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Abstract This paper presents a theoretical analysis in discrete time for a multi-tier weak radiofrequency (RF) signal estimation process with N simultaneous signals. Discrete time dynamic sampling is introduced and is shown to provide the capability to extract signal parameter values with increased accuracy compared with accuracy of estimates obtained in prior work. This paper advances phase measurement approaches by proposing discrete time dynamic sampling which our paper shows offers the desirable capability for more accurate weak signal parameter estimates. For $$N=2$$ N = 2 simultaneous signals with a strong signal at 850 MHz and a weak signal at 855 MHz, the results show that dynamically sampling the instantaneous frequency at 24 times the Nyquist rate provides weak signal frequency estimates that are within $$1.7 \times 10^{-5}$$ 1.7 × 10 - 5 of the actual weak signal frequency and weak signal amplitude estimates that are within 428 PPM of the actual weak signal amplitude. Results are also presented for situations with $$N=2$$ N = 2 simultaneous 5G signals. In one case, the strong signal is 3950 MHz, and the weak signal is 3955 MHz; in the other case the strong case is 5950 MHz, and the weak signal is 5955 MHz. The results for these cases show that estimates obtained with dynamic sampling are more accurate than estimates provided using a single sample rate of 65 MSPS. This work has promising applications for weak signal parameters estimation using instantaneous frequency measurements.