Coordinate registration (CR), using ionospheric information to map the measurement in radar slant coordinates into geodetic inertial coordinates, plays a crucial role in target tracking of over-the-horizon radar (OTHR). Due to the ionospheric inherent variability and inaccurate modeling, there exists uncertainty in the CR process, decreasing target tracking accuracy. By formulating the OTHR target tracking with uncertain CR as the variational optimization problem, this paper proposes an online Bayesian learning and inference (OBLI) scheme for joint OTHR target tracking and CR. For Bayesian learning, the Gaussian process (GP) models the spatial correlation of the ionosphere with GP hyperparameters learned by streaming sparse GP approximation, which updates the GP hyperparameters and optimizes pseudo-input locations in an online fashion. For Bayesian inference, the streaming variational Monte Carlo approximates the joint posterior distributions of the target state and CR parameters, enabling flexible and accurate nonlinear filtering for non-conjugate models. Bayesian learning enhances CR parameter identification by modeling ionospheric spatial correlation and utilizing prior information. This improvement benefits target tracking by incorporating a joint optimization mechanism of the Bayesian inference. Meanwhile, the proposed OBLI carries out the joint Bayesian learning and inference online, allowing real-time OTHR target tracking applications. Finally, the effectiveness of the OBLI method is verified on OTHR target tracking with uncertain ionospheric heights.

中文翻译：

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用于 OTHR 目标跟踪和注册的在线贝叶斯学习和推理


坐标配准（CR）利用电离层信息将雷达倾斜坐标中的测量值映射到大地惯性坐标中，在超视距雷达（OTHR）的目标跟踪中发挥着至关重要的作用。由于电离层固有的变异性和建模不准确，CR过程存在不确定性，降低了目标跟踪精度。通过将具有不确定CR的OTHR目标跟踪表述为变分优化问题，本文提出了一种联合OTHR目标跟踪和CR的在线贝叶斯学习和推理（OBLI）方案。对于贝叶斯学习，高斯过程 (GP) 对电离层的空间相关性与通过流式稀疏 GP 近似学习的 GP 超参数进行建模，从而更新 GP 超参数并以在线方式优化伪输入位置。对于贝叶斯推理，流式变分蒙特卡罗近似目标状态和 CR 参数的联合后验分布，从而为非共​​轭模型提供灵活、准确的非线性滤波。贝叶斯学习通过对电离层空间相关性进行建模并利用先验信息来增强 CR 参数识别。这一改进通过结合贝叶斯推理的联合优化机制有利于目标跟踪。同时，所提出的OBLI在线进行联合贝叶斯学习和推理，允许实时OTHR目标跟踪应用。最后，在电离层高度不确定的OTHR目标跟踪上验证了OBLI方法的有效性。