Fast implementation method of permutation test with valid strategy

As a classical nonparametric detection algorithm, the permutation test can obtain good performance without knowing the specific distribution type of the clutter. However, the large calculation load in implementation makes it very difficult for the permutation test to be used in the engineering practice. For the high calculation complexity problem in the permutation test, this paper proposes a new implementation method for the permutation test, called “valid strategy method”. This method first divides all the permutation strategies into the valid strategies and the invalid strategies according to their effect on the threshold. Then, calculate all the permutation statistics corresponding to the valid strategies. Next, use these permutation statistics to determine the threshold. Finally, compare the test statistic with the threshold and make a decision. Compared with the conventional direct calculation method which needs to calculate all the permutation statistics, the proposed method only needs to calculate the permutation statistics corresponding to the valid strategies, thus has a lower calculation cost. We analyze the calculation load of the valid strategy method and the direct calculation method in theory, and then study the effect of different parameters on the calculation efficiency of the valid strategy method in detail. The results show that the valid strategy method can implement the permutation test with very low calculation load for typical parameters of radar detection application, which has obvious application value in engineering.