3.5. Performance Analysis

The ability of the proposed CEKF and of its optimal covariance matrix tuning to accurately estimate the joint kinematics was assessed first by calculating the RMSD and the Pearson correlation coefficient (CC) between the estimated and reference joint angles. These calculations were performed for joints that were of interest for each task. Moreover, in order to assess the distribution of the differences between the estimated and reference joint trajectories, a statistical parametric mapping (SPM) analysis was devised [36]. SPM was developed to evaluate inferences regarding the topological features of statistical processes that are continuous functions of space and time. Statistical differences among continuous curves can be analyzed without reducing the dimensions of the test to summarize metrics such as mean, median, maximum or minimum values. The SPM method is used to analyze the performance of the CEKF when the elements of Q are optimized, as in Section 3.4.2, as opposed to when they are estimated based on a classical method from the literature [34].

In order to determine the influence of this tuning, the absolute difference between the estimated and reference joint angles was calculated and compared with a 1D paired t-test (α=0.05). Tests were carried out with the open-source package SPM1D for MATLAB [37], which generated the map of t-values SPM{t}, the t* boundaries and the areas for relevant p-values.