Method based on eigendecomposition spectrum estimation is used to replace lock-in amplifier which is widely used in battery resistance detection. The new method can reduce hardware costs and operational difficulties due to use software way instead of hardware circuit. Series analyses about the theory of eigendecomposition spectrum estimation are taken. Simulations about the extraction and measuring for voltage signal,which is the key step in the method, are done in the paper. Results of simulations shows good frequency resolution. The measurement error of the method can be around 2% under 50dB white Gaussian noise, while around 3% under 20dB non-Gaussian noise background. Analysis and simulations shows the method based on eigendecomposition spectrum estimation is efective in battery resistance detection under higher power non-Gaussian noise background and can be software method of Weak Signal Detection to replace lock-in amplifier.