# Mixed-Degree Cubature \(H_{\infty}\) Information Filter-Based Visual-Inertial Odometry
## 4 Evaluation Results  
As analyzed in the previous section, the measurement-update phase with operations of large matrixes is the bottleneck for real-time applications. However, the measurement-update phase of an information-based filter is parallelizable and can be implemented on a parallel processor. We used a laptop with the Geforce 940M GPU (NVIDIA, Santa Clara, CA, USA) and the i7-5600U CPU (Intel, Santa Clara, CA, USA) to test the proposed \(\text{MOCH}_{\infty}\text{IF-VIO}\) system. We implemented our method with CUDA (in Supplementary Materials) (Version 8.0, NVIDIA, Santa Clara, CA, USA, 2016) language. The time-update phase was executed on the CPU and the measurement-update phase was executed on the GPU. We used the Technical University of Munich (TUM) RGBD dataset [37] for evaluation. The TUM RGBD dataset contains multiple sequences of videos collected using an RGBD camera under different environmental conditions. The RGB images and depth images are collected at the rate of 30 Hz with a resolution of 640 \(\times\) 480. The TUM dataset does not contain IMU measurements, we simply used the differential and quadratic differential of the ground truth with the addition of random noises as the simulated IMU measurements.  
We compared the proposed \(\text{MCH}_{\infty}\text{IF-VIO}\) method with RGBDSLAM v2.0 in [38] and the lightweight visual tracking (LVT) in [12]. The results of RGBDSLAM were calculated with the corresponding ROS package, and the results of the LVT were directly obtained from the original paper. We conducted the evaluation for \(\text{MCH}_{\infty}\text{IF-VIO}\) with five different patch sizes: 2, 4, 8, 16, and 32. The numbers were selected as powers of two for the convenience of CUDA implementation. The absolute trajectory (ATE) and relative pose error (RPE) defined in [37] were used as error metrics. The ATE measures the global consistency of the estimated trajectory and is suitable for visual SLAM methods. On the other hand, the RPE measures the local accuracy of the trajectory over a fixed time interval and is suited for visual odometry methods. We used five sequences in the TUM dataset for testing the three methods. The basic parameters of the five sequences are shown in Table 3. The test results are shown in Figures 3-7. In these figures, \(\text{MCH}_{\infty}\text{IF-VIO}(n)\) represents the \(\text{MCH}_{\infty}\text{IF-VIO}\) with a patch size of \(n\).  
The RPE of \(\text{MCH}_{\infty}\text{IF-VIO}\) increased along with the patch size in all of the tests. The change in the ATE of \(\text{MCH}_{\infty}\text{IF-VIO}\) was similar to RPE with some exceptions. This is in line with the common knowledge that more measurements lead to better accuracy in visual navigation. The \(\text{MCH}_{\infty}\text{IF-VIO}\) in this paper and LVT are dead-reckoning algorithms, while RGBDSLAM is a compete SLAM algorithm with joint optimization and loop-closure. Therefore, RGBDSLAM is more consistent globally than \(\text{MCH}_{\infty}\text{IF-VIO}\) and LVT according to the ATE results. In our tests, \(\text{MCH}_{\infty}\text{IF-VIO}\) achieved a smaller ATE than LVT with only one exception, where the ATE of \(\text{MCH}_{\infty}\text{IF-VIO}\)(32) was larger than LVT in the test on _rf1_room_. \(\text{MCH}_{\infty}\text{IF-VIO}\)(2) had the smallest RPE in all of the tests. The estimation errors caused by the IMU measurement noises increased over time. Moreover, the simple frame-to-frame alignment  
\begin{table}
\begin{tabular}{c c c} \hline
**Sequence** & **Duration (s)** & **Trajectory length (m)** \\ \hline _rf1\_desk_ & 23.40 & 9.263 \\ _rf1\_desk2_ & 24.86 & 10.161 \\ _rf1\_room_ & 48.90 & 15.989 \\ _rf1\_xyz_ & 30.09 & 7.112 \\ _f3\_office_ & 87.09 & 21.455 \\ \hline \end{tabular}
\end{table}
Table 3: Parameters of the used sequences.