Calculating Lower Bounds within the PyTorch Framework

Abstract

Lower estimation bounds are an important tool in the development of parametric estimators, which form a basis for a large number of navigation and position solutions. The well-known Cramér-Rao bound (CRB) is such a bound and provides the optimal mean squared error performance of locally unbiased estimators based on a signal model. If the model depends on a random variable, the bound depends on the realization of this variable. We consider the R-Mode navigation system as a case study in this paper. In this case, the signal is influenced by a modulated signal where, in general, the transmitted bit sequence is unknown. Therefore, it becomes difficult to derive and evaluate the performance bound as the complexity of the computation increases. To overcome the aforementioned challenge, we suggest utilizing PyTorch and its automatic differentiation framework to calculate the bound for each realization, thus leveraging fast calculation for each given scenario.