Determining the noise parameters of a Kalman Filter (KF) has been researched for decades. The research focuses on estimation of the noise under various conditions, since noise estimation is considered equivalent to errors minimization. However, we show that even a seemingly small violation of KF assumptions can significantly modify the effective noise, breaking the equivalence between the tasks and making noise estimation a highly sub-optimal strategy. In particular, whoever tests a new learning-based algorithm in comparison to a (variant of) KF with standard parameters tuning, essentially conducts an unfair comparison between an optimized algorithm and a non-optimized one. We suggest a method (based on Cholesky decomposition) to apply gradient-based optimization efficiently to the symmetric and positive-definite (SPD) parameters of KF, so that KF can be optimized similarly to common neural networks. The benefits of this method are demonstrated for both Radar tracking and video tracking. For Radar tracking we also show how a non-linear neural-network-based model can seem to reduce the tracking errors significantly compared to a KF - and how this reduction entirely vanishes once the KF is optimized. Through a detailed case-study, we also demonstrate that KF requires non-trivial design-decisions to be made, and that parameters optimization makes KF more robust to these decisions.

翻译：确定 Kalman 过滤器( KF) 的噪音参数已经研究了几十年。 研究的重点是在各种条件下估计噪音, 因为噪音估计被认为相当于最小化错误。 然而, 我们显示, 即使是看起来小的违反 KF 假设, 也能大大改变有效噪音, 打破任务之间的等值, 使噪音估计成为一种高度最佳的战略。 特别是, 与标准参数调控的KF (变量) 相比, 测试一种新的基于学习的算法的人, 基本上对优化的算法和非优化的模型进行不公平的比较。 我们建议一种方法( 以 Choolesky 分解配置为基础), 将基于梯度的优化有效应用于 KF 的对称和正分解参数, 这样KF 就可以与普通的神经网络进行类似的优化。 这个方法的好处在雷达跟踪和视频跟踪方面都得到了证明。 关于雷达跟踪, 我们还展示了非线性网络模型如何明显减少与 KF 相比的跟踪错误。 我们建议一种方法( 以 Chosky ) 和如何在 KF 优化后, 使 KF 优化决定变得不再 。