The geometric structure of nonlinear least squares solution for signals by complex exponents is offered in this paper.Beginning with analysis for the convergent state of alternative algorithm solving two equations together contented by the model's nonlinear least squares solution

the recognition for geometric structure of nonlinear least squares solution is acquired.It would help to construct a fully effective algorithm and understanding for the solution's structure is deepened.The alternative algorithm presented by this paper is fully effective in higher SNR or when the difference of frequency in model is slightly increased.Nevertheless

the invalid convergence (large error) appears in the condition with lower SNR(10dB) and smaller difference of frequency (0.02 Hz)

if the convergent control condition of alternative algorithm is only in accordance with varying quantity of least squares error.