Bayesian particle filtering (PF) is a method for recursive estimation in non-linear and non-Gaussian dynamic systems. These methods are subject to high computational complexity when it comes to resampling, which is essential to maintain particle diversity. In this paper, aims to propose an efficient weighted-random sampling algorithm that reduces the time complexity of particle resampling by a factor of logN, where N is the number of particles. The proposed algorithm can be applied to a wide range of estimation problems, including robotics, signal processing, and navigation systems. We analyze the performance of our algorithm through both theoretical analysis and extensive simulations, demonstrating that it provides significant improvements in terms of computational efficiency without compromising the accuracy of the estimates. The algorithm use a probabilistic method to select particles based on their importance weights, while maintaining the accuracy of the state estimation process. This approach is particularly beneficial for real-time applications that require fast and scaleable particle filtering methods.