Lightweight and Fast Reconstruction Algorithm for 5D Spatio-Temporal-Frequency Situation Based on Kronecker Compressive Sensing

Large-scale UAV clusters make real-time reconstruction of joint spatio-temporal-frequency (STF) situations difficult because the monitored state is high-dimensional and strongly coupled. This paper proposes a lightweight reconstruction algorithm based on Kronecker Compressive Sensing (KCS). First, a Multi-Channel Random Demodulation (MCRD) sensing model is built, and a Spatio-Temporal-Frequency 5D Grid (STF-5D Grid) is used to represent space, frequency, and time resources in a unified form. Next, a Tensor Orthogonal Matching Pursuit (T-OMP) algorithm is developed under the KCS framework. By using the separability of Kronecker products, the method replaces storage and multiplication of a global high-dimensional sensing matrix with dimension-wise operations. Two simulation studies are conducted to evaluate computational feasibility and reconstruction quality. In the city-scale case with 62.91 million grid cells, the factorized implementation avoids constructing the global sensing matrix and completes the tested reconstruction in 9.44 s. The reported memory value is interpreted as additional algorithmic storage for the factorized operators rather than total process peak memory, and should be rechecked with full tensor input/output and runtime overhead included. In noise-free, highly sparse proxy tests, several reconstruction errors approach the numerical precision floor; these results are therefore treated as ideal upper-bound evidence rather than practical field accuracy. The simulations suggest that KCS-based T-OMP can reduce storage and computational pressure for STF reconstruction, while its engineering performance still requires validation under noisy observations and realistic platform constraints.