EVIO integrates the high-speed, high-contrast sensitivity of event cameras combined with inertial data from accelerometers and gyroscopes (Chen et al., 2023). Unlike traditional cameras, event cameras capture changes in a scene at up to 1 MHz, allowing them to handle rapid motion without issues like image blur, temporal aliasing, or saturation under intense lighting. These attributes make event cameras particularly useful for dynamic and low-light environments (Zhu et al., 2017).

The study in (Mueggler et al., 2017a) examines the integration of event frames and inertial data using a continuous-time model. However, real-time application remains challenging due to the computational burden of adjusting spline parameters for each incoming event. In a different approach, the authors in (Rebecq et al., 2017b) propose a real-time event-based VIO pipeline that uses optical flow estimation, grounded in the recent camera pose, scene configuration, and inertial data, to track visual features across multiple frames. These tracked features are subsequently combined with inertial measurements through keyframe-based nonlinear optimization. Similarly, in (Vidal et al., 2018), the authors integrate event streams, standard frames, and IMU data through nonlinear optimization process, achieving a notable accuracy enhancement of 130% over event-only frames and 85% over standard frames with IMU data. This system also supports real-time integration with a quadrotor. Furthermore, the authors in (Censi and Scaramuzza, 2014; Kueng et al., 2016) introduce low-latency, event-based VO techniques that accurately estimate rotation and translation using Dynamic Vision Sensors (DVS) alongside conventional CMOS cameras in natural scenes.

In (Kim et al., 2016), the authors discuss an event-based 6-degree-of-freedom (6-DoF) VO system, using three decoupled probabilistic filters to estimate the camera’s pose, a 3D scene model, and image intensity. However, this approach incurs a significant computational burden, requiring GPU use for real-time performance. In (Zhu et al., 2017), the EVIO method is presented, where an Extended Kalman Filter (EKF) fuses event data with pre-integrated IMU measurements, demonstrating the potential of event-based VIO for applications like planetary exploration. To further explore this potential (Mahlknecht et al., 2022), introduce the Event-based Lucas-Kanade Tracking VIO (EKLT-VIO), which integrates an event-based tracker developed by (Gehrig et al., 2020) in the front-end and a filter-based back-end to conduct VIO in Mars-like environments. Their results show a 32% improvement in MPE under low-light and HDR conditions compared to prior frame-based and event-based VIO techniques, although front-end and back-end parameter selection were not addressed. Expanding upon previous methodologies, PL-EVIO, proposed by (Guan et al., 2023), tightly integrates event-based point and line features, standard frame point features, and IMU data, thereby providing more geometric restrictions and enhancing robustness. While these advancements mark significant progress in Event SLAM, the literature reveals a gap in adaptive parameter optimization across various scenarios. Our approach aligns closely with methodologies in (Vidal et al., 2018; Rebecq et al., 2017b), which use motion-compensated images to represent event data but require significant manual parameter tuning for diverse environments. Our goal is to streamline the process by developing a pipeline capable of automating parameter optimization, thereby enhancing both the practicability and time efficiency of Event SLAM systems.

Integrating event cameras into VO/VIO systems presents a major challenge that arises from the asynchronous nature of event streams, which fundamentally differs from synchronous image data. Consequently, many methods designed for traditional image-based cameras cannot be directly applied to event-based systems. To address this gap, various techniques for representing event data have been introduced in the literature (Guan et al., 2023). Common approaches involve applying conventional feature detection and tracking methods to edge images created from motion-compensated event streams (Vidal et al., 2018; Rebecq et al., 2017b). However, these methods often require extensive parameter adjustments to adapt to specific fluctuations in event density, which can impact VIO system performance. Through a review of existing parameter optimization methods, we aim to identify the most effective strategies for enhancing event-based VIO systems and highlight areas where further optimization could improve system adaptability and reliability.

In (Li et al., 2020), the authors use a Stochastic Gradient Descent (SGD) approach for localization, coupled with scan matching via a 2D LiDAR system. This SGD-based approach enables the localizer to effectively track the robot’s state, generating a coherent trajectory of its movements. The technique attained a position error of 0.26 m and a heading error of around 5°. In (Torroba et al., 2023), the authors employ SGD to optimize the evidence lower bound (ELBO) on Gaussian process maps by estimating mini-batches, which allowed real-time performance on large-scale datasets and was successfully tested in a live Autonomous Underwater Vehicle (AUV) mission. Similarly, the authors in (Song et al., 2021) examine SGD for map classification in SLAM, while (Beomsoo et al., 2021) implements SGD to refine the policy network within the Proximal Policy Optimization algorithm. These approaches demonstrate the effectiveness of SGD in achieving both accuracy and efficiency for front-end and back-end optimization in dynamic environments.

In (Rebecq et al., 2017a), the authors use an intermediate representation by accumulating events into an edge-like image, employing a Gradient Descent (GD) approach that simplifies representation by randomly sampling pixels. This technique improves tracker speed and enhances robustness by increasing resilience to occlusions. In another approach, Luo et al. (2019) introduce a stage-wise SGD algorithm with a selective update mechanism to efficiently select a subset of training images for direct SLAM tracking, ensuring faster convergence.

As discussed, although significant research has focused on optimizing conventional SLAM methods, limited studies have applied GD approaches specifically to optimize Event SLAM parameters. Given the potential benefits, this work adopts the GD approach to optimize front-end and back-end parameters, particularly in challenging low-light and HDR scenarios.

The main approach in the front-end is to generate event frames from spatiotemporal clusters of events, followed by applying feature detection and tracking techniques. This state estimation system builds on methodologies from (Vidal et al., 2018; Rebecq et al., 2017b), where features are detected and tracked within edge images derived from motion-compensated events, employing conventional image-based feature detection and tracking methods. Particularly, the FAST corner detector (Rosten and Drummond, 2006) and the Lucas-Kanade tracker (Lucas and Kanade, 1981) are utilized for these purposes. Additionally, features from standard frames are extracted and incorporated into the back-end optimization module, enhancing overall robustness and accuracy.

In noise-free scenarios, event frames can be represented as e f = ( X f , t f , p f ) , where X f denotes the pixel value ( x f , y f ) , t f indicates the elapsed time, and p f signifies the polarity ranging from {-1,+1}. Additionally, the events e f are synchronized by aligning them with the spatio-temporal windows of events based on the timestamps of the conventional frames. For each conventional frame at time t f , a new spatiotemporal event window W k is defined as follows: W k = e j t f − F S + 1 ; … … ; e j t f . (1)

Here, j ( t f ) denotes the index of the first event with a timestamp t j < t f , and F S represents the size of the window. Subsequently, each spatiotemporal event window undergoes a transformation into an artificial event frame I k by applying motion compensation at its individual timestamp, as demonstrated in the next equation: I k x = ∑ e r ϵ W K δ x − x c ′ , (2) where δ ( x ) represents the Kronecker delta, x c denotes the adjusted event location acquired by shifting event e r to align with the specified event camera frame. Further, it is necessary to adjust the movement of every event locally based on its respective timestamp due to the limited information in small window sizes and the motion blur introduced by extensive window sizes. The x c ′ in Equation 2 can be calculated using the formula given by (Rebecq et al., 2017b), as shown in Equation 3: x c ′ = π o T t m , t n Z x c π o − 1 x c , (3) where x c denotes the event pixel location, π o ( : ) is the event camera projection sample derived from previous inherent calibration, ( T t m , t n ) signifies the gradual transition of the camera poses at times t m and t n , derived from integrating the inertial measurements, and Z ( x c ) represents the scene depth at time t f estimated through a 2D linear interpolation.

The count of events F S in each spatiotemporal window needs to be adapted and can be optimized according to the texture density present in the scene. Hence, in this work, it has been chosen as one of the optimized parameters ¹ . The median depth of the current landmarks M D can produce satisfactory results with reduced computational costs compared to linearly interpolating the depth Z ( x c ) . Therefore, the median depth of landmarks is optimized using the proposed method ¹ presented in Section 4.

New features are identified using the FAST corner detector, which is applied to both motion-compensated event frames and standard frames (Mueggler et al., 2017a). This approach ensures an even distribution of features across the image by using a bucketing grid: S x → y = D , if I x → y ≤ I x − T S , if I x − T < I x → y < I x + T B , if I x + T ≤ I x → y (4) where I x is the intensity at pixel x , T is the threshold value, I x → y denotes the intensity difference between pixel x and y , D is the darker corner, S is the similar pixel, and B is the brighter corner. To effectively detect these features, the threshold of the FAST detector is optimized in this work ¹ . These features are subsequently tracked from I x to I x + 1 , derived through an incremental transformation. Moreover, landmarks are tracked using the pyramidal Lukas-Kanade tracking algorithm (Lucas and Kanade, 1981), with the number of pyramid levels for feature extraction set as an automatically adjusted parameter ¹ . Furthermore, a two-point RANSAC approach (Mueggler et al., 2014) is used for additional filtering of outlier feature tracks. In this system, the parameters for detection and tracking are maintained consistently across both motion-compensated event frames and conventional frames. Moreover, if the number of tracked features drops below a certain threshold K T , features are re-detected.

This section explores the integration of feature tracks from the event stream with IMU data, using a smoothing-based nonlinear optimization method on chosen keyframes. A detailed comprehensive analysis of IMU biases and kinematics can be found in (Rebecq et al., 2017b; Guan et al., 2023). The visual-inertial nonlinear optimization is described by a cost function J V IO , which consists of three components: two weighted reprojection errors associated with event-based and conventional camera data, and an inertial error E s . The cost function J V IO is formulated as shown in Equation 5: J V IO = ∑ i = 0 1 ∑ k = 1 K ∑ j ϵ ȷ i , k E i , j , k T W r i , j , k E i , j , k + ∑ k = 1 K − 1 E s k T W s k E s k , (5) and the reprojection error E i , j , k is given by Equation 6: E i , j , k = z i , j , k − π i T c i s k T s W k I i , j . (6)

In the previous equations, i represents the sensor identifier, k signifies the frame identifier, and j refers to the landmark. The set ȷ ( i , k ) includes the landmarks tracked by sensor i in the k t h frame. The data matrix for each landmark measurement I i , j is represented as W r i , j , k , while W s k denotes the data matrix corresponding to the IMU error in the k t h frame. Additionally, z i , j , k denotes the calculated image coordinates for every k t h frame. The IMU error is computed as the disparity between predicted and actual trajectories (Leutenegger et al., 2013). Optimization is performed selectively, focusing on a subset comprising of keyframes and the last K frames in a sliding window, while predictions for intervening frames are propagated using IMU data. The number of keyframes employed in the back-end process is one of the parameters optimized in this study ¹ .

We evaluate the impact of varying the number of optimized parameters in the VIO-GO approach on the overall performance of the VIO system. This involves comparing VIO-GO2, VIO-GO4, VIO-GO6, and VIO-GO8 across various sequences from the Event Camera Dataset. Table 3 provides a detailed comparison of the results.

The results show that increasing the number of tuned parameters in the proposed model significantly enhances the overall performance of the VIO system. As illustrated in Table 3, optimizing 8 parameters (VIO-GO8) instead of 2 (VIO-GO2) results in a 24% reduction in the average MPE of the estimated trajectory across all sequences. Similarly, VIO-GO4 surpasses VIO-GO2 in most sequences, achieving a 4% reduction in average MPE. Further improvements are observed with VIO-GO6, which reduces the average MPE by 16% compared to VIO-GO4. Finally, VIO-GO8 delivers the most accurate trajectories, achieving an additional 5% reduction in average MPE compared to VIO-GO6 across all tested sequences.

Figure 4 presents heatmaps of the estimated trajectories obtained from various VIO-GO approaches for the hdr_boxes sequence, aligned with the ground truth trajectory. The plots demonstrate that all VIO-GO variants produce precise trajectory estimations, as indicated by the low APE values. Notably, the graphs highlight clear improvement in trajectory accuracy with an increasing number of optimized parameters. This is shown by the significant reduction in the mean APE from 0.031 m for VIO-GO2 to 0.020 m for VIO-GO8. Figure 5 presents relative error metrics to evaluate the performance of different VIO-GO approaches on the hdr_boxes and boxes_translation sequences. The charts clearly demonstrate the effectiveness of VIO-GO in reducing trajectory drift over time, with notable improvements observed as the number of optimized parameters increases.

To further evaluate computational efficiency, we measured the elapsed time of each VIO-GO configuration (with 2, 4, 6, and 8 parameters) using the same hardware setup. The experiments show that the VIO-GO8 consistently achieves lower elapsed time across most sequences, with an average elapsed time of 16.39 s, compared to 18.98 s for VIO-GO2, 18.51 s for VIO-GO4, and 18.90 s for VIO-GO6. Therefore, an average computational improvement of 13.6% over VIO-GO2 was observed, primarily due to the fine-tuning of key parameters. This computational efficiency gain is achieved during the feature extraction phase, specifically the number of features used to trigger keyframe selection and the maximum number of features extracted per frame. By optimizing these parameters, VIO-GO8 reduces the computational overhead associated with processing redundant or suboptimal features, leading to faster execution. It is important to note that VIO-GO8 requires a higher optimization cost upfront compared to other approaches, due to the increased number of parameters being tuned. Nevertheless, this does not significantly impact the time required to find the optimal parameters, as the BGD algorithm efficiently explores the parameter space in parallel and requires minimal computational resources.

Although VIO-GO8 delivers the best results in terms of both accuracy and computational efficiency, it is worth noting that increasing the number of optimized parameters beyond eight may further enhance performance. However, such an expansion would also introduce greater complexity into the optimization process. As noted previously, the choice to limit the parameter set to eight was driven by practical considerations, including the constraints of maintaining a fixed learning rate and controlling computational overhead associated with parameter tuning. Nonetheless, extending the optimization to a broader set of parameters remains a promising direction for future research.

In our evaluation, we benchmark the proposed system against the raw results of Ultimate SLAM, as reported by its authors who used per-sequence parameter tuning and accurate IMU bias initialization. Building upon the Ultimate SLAM framework, our model is evaluated against this baseline to demonstrate its capability to automatically identify optimal parameters for each sequence in the Event Camera Dataset. Additionally, we compare it with Ultimate SLAM results obtained using a fixed parameter set adjusted across all sequences simultaneously and initialized with zero IMU bias, as presented in (Mahlknecht et al., 2022).

The aim of this comparison is to demonstrate the importance of parameter optimization in event-based VIO methods and to highlight the performance of the proposed model against a fixed parameter set across various scenarios. Moreover, we compare VIO-GO with (Rebecq et al., 2017b), an event-based algorithm coupled with an IMU, considered the foundational pipeline for Ultimate SLAM. The evaluation also includes EKLT-VIO (Mahlknecht et al., 2022), a system that integrates the EKLT feature tracker with a filter-based back-end, and EVIO (Zhu et al., 2017), an event-based tracking algorithm combined with an IMU. Similar to the proposed approach, both EKLT-VIO and EVIO are developed to perform efficiently under diverse conditions, including HDR environments and different lighting scenarios. The developers of the selected EVIO methods evaluated them using MPE as the error metric and the Event Camera Dataset as the simulation environment, following the same evaluation methodology employed in this work.

Table 4 provides a comprehensive comparison of the MPE five benchmark algorithms and VIO-GO using the 8-parameter configuration (VIO-GO8), across various sequences from the Event Camera Dataset. As shown in Table 4, the presented integrated system achieves state-of-the-art performance. Compared to Ultimate SLAM with a fixed parameter set (Vidal et al., 2018; Mahlknecht et al., 2022), which has an average MPE of 0.89%, VIO-GO8 demonstrates superior performance across all sequences with an average MPE of 0.36%. In contrast to the raw results of Ultimate SLAM (Vidal et al., 2018), VIO-GO8 successfully identifies optimal parameters, resulting in a lower MPE in the boxes_translation, hdr_boxes, and hdr_poster sequences, with MPE values of 0.25%, 0.35%, and 0.25%, respectively. Although the raw results of Ultimate SLAM exhibit better performance compared to VIO-GO, it is important to note that Ultimate SLAM heavily relies on manual parameter tuning for each sequence, which is considered impractical. Conversely, VIO-GO automatically fine-tunes the selected parameters across different environments. Furthermore, as explained in Section 4, we opted for only eight key parameters that we identified as directly influencing the system performance. In contrast, Ultimate SLAM has a much larger set of parameters that can be adjusted for improved results, but this comes at the cost of requiring substantial computational time. For these reasons, we have grayed-out the Ultimate SLAM results in Table 4. This decision to downplay Ultimate SLAM was made to highlight the practical advantages of our simpler parameter set over the more computationally intensive Ultimate SLAM, thereby focusing on the efficiency and practicality of VIO-GO in real-world scenarios. Notably, VIO-GO8 surpasses all other approaches in 7 out of 10 sequences. With an average MPE of 0.36%, VIO-GO8 exhibits a 16% reduction in MPE compared to the 0.43% reported in (Rebecq et al., 2017b), a 33% lower MPE than EKLT-VIO (Mahlknecht et al., 2022) with 0.54% MPE, and an 86% lower MPE compared to EVIO (Zhu et al., 2017), which reports an MPE of 2.57%.

Figures 6–8 illustrate heatmaps of the estimated trajectories from the proposed approach alongside the raw trajectory from Ultimate SLAM, both aligned with the ground truth trajectory for three different sequences from the Event Camera Dataset. In Figure 6, which corresponds to the boxes_6dof sequence, VIO-GO8 demonstrates high trajectory accuracy, closely aligning with the ground truth and achieving a low APE. However, its APE is slightly higher than that of Ultimate SLAM. This difference is primarily attributed to Ultimate SLAM relying on extensive manual tuning across a wide range of parameters. In contrast, VIO-GO automatically optimizes a fixed subset of eight key parameters. While broader manual tuning can improve accuracy, it increases system complexity and limits scalability. VIO-GO prioritizes efficiency and generalizability by eliminating the need for manual intervention. Figures 7, 8 present results for the hdr_boxes and boxes_translation sequences, respectively. In both cases, VIO-GO8 outperforms Ultimate SLAM by producing trajectories that more closely align with the ground truth and achieving lower APE values. These improvements highlight VIO-GO’s ability to adapt parameter configurations to challenging conditions without requiring manual tuning. The results further demonstrate the robustness and flexibility of the proposed framework across diverse scenarios.

In Figure 9, we employ relative error metrics to compare VIO-GO8 to Ultimate SLAM with its default parameter configuration applied to the hdr_boxes and boxes_translation sequences. The results show that VIO-GO8 notably reduces drift in the estimated trajectory over time. Table 5 presents a time analysis comparison between Ultimate SLAM, using its default parameters, and VIO-GO8 with its optimal parameter set. As shown, VIO-GO8 requires significantly less time to process all datasets compared to Ultimate SLAM. This performance improvement is attributed to VIO-GO8’s ability to dynamically select the best parameter set for each sequence, thereby reducing processing overhead in both the front-end and back-end stages. Furthermore, as previously discussed, VIO-GO8 outperforms the fixed parameter set approach by achieving an average MPE that is 58% lower than Ultimate SLAM’s default parameters across all sequences.

The primary contribution of VIO-GO is its ability to automatically optimize parameters for event-based VIO systems, significantly improving both accuracy and computational efficiency. Specifically, the VIO-GO8 approach, which optimizes eight key parameters, achieves an average MPE of 0.36%, outperforming fixed-parameter approaches such as Ultimate SLAM and other state-of-the-art methods, including EKLT-VIO and EVIO. These results underline the effectiveness of adaptive parameter tuning in enhancing VIO performance across diverse and dynamic environments.

A critical observation is the scalability of VIO-GO, where system performance improves with the inclusion of additional optimized parameters. For instance, a comparison between VIO-GO2 and VIO-GO8 demonstrates the benefits of comprehensive parameter optimization. Moreover, VIO-GO eliminates the need for manual parameter tuning required by previous methods, significantly reducing deployment time and effort. This makes it particularly well-suited for applications in Industry 4.0, where environments are highly variable and demand rapid adaptation. The core design of VIO-GO emphasizes generalizability. By dynamically optimizing a fixed set of key parameters based on scene characteristics, it adapts automatically to diverse conditions without relying on predefined configurations. In contrast to traditional motion-compensation approaches that require extensive manual adjustment for each new environment, VIO-GO offers a more scalable and practical solution.

In comparison with existing approaches, VIO-GO introduces a paradigm shift by automating the parameter optimization process. Our results show that VIO-GO significantly reduces trajectory drift over time and achieves a lower APE compared to fixed-parameter approaches. This is crucial for real-time applications, making VIO-GO an ideal candidate for resource-constrained scenarios in industrial robotics and autonomous navigation.

While VIO-GO demonstrates promising results, several limitations remain. One key challenge is its dependency on a predefined set of key parameters, which may constrain its adaptability to highly diverse or previously unseen environments. Future iterations could expand the parameter set or incorporate environment-specific variables, allowing the system to adapt more effectively to complex scenarios. Another limitation is the sensitivity of the system to initial conditions, such as IMU bias and feature selection, which may affect stability during extended operations. Future efforts could address these challenges through advanced initialization methods and noise mitigation strategies.

Additionally, while the Event Camera Dataset provides a valuable and well-calibrated benchmark for evaluating event-based VIO systems, it represents a relatively controlled environment. In real-world scenarios, factors like unstructured environments, sensor noise, and erratic motion patterns can significantly affect event data quality. VIO-GO is designed to address such variability through its core capability of dynamically optimizing key system parameters based on the characteristics of each scene. This allows the system to adapt in real time without requiring manual reconfiguration. Nevertheless, transferring the system from a controlled dataset to real-world deployment may affect the effectiveness of the selected parameter sets. Real-world conditions could present edge cases or variations not fully represented in the dataset, potentially impacting the convergence behavior or responsiveness of the optimization process. For instance, parameters such as the frame size and noise event rate might need adjustments to account for fluctuating event densities caused by background activity. Furthermore, parameters related to feature extraction may need to be tuned to handle less structured or more repetitive textures commonly found in natural scenes. These factors underscore that testing VIO-GO in real-world environments would provide a deeper understanding of its robustness in diverse and unpredictable conditions. Lastly, the use of BGD for parameter optimization, while effective, could be complemented by exploring alternative techniques, such as SGD, Bayesian optimization, or Gauss-Newton methods, to improve convergence speed and efficiency.

Building on the current success of VIO-GO, several promising research avenues could extend its capabilities:

Expansion of the Parameter Optimization Scope: Extending the optimization to a larger set of parameters remains a promising avenue for future work. While this study limited the number of optimized parameters to maintain practical feasibility, expanding this scope could potentially unlock additional performance improvements.

By addressing these limitations and expanding the scope of the study, future research could significantly advance the field of Event SLAM, contributing to the development of more robust, efficient, and adaptable systems for autonomous navigation in dynamic environments.