[en] The operation of solid-state qubits often relies on single-shot readout using a nanoelectronic charge sensor, and the detection of events in a noisy sensor signal is crucial for high fidelity readout of such qubits. The most common detection scheme, comparing the signal to a threshold value, is accurate at low noise levels but is not robust to low-frequency noise and signal drift. We describe an alternative method for identifying charge sensor events using wavelet edge detection. The technique is convenient to use and we show that, with realistic signals and a single tunable parameter, wavelet detection can outperform thresholding and is significantly more tolerant to $1/f$ and low-frequency noise. (paper)