## 5 Results
### Signal Level Evaluation
For all other motions on the other hand, the value of the acceleration is always equal to or above, at least in the norm, 1 g. Given the limited size of the training set for the regression model and the fact that we did not include any semantic analysis to detect the \"down\" direction it is not surprising that our model struggles to capture this phenomenon. One way of dealing with the problem is to use linear acceleration which can be derived by IMUs, which is discussed below. To get a better understanding how the system handles detailed signal features Figures 9 and 10 show zoomed views of 2 signal segments that were selected to cover the \"good\" as well as the \"bad\" cases. Figure 9 shows for each signal a comparison of the acceleration and gyro norms. To explore in more detail the issue raised in point 4 above Figure 10 shows not just the acceleration norm, but also the norm of the linear acceleration which excludes the gravity contribution. The main observations are:  
1. The left part of Figure 9 shows an example of a \"good\" simulation. It can be seen that the simulated gyro signal nearly perfectly tracks the real gyro, even through fairly subtle features. Except for the amplitude issues the same holds for the accelerometer signal. Note that while the signal segment contains subtle and fast components, it does not have very high frequency \"singular\" peaks, which is a key reason why the system works so well here. 2. On the right side of Figure 9 a case of much poorer performance is shown. This is largely due to the presence of many singular high frequency, high amplitude peaks which especially the acceleration signal fails to track correctly. 3. With respect to the linear acceleration Figure 9 shows two things. First we see on the right side that using the norm linear acceleration instead of the norm raw acceleration signal indeed does solve the problem of the system refusing to model signal values below the baseline of 1 g. On the other hand, as shown in the left part of the figure, using linear acceleration may lead to signal characteristics changing and acquiring additional high frequency peaks which can be difficult to model. To probe further we have plotted signals from individual acceleration axes as both raw acceleration and linear acceleration in Figure 11 including a zoomed in version in Figure 12. The single axis acceleration signal is richer in features than both the linear acceleration on the same axis and the norm signals discussed above. This in itself is well known and not surprising. What is surprising is how well the simulated signals replicate the real ones given the issues described in Section 2 (e.g., the difficulty of estimating the projection of gravity into individual axis). This applies to both the overall, broad structure of the signal (Figure 11) and, in many cases to the detailed structure. An example is illustrated in Figure 12 on the left where some very subtle features have been matched nearly perfectly. Clearly, other examples exist, as shown on the right of the Figure where there is much more difference between the features of the simulated and the real signal.