Comparison of Kalman filters and LSTM networks for error reduction problem

The aim of this project is to compare the performance of LSTM and Linear Kalman Filter in the presence of a multipath noise. The Kalman filter approach is based on an intuitively defined process and dynamically changing matrices. Using the past data, the next point of the system is tried to be predicted. This filter may not represent the time correlation between data very well because it uses a user-specified dynamic model. In addition, although the Kalman filter is known to be ideal in the presence of Gaussian noise, its performance in the presence of non-Gaussian noise is not good.RNN's are used to model time series, sequential data. LSTM is a special type of RNN with memory. LSTM aims to overcome these problems by learning noisy and dynamic models. This is an area where the Kalman filter is expected to perform poorly. Instead of testing this approach in sensor data, randomly generated 1 and 2 dimensional trajectory data were used. Although LSTM was trained with little data, it was concluded that it provided better performance than Kalman filter when appropriate hyper-parameters were provided.