Pure Random Orthogonal Search (PROS): A Plain and Elegant Parameterless Algorithm for Global Optimization

A new, fast, elegant, and simple stochastic optimization search method is proposed, which exhibits surprisingly good performance and robustness considering its simplicity. We name the algorithm pure random orthogonal search (PROS). The method does not use any assumptions, does not have any parameters to adjust, and uses basic calculations to evolve a single candidate solution. The idea is that a single decision variable is randomly changed at every iteration and the candidate solution is updated only when an improvement is observed; therefore, moving orthogonally towards the optimal solution. Due to its simplicity, PROS can be easily implemented with basic programming skills and any non-expert in optimization can use it to solve problems and start exploring the fascinating optimization world. In the present work, PROS is explained in detail and is used to optimize 12 multi-dimensional test functions with various levels of complexity. The performance is compared with the pure random search strategy and other three well-established algorithms: genetic algorithms (GA), particle swarm optimization (PSO), and differential evolution (DE). The results indicate that, despite its simplicity, the proposed PROS method exhibits very good performance with fast convergence rates and quick execution time. The method can serve as a simple alternative to established and more complex optimizers. Additionally, it could also be used as a benchmark for other metaheuristic optimization algorithms as one of the simplest, yet powerful, optimizers. The algorithm is provided with its full source code in MATLAB for anybody interested to use, test or explore.

A Fine Frequency Estimation Algorithm Based on Fast Orthogonal Search (FOS) for Base Station Positioning Receivers

Base station signals have been widely studied as a promising navigation and positioning signal. The time and code division-orthogonal frequency division multiplexing (TC-OFDM) signal is a novel communication and navigation fusion signal that can simultaneously implement communication and positioning services. The TC-OFDM signal multiplexes the pseudorandom noise (PRN) code, called positioning code, and the Chinese mobile multimedia broadcasting (CMMB) signal in the same frequency band. For positioning in the TC-OFDM receiver, it is necessary to acquire and track the PRN code phase and the carrier frequency. The tracking performance is directly influenced by the accuracy of the signal acquisition, especially the acquired carrier frequency accuracy. This paper focuses on the fine frequency acquisition of TC-OFDM receivers and proposes a novel fine frequency estimation algorithm, which uses a non-linear modelling method, called fast orthogonal search (FOS), to improve the frequency acquisition accuracy of TC-OFDM receivers. With this algorithm, the PRN code is first stripped off in coarse code phase. Then, the candidate functions at each of the interest frequencies are generated, which consist of pairs of sine and cosine terms. Finally, the FOS algorithm is used to detect the carrier frequency. Simulation and experimental results show that, compared with the current carrier frequency estimation algorithms, the proposed algorithm effectively improves carrier frequency estimation accuracy and then reduces the time to the first fix.