An ultrasonic measuring system is described for detecting an obstacle using a resonant transducer element for transmitting an ultrasonic pulse and for generating a received signal which includes the ultrasonic echo pulse reflected from the obstacle, the transducer element generating a decay signal having its resonance frequency after transmitting an ultrasonic pulse. The ultrasonic measuring system includes an evaluation unit having a control unit which is designed to activate the transducer element for transmitting the ultrasonic pulse with the aid of a frequency-modulated transmitted signal generated by the control unit, the frequency modulation taking place with the aid of a modulation signal in such a way that the signature of the ultrasonic pulse differs from that of the decay signal. The evaluation unit is designed to recognize the echo pulse based on an evaluation of a correlation signal which is generated with the aid of at least one correlation filter and which originates from the correlation of the signal generated by the resonant transducer element with the transmitted signal. Furthermore, a corresponding method is provided for detecting an obstacle with the aid of ultrasound, as well as a vehicle assistance system having the ultrasonic measuring system.