CVPCNN: Conditionally variational parameterized convolution neural network for HRRP target recognition with imperfect side information.

• To the best of our knowledge, this is the first study to consider the azimuth estimation errors of the HRRP and relate them to deep neural network parameter control. • We proposed two new convolutional kernel parameterization methods, VPCONV and extended CVPCONV, which embed SI into deep network by using it to parameterize the convolutional kernel. This enables direct control of the network structure. Simultaneously, variational encoding is introduced in the reparameterization process to generalize the azimuth estimation error using a heteroscedastic Gaussian distribution with varying mean and variance. Notably, VPCONV and CVPCONV exhibit good transferability and can be used as plug-and-play modules. • Based on CVPCONV, we designed a lightweight network CVPCNN, which can make full use of the azimuth of the HRRP, decouple the tight coupling between the azimuth and target HRRPs, and extract discriminative characteristics that are more relevant to the current environment (azimuth). This helps obtain a more robust and accurate recognition performance. In addition, the CVPCNN introduces a sample-dependent kernel attention mechanism based on parallel convolution to achieve efficient inference, even with increased model complexity. • The effectiveness of the proposed model was tested in a target recognition task using a three-class measured aircraft HRRP dataset. The experiments show that the CVPCNN model, with just three convolutional layers, demonstrate optimal performance on this dataset. This represents a 4 % improvement over the standard CNN model under identical experimental conditions and model structure. Significantly, the CVPCNN maintain good recognition performance under non-ideal conditions, such as small sample and incomplete HRRP attitudes. Radar target recognition tasks often incorporate valuable side information (SI) that aids in the recognition task. The effectiveness of SI has been fully verified in traditional statistical modeling approaches. Its full potential remains untapped in deep learning-based high-resolution range profile (HRRP) target recognition tasks. Taking into account the azimuth sensitivity of HRRP, azimuth is chosen as the SI of the proposed model. To integrate SI into deep neural networks, we propose two novel parameterized convolution methods, namely variational parameterized convolution (VPCONV) and the extended conditionally VPCONV (CVPCONV). Specifically, VPCONV makes the convolutional kernel weights as the function of the auxiliary azimuth, which gives the network the capability of adaptively adjusting to changes in azimuth. Acknowledging the challenge of estimating HRRP azimuth accurately in practical scenarios, VPCONV employs a heteroscedastic Gaussian distribution, featuring varying mean and variance, to generalize the estimation error of SI through variational encoding. Moreover, CVPCONV incorporates the properties of the HRRP samples themselves by kernel attention module. Finally, we present a lightweight SI-based network. The experimental results based on the measured HRRPs validate the effectiveness of proposed method across various extended recognition tasks, underscoring the potential of fusing SI via parameterized convolution in advancing target recognition systems. [ABSTRACT FROM AUTHOR]