Conventional velocity-filtering-based track-before-detect (VF-TBD) methods integrate the energy of a cell in a frame with that of the cell closest to the predicted target position in the last frame of the processing batch, assuming a certain target velocity. However, the target may not exactly be on the quantized cell and its echo envelope may occupy multiple adjacent cells. This often leads to significant energy loss and echo envelope degradation. In this paper, a novel VF-TBD method based on pseudo-spectrum (PS-VF-TBD) is presented to address this problem. For every cell, a pseudo-spectrum is constructed around the predicted position according to the assumed velocity using a truncated point spread function. Samples of the pseudo-spectrum on the cells that are located in the truncated spread area are added onto the last frame of the processing batch to integrate the target energy within multiple cells. Due to the use of the point spread model and the accurate sampling of the predicted spectrum, energy loss can be mitigated and the echo envelope is well maintained. This approach simultaneously maximizes the signal-to-noise ratio (SNR) gain and enables improved parameter estimation utilizing the envelope characteristics. The procedure for pseudo-spectrum construction and multiframe accumulation is derived in detail and the output SNR is analyzed theoretically. It is found that the proposed PS-VF-TBD can achieve an SNR gain greater than that by the conventional VF-TBD method. To deal with a target with unknown velocity, a bank of pseudo-spectrum-based velocity filters is proposed. The signal gain loss resulting from velocity mismatch is investigated and the $\mu$-width of the envelope in the velocity domain is analyzed. Finally, a method for improved position and velocity estimation is presented. Simulation results demonstrate the superiority of the proposed method in terms of SNR gain, detection probability, and estimation accuracy at the expense of increased computational complexity.

中文翻译：

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一种用于弱目标检测和跟踪的伪谱方法

传统的基于速度过滤的跟踪前检测 (VF-TBD) 方法将帧中单元格的能量与处理批次的最后一帧中最接近预测目标位置的单元格的能量相结合，假设某个目标速度。然而，目标可能并不完全在量化单元上，其回波包络可能占据多个相邻单元。这通常会导致显着的能量损失和回声包络退化。在本文中，提出了一种基于伪频谱（PS-VF-TBD）的新型 VF-TBD 方法来解决这个问题。对于每个单元格，使用截断点扩展函数根据假定速度在预测位置周围构建伪谱。位于截断扩散区域的细胞上的伪光谱样本被添加到处理批次的最后一帧，以整合多个细胞内的目标能量。由于使用点扩展模型和预测频谱的准确采样，可以减轻能量损失并很好地保持回波包络。这种方法同时最大限度地提高了信噪比 (SNR) 增益，并能够利用包络特性改进参数估计。详细推导了伪频谱构建和多帧累积的过程，并从理论上分析了输出信噪比。发现所提出的 PS-VF-TBD 可以获得比传统 VF-TBD 方法更大的 SNR 增益。处理未知速度的目标，提出了一组基于伪谱的速度滤波器。研究了速度失配导致的信号增益损失，并分析了速度域中包络的 $\mu$-width。最后，提出了一种改进位置和速度估计的方法。仿真结果证明了所提出的方法在信噪比增益、检测概率和估计精度方面的优越性，但代价是增加了计算复杂度。