Keywords: Kalman Filter, noise estimation, optimization, gradient descent, parameterization
Abstract: Determining the noise parameters of a Kalman Filter (KF) has been studied for decades. A huge body of research focuses on the task of noise estimation under various conditions, since precise noise estimation is considered equivalent to minimization of the filtering errors. However, we show that even a small violation of the KF assumptions can significantly modify the effective noise, breaking the equivalence between the tasks and making noise estimation an inferior strategy. We show that such violations are common, and are often not trivial to handle or even notice. Consequentially, we argue that a robust solution is needed - rather than choosing a dedicated model per problem. To that end, we apply gradient-based optimization to the filtering errors directly, with relation to an efficient parameterization of the symmetric and positive-definite parameters of the KF. In a variety of state-estimation and tracking problems, we show that the optimization improves both the accuracy of the KF and its robustness to design decisions. In addition, we demonstrate how an optimized neural network model can seem to reduce the errors significantly compared to a KF - and how this reduction vanishes once the KF is optimized similarly. This indicates how complicated models can be wrongly identified as superior to the KF, while in fact they were merely more optimized.
One-sentence Summary: Optimization of the KF parameters (instead of determining them by noise estimation) is crucial whenever the KF assumptions are violated, and sometimes removes the need for more complicated models such as neural networks.