## 3 Spatial Enhanced Detection Algorithm
### Energy-Weighted Local Uncertainty Measure  
In the process of the ultra-long distance detection of small moving targets, due to the interference of atmospheric conditions, noise, and other factors, as well as the limitation of detection equipment and precision, the target information will be polluted when transmitted through the signal acquisition channel. As the accuracy of the observation information decreases gradually, it becomes more difficult to accurately identify the target position from the detection data. The object and its background in the image correspond to different component signals, and the occurrence of a fluctuating background, noise, and target signals in different regions brings uncertainty to the spatial characteristics of the observed data. Common methods use the local entropy operator to calculate the image complexity of the local region to measure the difference between the target and context, suppressing the cloud background. However, it is difficult to process complex background data without considering the relationship between different component signals and the relationship between the same component signals. Based on the uncertainty thought driven by the spatial variation of each component, this paper first analyzes the characteristic uncertainty of dim target detection and proposesa Local Uncertainty Measure (LUM) based on the principle of component consistency, hoping to achieve dim target detection with a complex background. The uncertainty measurement method evaluates local component consistency. This helps distinguish the target from the background. The method is divided into two stages: the local component uncertainty measurement and signal enhancement based on the energy-weighting function. In order to suppress the background clutter, the component consistency confidence is assigned by analyzing the component consistency of the local signal, and the uncertainty in the local region is measured by the local entropy operator. Then, the target energy information is introduced through the energy-weighting function to further enhance the target signal. Finally, an adaptive threshold segmentation algorithm is used to extract the target. Figure 4 shows the detailed ELUM processing flow. Increasing the size of the computational unit results in a quadratic increase in resource consumption, while excessively small computational units struggle to capture critical image information. Consequently, the minimum unit of the computational module is defined as \(3\times 3\). (1). Construction of the three-layer nested sliding window: First, the algorithm constructs a three-layer nested sliding window structure centered on the target-detection area. This structure expands outward from the central window to form a \(5\times 5\) multi-level window, comprising the central layer, the neighborhood layer, and the outermost environmental layer. The central layer directly corresponds to the target area, while the neighborhood and environmental layers are designed to capture the contextual information surrounding the target. (2). Assessment of local signal component consistency: The environmental layer is utilized to evaluate the consistency of signals within the neighborhood layer. The objective of this step is to identify signal patterns that significantly differ from background noise or other interfering factors by comparing the signal characteristics of the various components in the neighborhood layer. Through this evaluation, the method effectively distinguishes target signals from surrounding environmental noise, thereby enhancing the accuracy of subsequent processing. (3). Generation of the uncertainty distribution map: Based on the consistency assessment results obtained from the neighborhood layer, confidence levels regarding component consistency are assigned to each measurement point.