## 1 Introduction  
Ground-penetrating radar (GPR) is a nondestructive technique used to detect and locate underground targets and interfaces with high efficiency and resolution; it has become one of the most popular tools used in top-coal structure detection in mine engineering [1, 2]. Usually, the structure of top coal in mines with fully mechanized cave faces is very complex and usually contains multi-layer gangues, which often seriously affect the effective level of the fully mechanized cave face. The main reason is that the existence of multi-layer gangues in the top coal will lead to the misjudgment or closure of the coal outlet in the mining process and cause the interruption of effective mining. Therefore, it is urgent to accurately detect detailed top-coal internal structure information (including gangue thickness and layers) before effective mining in fully mechanized cave faces [3, 4]. Normally, a high-frequency GPR signal can yield high resolution but limited detection depth, while a low-frequency GPR signal possesses deeper detection depth but lower resolution [5; 6]. However, the detection resolution and depth of complex top-coal structures are always limited when using a single-frequency GPR signal, as it is difficult to simultaneously achieve a deep detection depth and high resolution for top-coal structure detection [7; 8]. To overcome the above limitations, a multi-frequency GPR data fusion method is proposed to resolve the unavoidable trade-off between resolution and depth. Furthermore, multi-frequency GPR signals fused and displayed into one profile can enhance GPR data interpretation capacity and accuracy, simultaneously reducing the probability of misjudgment in top-coal structure detection [9; 10]. Multi-frequency data fusion is a promising technique for enriching effective frequency signals into one profile. Normally, according to the data collection type, it can be classified into three categories: one involves multi-channel GPR antennas placed at one acquisition site, the next involves multi-frequency antennas placed along the same line, and the last one involves the same antenna placed at different locations. Recently, several GPR data fusion methods have been presented and tested by many researchers: [PERSON] et al. [11] presented an adaptively weighted fusion method for multi-frequency GPR data based on genetic algorithms. [PERSON] et al. [12] presented a fusion method for ground-penetrating radar data acquired at different center frequencies. [PERSON] et al. [13] proposed a novel physically based method to merge radar data coming from antennas operating in different frequency ranges. [PERSON] et al. [14] proposed a novel multi-frequency GPR data fusion method based on a time-varying weighting strategy. [PERSON] et al. [15] proposed a joint deconvolution approach to associate single-frequency data with the target function directly. [PERSON] et al. [16] presented an advanced multi-frequency and multi-attribute GPR data fusion approach based on a 2-D wavelet transform, utilizing a dynamic fusion weight scheme derived from an edge detection algorithm. [PERSON] et al. [17] proposed a fusion framework by combining original profiles with the abovementioned three features based on a two-dimensional wavelet transform. [PERSON] et al. [18] applied multi-frequency GPR data fusion with three algorithms that were evaluated and compared with a fused radar profile and by a Laplacian operator. [PERSON] et al. [19] developed a signal fusion method to extrapolate a high-frequency, high-resolution GPR signal at a greater depth based on a lower-frequency, greater-penetration signal using extrapolation with a deterministic deconvolution algorithm. [PERSON] et al. [20] presented a multi-station fusion detection method for a moving maritime moving target based on a three-dimensional sliding window.