In an integrated sensing and communication (ISAC) system, improving the accuracy of delay and Doppler shift sensing parameter estimation is a critical task that sustains the performance of the communication system. To tackle this task, we introduce a two-stage estimation algorithm named matched filter-Fibonacci (MF-F), which employs the orthogonal time frequency space (OTFS) waveform characteristics in the delay-Doppler (DD) domain. In the first step (MF), the sensing parameters are approximated on an integer grid using the relationship between the input and output signals of the DD domain ISAC model. This approximation is executed on an integer grid using the cyclic shift property of the matrix. In the following step (F), we implement a two-dimensional (2D) searching technique based on the Fibonacci sequence, called the Fibonacci search method, to achieve sensing parameter estimation with fractional accuracy. This method decreases the number of comparisons needed and enhances the search process speed. Finally, the proposed method in this study was tested using numerical simulations and hardware experiments. The results demonstrate that the MF-F method can precisely estimate the speed and distance with millimeter-level accuracy and has the robustness and low complexity in numerical simulation. Moreover, the hardware experiment’s estimated Doppler and delay parameters can reach the centimeter and meter levels.