With the improvement of people's health awareness, the state increases the construction of public sport facilities, which complicates the allocation and management of resources. The existing spatial spectrum estimation method cannot eliminate the relevant interference data, resulting in duplicate data in the results of resource allocation and management, reducing the accuracy of resource allocation and management. In order to optimize the allocation and management of public sport facilities resources, this study proposes a spatial spectrum estimation method, which is used to deeply tap the potential information in public sport facilities resources and optimize the allocation and management. First, analyze the resources of public sport facilities and put forward the feature vector of allocation and management optimization. Then, use the spatial spectrum estimation method to learn the test samples, get the optimal threshold and weight, and build the resource allocation and management model of public sport facilities. Finally, the accuracy of spatial spectrum estimation method is 98% and the variation range is (0, 10), which is better than the accuracy of the original algorithm is 80% and the variation range is (0, 20). Moreover, change of the spatial spectrum estimation method is smoother, and the correlation between various analyses is better. In unit time, the amount of configuration and management data of spatial spectrum estimation method is higher than that of existing algorithms, which indirectly indicate that the configuration and management time of the spatial spectrum estimation method is short. At the same time, unstructured data account for a large proportion of the data tested this time. Therefore, the accuracy and variation range of the spatial spectrum estimation method is good, which is suitable for the construction of public sport facilities and realizes the optimization of resource allocation and management.
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