentioned optimization method. The objective weighting function W d has the form defined in equation (iv), where the rising edge 8 corresponds to the first sigmoid function (with a- sig1 / b sig1 ), and the falling edge 10 to the second sigmoid function (with a sig2 / b sig2 ). The bulge 12, which contains an additional inflection point 14 and leads to an indicated plateau 16, corresponds to the Gaussian function in equation (iv). The rising edge 8 represents a lower band limit 9 of the objective weighting function W d , which in this case is localized in the range of approximately 65-70 Hz (drop to half the maximum value), the falling edge 10 an upper band limit 11 at approximately 500 Hz.

[0052] In the picture below the Figure 4A spectrum measured on a subject for a noise process is shown. It is clearly evident that the objective weighting function W d exhibits a more pronounced bandpass behavior and is also significantly smoother, which significantly simplifies the parameterization of a filter.

[0053] Although the invention has been illustrated and described in detail by the preferred embodiment, the invention is not limited to the disclosed examples and other variations may be derived therefrom by those skilled in the art without departing from the scope of the invention. List of reference symbols

[0054] 1Hearing instrument 2Ear canal 4Ear 8Rising edge 9Lower band limit 10Falling edge 11Upper band limit 12Bump 14Additional inflection point 16Indicated plateau ANCActive noise reduction dNoise (in the ear canal) eError signal eResidual error signal FFilter GSecondary transmission path ĜSecondary filter Hprimary (acoustic) transmission path Ininside kCorrection sound L1Speaker M1In-ear microphone Outoutside QControl filter q Filter coefficients rNoise S1Sound (in the ear canal) uCorrection signal W d Objective weighting function yOutput sound ŷ resulting signal (from secondary filter)

Claims

1. Method for parameterizing a filter (F) for active noise reduction (ANC) of a hearing instrument (1) which is to be worn by a user in an ear canal (2), wherein the filter (F) is configured to generate, on the basis of an error signal (e) of an in-ear microphone (M1) of the hearing instrument (1), which microphone records a sound (S1) containing an interfering noise (d) in the ear canal (2), a correction signal (u) for a loudspeaker (L1) of the hearing instrument (1) directed into the ear canal (2), which loudspeaker, during operation of the active noise reduction (ANC) of the hearing instrument (1), generates from the correction signal (u) a correction sound (k) for compensating the interfering noise (d) in the ear canal (2), wherein filter coefficients ( q ) of the filter (F) are determined by means of an optimization problem, wherein in said optimization problem one of said filter coefficients ( q) and / or said filter (F) dependent sensitivity function, which describes a transfer of the noise (d) into the error signal (e), with an objective weighting function (W d ) is weighted and optimized, in particular minimized, wherein said optimization, in particular minimization, is carried out under at least one constraint on said sensitivity function and / or on a sensitivity function complementary to said sensitivity function, wherein the objective weighting function (W d ) - is given by a number of continuously differentiable, in particular analytical functions, and - has a bandpass characteristic.

2. Method according to claim 1, wherein the objective weighting function (W d) - has a lower band limit (9) in a frequency interval of 10 Hz to 100 kHz, and / or - has an upper band limit (11) in a frequency interval of 200 Hz to 800 kHz, wherein the lower or upper band limit (9, 11) is given by the frequency at which a frequency response of the objective weighting function (W d ) has dropped to half of the maximum value in dB.

3. Method according to one of the preceding claims, wherein the objective weighting function (W d ) comprises a sum of an ascending, smoothed step function and a descending, smoothed step function, and wherein the ascending and descending smoothed step functions are each given by a sigmoid function or an arctangent or arccotangent function.

4. Method according to one of the preceding claims, wherein the objective weighting function (W d) further includes a Gaussian function and / or a constant term.

5. Method according to claim 3 in conjunction with claim 4, wherein the objective weighting function W d (Ω k ) of the frequency argument Ω k which has the following form: W d Ω k = K 0 + a sig 1 1 + e b sig 1 log 10 Ω k Ω sig 1 + a sig 2 1 + e b sig 2 log 10 Ω k Ω sig 2 + a g e − b g log 10 2 Ω k Ω g , Ω sig 1 < Ω sig 2 where K0 is a constant term, with the amplitude parameters a sig1 , a sig2 , a g , the frequency parameters Ω sig1 , Ω sig2 , Ω g and the gradient parameters b sig1 , b sig2 , b g be used to parameterize the frequency response, using the products of a sig1 and b sig1 on the one hand and from a sig2 and b sig2 on the other hand, have opposite signs.

6. Method according to one of the preceding claims, - wherein said filter (F) applied to the error signal (e) generates the correction signal (u), - wherein the filter (F) comprises a control filter (Q) and a secondary filter ( G), - wherein the control filter (Q) is applied to a residual error signal (e res ), and from this the correction signal (u) is generated up to a constant factor, - whereby the residual error signal (e res ) is generated from a difference between the error signal (e) and the feedback and filtered correction signal (u) with the secondary filter (G), and wherein said filter coefficients ( q ) in the optimization the coefficients of the control filter (Q) are determined.

7. The method according to claim 6, wherein the secondary filter ( G ) is selected such that it simulates a secondary path (G) which leads in the ear canal (2) from the loudspeaker (L1) to the in-ear microphone (M1).

8. The method according to claim 7, wherein the secondary path (G) is measured frequency-wise for a plurality of subjects, and wherein the secondary filter ( G) is formed as the one of all measured secondary paths (G) which has the largest maximum over all frequencies considered.

9. Method according to one of claims 6 to 8, wherein the sensitivity function S ( q , e jΩk ) depending on the filter coefficients q of the control filter Q and the frequency argument e jΩk and depending on the secondary filter Ĝ(e jΩk ) is formed as S q e jΩ k = 1 + Q e jΩ k G ^ e jΩ k 10. Method according to one of the preceding claims, wherein the optimization problem is of the following form: min q ‖ S q e jΩ k W d e jΩ k ‖ 2 2 s . t . ‖ T q e jΩ k W T e jΩ k ‖ ∞ < 1 ‖ S q e jΩ k W S e jΩ k ‖ ∞ < 1 where S denotes the sensitivity function, W d the objective weight function, q the vector of filter coefficients, T the complementary sensitivity function (i.e. T = 1 - S), and Ws and W T frequency-wise conditions for the sensitivity function or the complementary sensitivity function, 11. The method according to claim 10, wherein the condition W T is formed based on an analysis of the variance of a plurality of measured secondary paths (G), and / or wherein the condition Ws is formed as a function of a nominal performance or an upper limit for a noise amplification.

12. Method for active noise cancellation (ANC) in a hearing instrument (1), in particular a hearing aid, wherein a sound (S1) comprising an interfering noise (d) is converted into an error signal (e) by means of an in-ear microphone (M1) of the hearing instrument (1) in an ear canal (2) of a user, wherein a correction signal (u) is generated by a filter (F) on the basis of the error signal (e), wherein the correction signal (u) is converted into a correction sound (k) for compensating the interfering noise (d) by a loudspeaker (L1) of the hearing instrument (1) directed into the ear canal (2), and wherein filter coefficients ( q) of the filter (F) are parameterized by means of a method according to one of the preceding claims.

13. Hearing instrument (1), comprising: - an in-ear microphone (M1) which is configured to record a sound (S1) in an ear canal (2) of the user when worn as intended by a user, - a loudspeaker (L1) which is directed into the ear canal (2) when worn as intended by the user, and - a signal processing unit, wherein the hearing instrument (1) is configured to carry out the method according to claim 12.

14. Method for modeling a secondary filter ( G), which simulates a secondary path (G) which leads in an ear canal (2) of a user of a hearing instrument (1) from a loudspeaker (L1) of the hearing instrument (1) arranged there to an in-ear microphone (M1) of the hearing instrument (1) directed into the ear canal (2), wherein the secondary path (G) is measured frequency-wise for a plurality of test subjects, and wherein the secondary filter ( G ) is formed frequency by frequency based on the respective minimum across all secondary paths (G) at the relevant frequency.

15. The method according to claim 14, wherein the secondary filter Ĝ(e jΩk ) depending on the frequency Ω k is formed as the one of all measured secondary paths (G) which has the largest maximum over all frequencies considered, G ^ e jΩ k = arg max G ∈ G d ‖ G e jΩ k ‖ ∞ ⇔ arg max G ∈ G d max Ω k G e jΩ k , k = 0 , … , N Ω − 1 where the amount G d denotes the set of all measured secondary paths, and N Ω the number of discrete frequencies.

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