Method for operating a hearing system , which hearing system comprises a first input transducer , a second input transducer and a signal processing device , wherein an activity of a lateral useful signal source in an environment of the hearing system is determined, by - generating a first input signal (ES1) by an acoustic signal (AS) impinging on the first input transducer and generating a second input signal (ES2) by the acoustic signal (AS) impinging on the second input transducer , - generating a filtered input signal (GS) based on the first input signal (ES1) and based on the second input signal (ES2) by means of a direction-dependent notch filter unit , - based on the filtered input signal (GS) and based on the first input signal (ES1) and/or on the second input signal (ES2), determining a measure (M) of an attenuation caused by the direction-dependent notch filter unit , - comparing the measure (M) to a reference (R), wherein the comparison is used to infer the presence or absence of activity of a lateral useful signal source in the environment, - determining the reference (R) by determining a power spectral density for noise based on the first input signal (ES1) and/or based on the second input signal (ES2), characterized in that - at least one correction parameter is derived by means of the direction-dependent notch filter unit , and - either based on the spectral power density for noise and based on the at least one correction parameter, a modified spectral power density for noise is determined, or by means of the direction-dependent notch filter unit , a parameter value (P) is determined for at least one correction parameter, and wherein based on the spectral power density for noise and by means of the parameter value (P) for the at least one correction parameter, a modified spectral power density for noise is determined. - generating a first input signal (ES1) by an acoustic signal (AS) impinging on the first input transducer and generating a second input signal (ES2) by the acoustic signal (AS) impinging on the second input transducer , - generating a filtered input signal (GS) based on the first input signal (ES1) and based on the second input signal (ES2) by means of a direction-dependent notch filter unit , - based on the filtered input signal (GS) and based on the first input signal (ES1) and/or on the second input signal (ES2), determining a measure (M) of an attenuation caused by the direction-dependent notch filter unit , - comparing the measure (M) to a reference (R), wherein the comparison is used to infer the presence or absence of activity of a lateral useful signal source in the environment, - determining the reference (R) by determining a power spectral density for noise based on the first input signal (ES1) and/or based on the second input signal (ES2), - at least one correction parameter is derived by means of the direction-dependent notch filter unit , and - either based on the spectral power density for noise and based on the at least one correction parameter, a modified spectral power density for noise is determined, or by means of the direction-dependent notch filter unit , a parameter value (P) is determined for at least one correction parameter, and wherein based on the spectral power density for noise and by means of the parameter value (P) for the at least one correction parameter, a modified spectral power density for noise is determined. <EOS>