This paper proposes a novel multi-parameter estimation algorithm for thek-µfading channel model to analyze wireless transmission performance in complex time-varying and non-line-of-sight communication scenarios involving moving targets. The proposed estimator offers a mathematically tractable theoretical framework for the application of thek-µfading channel model in realistic scenarios. Specifically, the algorithm obtains expressions for the moment-generating function of thek-µfading distribution and eliminates the gamma function using the even-order moment value comparison method. It then obtains two sets of solution models for the moment-generating function at different orders, which enable the estimation of thekandµparameters using three sets of closed-form solutions. Thekandµparameters are estimated based on received channel data samples generated using the Monte Carlo method to restore the distribution envelope of the received signal. Simulation results show strong agreement between theoretical and estimated values for the closed-form estimated solutions. Additionally, the differences in complexity, accuracy exhibited under different parameter settings, and robustness under decreasing SNR may make the estimators suitable for different practical application scenarios.