Experiments

To experimentally measure the performance of our proposed new method, we used two different data sets. The first data set was generated using a simulated double inverted pendulum system with known dynamics. As the second data set we used real-world speech data with unknown dynamics.

In all the experiments, IEKS and IUKS were run for 50 iterations and NDFA algorithm for 500 iterations. In most cases this was long enough for the algorithms to converge to a local minimum. For comparison purposes, the NDFA experiments were also repeated without using the total derivatives.

Even with a relatively high number of particles, particle smoother performed poorly compared to the iterative algorithms. The results for particle smoother are therefore omitted from the figures. They are however discussed where appropriate. Even though the particle smoother performed relatively poorly, it should be noted that many different schemes exists to improve the performance of particle filters [9], and therefore direct comparison between the iterative algorithms and the plain particle filter algorithm used in these experiments may be somewhat unjustified. The experiments were also repeated with the original NDFA algorithm presented in [1]. The results were quite poor, as was to be excepted, as the heuristic update rules are optimized for learning.