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The standard short-time Fourier transform and the Wigner distribution can be obtained as solutions of the minimization problem, with the absolute square error as a loss function. It has been shown that some other loss functions, like for example the absolute error, can produce more robust results in the case of signals corrupted with impulse, heavy-tailed, noise. This paper presents robust time frequency-signal analysis of nonstationary signals, corrupted with heavy-tailed noise. For this purpose the robust Wigner distribution is introduced, as an extension of the robust M-periodogram concept. The theory is illustrated on several examples, including application of the proposed distribution on the instantaneous frequency estimation.