A three-dimensional gaussian spatter adaptive reconstruction method based on extended state observer

Abstract

The application discloses a three-dimensional Gaussian splash adaptive reconstruction method based on an extended state observer. In view of the defects that the uncertainty variance is taken as a static weight and the back-end optimization is an open-loop structure in the existing three-dimensional Gaussian splash synchronous positioning and map construction method, the uncertainty variance is modeled as a pixel-by-pixel dynamic state quantity, a discrete-time state space equation is constructed, a pixel-by-pixel second-order extended state observer is designed, a nonlinear error feedback function is introduced to distinguish high-frequency measurement noise and low-frequency environmental degradation signals, a pixel-by-pixel variance estimation value and a disturbance estimation value are dynamically estimated, the variance estimation value is used to construct a rendering loss adaptive pixel weight, the disturbance estimation value is spatially aggregated to obtain a global degradation index, and the learning rate is dynamically modulated. When the disturbance estimation value exceeds a dynamic threshold, the densification operation of the corresponding region is suspended, and the learning rate, the weight and the density are closed-loop compensated in three dimensions, so that the mapping precision in a degraded environment is improved.

Description

Technical Field

[0001] This invention relates to the fields of computer vision, robot environmental perception and 3D reconstruction technology, and specifically to a 3D Gaussian splash adaptive reconstruction method based on an extended state observer. Background Technology

[0002] In industrial scenarios such as coal mine inspection, fire rescue, and autonomous driving in snowy environments, robots or autonomous systems need to operate continuously for extended periods in complex and harsh conditions, while maintaining high-precision environmental perception and positioning capabilities. With the increasing urgency of developing intelligent mines, automated urban firefighting, and unmanned winter roads, traditional manual labor-intensive methods are no longer sufficient to meet the requirements of safe production and efficient operation. However, these industrial scenarios commonly suffer from dynamic degradation of sensor observation quality due to drastic changes in ambient light, dust / smoke obstruction, and snow reflection, posing significant challenges to the practical deployment of robot autonomous localization and mapping systems.

[0003] Simultaneous localization and mapping (SLR) technology, as a core support for mobile robots to achieve autonomous navigation in unknown environments, has made significant progress in recent years. 3D Gaussian splashing, due to its superior rendering quality and real-time rasterization efficiency, is gradually replacing traditional point clouds and neural radiation fields, becoming a research hotspot in the fields of SLR and 3D reconstruction. Existing research introduces a pixel-wise uncertainty modeling mechanism into the 3D Gaussian splashing (3DGS) framework. By learning the Gaussian appearance variance and rendering a pixel-wise uncertainty map, the robustness of the system on standard indoor datasets is improved. However, most of these methods are validated in laboratory or ideal environments. Their uncertainty variance is only used as a static weight in the backend optimization, assigned a value at the beginning of each frame of optimization, and not updated during the optimization process, forming an open-loop structure.

[0004] Extended state observers (ESOs) are a core component of active disturbance rejection control (ADC) theory. Their core idea is to unify system modeling errors and external disturbances into a unified system state. Through online estimation and compensation by the observer, real-time tracking and active suppression of unknown disturbances can be achieved without an accurate disturbance model. ESOs have been widely used in industrial control fields such as motor control, aircraft attitude control, and mobile robot trajectory tracking, but they have not yet been incorporated into the 3D Gaussian splashing simultaneous localization and mapping (3DGS-SLAM) framework to address the problem of environmental observation quality degradation.

[0005] The data collection environment of existing industrial datasets differs significantly from real-world deployment scenarios. Most publicly available datasets are recorded under relatively ideal conditions, lacking coverage of real-world degradation scenarios such as dust obstruction, sudden changes in dense smoke, and snow reflection. This leads to a significant performance drop in models trained on existing datasets in actual industrial deployments, making it difficult to meet the stringent robustness requirements of scenarios such as coal mine inspection, fire rescue, and autonomous driving in snowy environments.

[0006] To address these challenges, we need a simultaneous localization and mapping method capable of achieving consistently high-quality mapping in complex industrial environments. This method should be able to perceive the dynamic degradation of environmental observation quality in real time and proactively adjust backend optimization strategies, fundamentally solving the core problem of map noise accumulation over time in industrial scenarios using existing 3D Gaussian splash mapping methods. Based on this need, this invention proposes a 3D Gaussian splash adaptive reconstruction method based on an extended state observer. By upgrading the uncertainty variance from static open-loop weights to dynamic closed-loop state variables, it achieves real-time estimation and proactive compensation for environmental disturbances at the perception, decision-making, and optimization levels. This provides a high-precision and robust 3D reconstruction solution for industrial scenarios such as coal mine inspection, fire rescue, and autonomous driving in snowy environments. Summary of the Invention

[0007] This invention designs a 3D Gaussian splash adaptive reconstruction method based on an extended state observer to achieve continuous and stable mapping quality in complex industrial environments. First, the proposed 3D Gaussian splash adaptive reconstruction architecture based on an extended state observer integrates three core modules: Gaussian uncertainty discrete-time state-space modeling, pixel-by-pixel extended state observer design, and hierarchical closed-loop feedback control. This integrated design method enables the system to comprehensively handle the entire closed-loop process from environmental degradation perception to adaptive adjustment of mapping parameters. Secondly, the uncertainty variance is upgraded from static open-loop weights to dynamic closed-loop state variables. An expanded state observer is used to jointly estimate the uncertainty variance and environmental degradation disturbances for each pixel. Closed-loop compensation is implemented from three dimensions: weights, learning rate, and density. This fundamentally solves the core problem of the continuous accumulation of map noise over time in complex industrial environments using existing 3D Gaussian splash mapping methods. Finally, the proposed pixel-by-pixel expanded state observer differs fundamentally from existing time-smoothing methods. It can simultaneously output two independent signals—denoised state estimation and disturbance estimation—based on the state-space equation, possessing active disturbance resistance rather than passive smoothing. Furthermore, a global degradation index is obtained through spatial aggregation, forming a multi-scale hierarchical closed-loop compensation structure from pixel-level to map-level. To achieve the above objectives, the following steps are taken:

[0008] Step 1: Obtain the uncertainty metric and rendering residuals output from the 3D Gaussian splash simultaneous localization and mapping backend. The uncertainty metric includes the pixel-wise uncertainty variance. The rendering residual includes pixel-by-pixel photometric error, with the pixel-by-pixel uncertainty variance. Using the system state variables, rendering residuals as input variables, and environmental degradation disturbances as extended state variables, a Gaussian uncertain discrete-time state-space equation is constructed.

[0009] Step 1.1: Place the first Uncertainty variance at each pixel Defined as system state variables Expansion state quantity For the first Environmental disturbances at each pixel affect the uncertainty variance. Systematic perturbations caused by evolution, observable inputs For the first The pixel-by-pixel photometric error between the rendered image and the input image at each pixel;

[0010] Step 1.2: Construct the first The discrete-time state-space equation for each pixel is given by the following formula:

[0011] ,

[0012] ,

[0013] ,

[0014] in, It is about controlling the gain. It is the inter-frame time step. It is the first The pixel in the first Uncertainty variance of frames It is the first The pixel in the first Frame environmental perturbation state variables. It is the first The pixel in the first Uncertainty variance of frames It is the first The pixel in the first Frame environmental perturbation state variables. It's rendering residuals. These are noisy observations. It is observation noise. Satisfying the slowly varying perturbation assumption, within extremely short time steps between adjacent frames. Within this range, the rate of change of environmental disturbances is extremely small, thus approximating the slowly varying disturbance assumption;

[0015] Step 1.3: Adjust the control gain The initial frame calibration is performed, and its control gain expression is as follows:

[0016] ,

[0017] in, It is about controlling the gain. It is the variance of the initial frame mean uncertainty. It is the mean of the rendering residuals of the initial frame.

[0018] Step 2: Based on the state-space equation, design a pixel-by-pixel expanded state observer, introduce a nonlinear error feedback function to distinguish between high-frequency measurement noise and low-frequency environmental degradation signals, and dynamically estimate the uncertainty variance of each pixel to obtain a pixel-by-pixel estimate. The environmental degradation perturbation of each pixel is estimated online to obtain the pixel-by-pixel perturbation estimate. ;

[0019] Step 2.1: Based on the discrete-time state-space equation established in Step 1, a second-order linear extended state observer is independently designed for each pixel. The prediction step is calculated using the estimated value and input of the previous frame. The prediction step incorporates the dynamic estimated value and rendering residual of the previous frame to achieve forward extrapolation of the state variables and unknown environmental disturbances in the current frame in the temporal domain. Prior estimation of the uncertainty variance and environmental disturbances of the current frame is performed. The expression for the prediction step is as follows:

[0020] ,

[0021] ,

[0022] in, It is the first The pixel in the first The predicted value of the uncertainty variance of the frame. It is the first The pixel in the first The predicted environmental disturbance value of the frame. It is the first The pixel in the first The dynamic estimate of the uncertainty variance of the frame. It is the first The pixel in the first Frame-by-pixel perturbation estimate, It is the first The pixel in the first Frame rendering residual input, It is about controlling the gain. It is the inter-frame time step;

[0023] Step 2.2: Obtain the first The pixel in the first Uncertainty variance observations of frames The observation error between the predicted value and the actual observed value is calculated, and its expression is as follows:

[0024] ,

[0025] in, It is the first The pixel in the first Frame observation error, It is the first The pixel in the first The predicted value of the uncertainty variance of the frame. It is the first The pixel in the first The noisy observations of the frame, i.e., observations with noisy uncertainty variance;

[0026] Step 2.3: Based on the observation error, the state of the prediction step is corrected by feedback to complete the update step of the pixel-by-pixel expansion state observer. The update step achieves nonlinear filtering of high-frequency measurement noise and real-time dynamic correction of low-frequency environmental degradation disturbances by substituting the deviation between the predicted state and the actual observation value into a nonlinear continuous function, thus obtaining the final dynamic estimate. The expression of the update step is as follows:

[0027] ,

[0028] ,

[0029] in, It is the first The pixel in the first The pixel-by-pixel estimate output after frame update. It is the first The pixel in the first The pixel-by-pixel perturbation estimate output after frame update. It is the first The pixel in the first The predicted value of the uncertainty variance of the frame. It is the first The pixel in the first The predicted environmental disturbance value of the frame. It is the first The pixel in the first Frame observation error, , These are the observer feedback gain matrix coefficients. It is a nonlinear continuous function used to suppress high-frequency measurement noise and extract low-frequency environmental disturbances. , and It is the adjustment parameter of the nonlinear continuous function. It is a linear interval threshold;

[0030] The nonlinear continuous function The mathematical expression is as follows:

[0031] ,

[0032] in, It is a nonlinear continuous function. This is the input error value. It is a non-linear factor. It is a linear interval threshold. It is a symbolic function, and this function is... It exhibits linear scaling within the interval, used to suppress high-frequency measurement noise. It exhibits a nonlinear power function within the interval, which is used to amplify low-frequency environmental degradation signals and achieve adaptive separation of high-frequency noise and low-frequency disturbances.

[0033] Step 3: Using the pixel-by-pixel estimated value Construct adaptive pixel weights for the rendering loss function, and apply them to the pixel-by-pixel perturbation estimate. Spatial aggregation yields global degradation indices. ,by Adaptive modulation of Gaussian parameters optimizes the learning rate when the absolute value of the pixel-by-pixel perturbation estimate is... Exceeding the dynamic topology gating threshold The corresponding region's Gaussian densification operation is paused when the time is triggered, realizing the joint closed-loop compensation of weight adaptation, learning rate adaptation and densification gating;

[0034] Step 3.1: Perform loop closure compensation from the weight dimension, using the updated uncertainty variance as a pixel-by-pixel estimate. For input, construct an exponential spatial adaptive weight allocation function, whose adaptive weight expression is as follows:

[0035] ,

[0036] in, It is the first The pixel in the first Adaptive weighting of frames It is the attenuation coefficient. It is the first The pixel in the first Pixel-by-pixel estimates of the frame;

[0037] Step 3.2: Perform closed-loop compensation from the learning rate dimension, estimating the pixel-by-pixel perturbation value for all valid pixels in the current frame. The absolute value is taken and global average spatial aggregation is performed to calculate the global degradation index. Furthermore, a dynamic learning rate modulation function based on a global degradation index is constructed, and the specific implementation steps are as follows:

[0038] ,

[0039] ,

[0040] ,

[0041] in, It is the first Global degradation metrics for frames. It is the total number of pixels. It is the first The pixel in the first Frame-by-pixel perturbation estimate, It is the first Adaptive learning rate of frames, It is the minimum learning rate scaling factor. It is the base learning rate. It is the minimum learning rate limit. It is a smoothing adjustment factor. This is the normal perturbation threshold; when the global degradation index... Exceeding the threshold At that time, learning rate It adaptively decreases as the disturbance increases;

[0042] Step 3.3: Perform closed-loop compensation from the density dimension, and calculate the dynamic topology gating threshold based on the global degradation index of the current frame. In the 3D Gaussian compaction control process, each pixel is traversed until... At that time, the extracted projection covers the first The set of 3D Gaussian element indices on each pixel is given. The positional gradient accumulation of the 3D Gaussian elements in the set is forcibly truncated, and their cloning and splitting operations are frozen. The dynamic topology gating threshold expression is as follows:

[0043] ,

[0044] in, It is the first Frame dynamic topology gating threshold, It is the proportional adjustment coefficient. It is the first Global degradation metrics for frames. It is a fixed bias constant.

[0045] Compared with the prior art, the advantages of the present invention are as follows:

[0046] This invention addresses the problem in existing 3D Gaussian splash simultaneous localization and mapping methods where uncertainty variance is used only as a static open-loop weight and cannot respond in real-time to dynamic degradation of environmental observation quality. It constructs a 3D Gaussian splash adaptive reconstruction method based on an extended state observer. The key features are: First, this invention introduces a nonlinear error feedback function into the extended state observer, decoupling high-frequency measurement noise from the noisy observation signal with low-frequency environmental degradation signals in real time. This solves the defect in existing methods where directly using noisy uncertainty variance for back-end optimization leads to decreased mapping accuracy. Simultaneously, it achieves joint estimation of pixel-by-pixel variance and disturbance, enhancing the system's performance in smoke-related scenarios. First, the invention enhances environmental perception capabilities in degraded scenarios such as dust, snow reflections, etc. Second, it employs a three-layer joint closed-loop compensation structure using variance estimates and perturbation estimates from the output of an extended state observer. This structure incorporates adaptive weights, adaptive learning rates, and densification gating. It adjusts rendering loss weights pixel-by-pixel using variance estimates, optimizes the learning rate by globally modulating Gaussian parameters after spatial aggregation of perturbation estimates, and pauses Gaussian densification operations by comparing pixel-by-pixel perturbation values ​​with dynamic thresholds. This achieves multi-scale hierarchical compensation for complex environmental degradation perturbations from the pixel level to the map level, improving mapping accuracy and robustness without relying on specific degraded datasets or offline retraining. Attached Figure Description

[0047] Figure 1 This is an overall flowchart of an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram comparing the reconstruction results of the method of this invention and the baseline method, wherein, Figure 2 (a) is a schematic diagram of the reconstruction effect of the baseline method. Figure 2 (b) is a schematic diagram of the reconstruction effect of the present invention; Detailed Implementation

[0049] To more clearly illustrate the purpose, technical solution, and advantages of this invention, the following detailed description of the invention will be provided with the aid of the accompanying drawings and specific embodiments.

[0050] Figure 1The flowchart of this embodiment illustrates a 3D Gaussian splash adaptive reconstruction method based on an extended state observer. The data input originates from a multimodal sensor including a camera, LiDAR, and inertial measurement unit. The specific process includes: acquiring the pixel-wise uncertainty variance and rendering residuals output from the backend of the 3D Gaussian splash framework; constructing a Gaussian uncertainty discrete-time state-space equation; designing a pixel-wise extended state observer to dynamically estimate the uncertainty variance of each pixel to obtain a pixel-wise estimate, and performing online estimation of environmental disturbances for each pixel to obtain a pixel-wise disturbance estimate; constructing adaptive pixel weights using the pixel-wise estimates; spatially aggregating the pixel-wise disturbance estimates to obtain a global disturbance index and modulating the Gaussian parameters to optimize the learning rate; and triggering a Gaussian unit densification pause mechanism by comparing the pixel-wise disturbance estimates with a dynamic threshold, thus achieving closed-loop compensation for environmental disturbances from three dimensions: weight, learning rate, and density. The pixel-wise extended state observer involves only scalar recursive operations (only 3 multiplication-addition operations per pixel per frame), without matrix inversion or iterative optimization, and the computational load is linearly related to the number of pixels. At typical resolutions, million-pixel extended state observer (ESO) updates can be performed in parallel on GPUs using CUDA, meeting the real-time mapping needs of mobile robots.

[0051] A three-dimensional Gaussian splash adaptive reconstruction method based on an extended state observer includes the following steps:

[0052] Step 1: Obtain the uncertainty metric and rendering residuals output from the 3D Gaussian splash simultaneous localization and mapping backend. The uncertainty metric includes the pixel-wise uncertainty variance. The rendering residual includes pixel-by-pixel photometric error, with the pixel-by-pixel uncertainty variance. Using the system state variables, rendering residuals as input variables, and environmental degradation disturbances as extended state variables, a Gaussian uncertain discrete-time state-space equation is constructed.

[0053] Step 1.1: Place the first Uncertainty variance at each pixel Defined as system state variables Expansion state quantity For the first Environmental disturbances at each pixel affect the uncertainty variance. Systematic perturbations caused by evolution, observable inputs For the first The pixel-by-pixel photometric error between the rendered image and the input image at each pixel;

[0054] Step 1.2: Construct the first The discrete-time state-space equation for each pixel is given by the following formula:

[0055] ,

[0056] ,

[0057] ,

[0058] in, It is about controlling the gain. It is the inter-frame time step. It is the first The pixel in the first Uncertainty variance of frames It is the first The pixel in the first Frame environmental perturbation state variables. It is the first The pixel in the first Uncertainty variance of frames It is the first The pixel in the first Frame environmental perturbation state variables. It's rendering residuals. These are noisy observations. It is observation noise. Satisfying the slowly varying perturbation assumption, within extremely short time steps between adjacent frames. Within this range, the rate of change of environmental disturbances is extremely small, thus approximating the slowly varying disturbance assumption;

[0059] Step 1.3: Adjust the control gain The initial frame calibration is performed, and its control gain expression is as follows:

[0060] ,

[0061] in, It is about controlling the gain. It is the variance of the initial frame mean uncertainty. It is the mean of the rendering residuals of the initial frame.

[0062] Step 2: Based on the state-space equation, design a pixel-by-pixel expanded state observer, introduce a nonlinear error feedback function to distinguish between high-frequency measurement noise and low-frequency environmental degradation signals, and dynamically estimate the uncertainty variance of each pixel to obtain a pixel-by-pixel estimate. The environmental degradation perturbation of each pixel is estimated online to obtain the pixel-by-pixel perturbation estimate. ;

[0063] Step 2.1: Based on the discrete-time state-space equation established in Step 1, a second-order linear extended state observer is independently designed for each pixel. The prediction step is calculated using the estimated value and input of the previous frame. The prediction step incorporates the dynamic estimated value and rendering residual of the previous frame to achieve forward extrapolation of the state variables and unknown environmental disturbances in the current frame in the temporal domain. Prior estimation of the uncertainty variance and environmental disturbances of the current frame is performed. The expression for the prediction step is as follows:

[0064] ,

[0065] ,

[0066] in, It is the first The pixel in the first The predicted value of the uncertainty variance of the frame. It is the first The pixel in the first The predicted environmental disturbance value of the frame. It is the first The pixel in the first The dynamic estimate of the uncertainty variance of the frame. It is the first The pixel in the first Frame-by-pixel perturbation estimate, It is the first The pixel in the first Frame rendering residual input, It is about controlling the gain. It is the inter-frame time step;

[0067] Step 2.2: Obtain the first The pixel in the first Uncertainty variance observations of frames The observation error between the predicted value and the actual observed value is calculated, and its expression is as follows:

[0068] ,

[0069] in, It is the first The pixel in the first Frame observation error, It is the first The pixel in the first The predicted value of the uncertainty variance of the frame. It is the first The pixel in the first The noisy observations of the frame, i.e., observations with noisy uncertainty variance;

[0070] Step 2.3: Based on the observation error, the state of the prediction step is corrected by feedback to complete the update step of the pixel-by-pixel expansion state observer. The update step achieves nonlinear filtering of high-frequency measurement noise and real-time dynamic correction of low-frequency environmental degradation disturbances by substituting the deviation between the predicted state and the actual observation value into a nonlinear continuous function, thus obtaining the final dynamic estimate. The expression of the update step is as follows:

[0071] ,

[0072] ,

[0073] in, It is the first The pixel in the first The pixel-by-pixel estimate output after frame update. It is the first The pixel in the first The pixel-by-pixel perturbation estimate output after frame update. It is the first The pixel in the first The predicted value of the uncertainty variance of the frame. It is the first The pixel in the first The predicted environmental disturbance value of the frame. It is the first The pixel in the first Frame observation error, , These are the observer feedback gain matrix coefficients. It is a nonlinear continuous function used to suppress high-frequency measurement noise and extract low-frequency environmental disturbances. , and It is the adjustment parameter of the nonlinear continuous function. It is a linear interval threshold;

[0074] Based on observer bandwidth parameter Pole placement calibration is performed to ensure the stability of the discrete system. The specific calibration formula is as follows:

[0075] ,

[0076] ,

[0077] ,

[0078] Among them, bandwidth parameter The calibration is based on the following: The mobile robot is placed in a standard test environment without sensor degradation, and the temperature is gradually increased... until the state estimate Slight high-frequency oscillations begin to appear; record the critical bandwidth value at this point. , These are the final calibrated bandwidth parameters. It is a state estimate. The critical bandwidth value at which high-frequency oscillations begin to appear. It is a safety factor. This calibration formula introduces a safety margin on the basis of the critical bandwidth value, so that the observer can achieve a balance between response speed and noise suppression, and avoid amplifying measurement noise due to excessive gain in actual scenarios.

[0079] The nonlinear continuous function The mathematical expression is as follows:

[0080] ,

[0081] in, It is a nonlinear continuous function. This is the input error value. It is a non-linear factor. It is a linear interval threshold. It is a symbolic function, and this function is... It exhibits linear scaling within the interval, used to suppress high-frequency measurement noise. It exhibits a nonlinear power function within the interval, which is used to amplify low-frequency environmental degradation signals and achieve adaptive separation of high-frequency noise and low-frequency disturbances.

[0082] Step 3: Using the pixel-by-pixel estimated value Construct adaptive pixel weights for the rendering loss function, and apply them to the pixel-by-pixel perturbation estimate. Spatial aggregation yields global degradation indices. ,by Adaptive modulation of Gaussian parameters optimizes the learning rate when the absolute value of the pixel-by-pixel perturbation estimate is... Exceeding the dynamic topology gating threshold The corresponding region's Gaussian densification operation is paused when the time is triggered, realizing the joint closed-loop compensation of weight adaptation, learning rate adaptation and densification gating;

[0083] Step 3.1: Perform loop closure compensation from the weight dimension, using the updated uncertainty variance as a pixel-by-pixel estimate. For input, construct an exponential spatial adaptive weight allocation function, whose adaptive weight expression is as follows:

[0084] ,

[0085] in, It is the first The pixel in the first Adaptive weighting of frames It is the attenuation coefficient. It is the first The pixel in the first Pixel-by-pixel estimates of the frame;

[0086] Step 3.2: Perform closed-loop compensation from the learning rate dimension, estimating the pixel-by-pixel perturbation value for all valid pixels in the current frame. The absolute value is taken and global average spatial aggregation is performed to calculate the global degradation index. Furthermore, a dynamic learning rate modulation function based on a global degradation index is constructed, and the specific implementation steps are as follows:

[0087] ,

[0088] ,

[0089] ,

[0090] in, It is the first Global degradation metrics for frames. It is the total number of pixels. It is the first The pixel in the first Frame-by-pixel perturbation estimate, It is the first Adaptive learning rate of frames, It is the minimum learning rate scaling factor. It is the base learning rate. It is the minimum learning rate limit. It is a smoothing adjustment factor. This is the normal perturbation threshold; when the global degradation index... Exceeding the threshold At that time, learning rate It adaptively decreases as the disturbance increases;

[0091] Step 3.3: Perform closed-loop compensation from the density dimension, and calculate the dynamic topology gating threshold based on the global degradation index of the current frame. In the 3D Gaussian compaction control process, each pixel is traversed until... At that time, the extracted projection covers the first The set of 3D Gaussian element indices on each pixel is given. The positional gradient accumulation of the 3D Gaussian elements in the set is forcibly truncated, and their cloning and splitting operations are frozen. The dynamic topology gating threshold expression is as follows:

[0092] ,

[0093] in, It is the first Frame dynamic topology gating threshold, It is the proportional adjustment coefficient. It is the first Global degradation metrics for frames. It is a fixed bias constant;

[0094] In the first 100 frames of the initial system startup phase, the statistical spatial average perturbation value was... The normal disturbance threshold is calibrated using the following formula:

[0095] ,

[0096] in, This is the normal disturbance threshold. It is the first Spatial average perturbation value of the frame, It is the mean function. It is the standard deviation function, and [1, 100] is the time window of the first 100 frames in the initial calibration phase. This calibration method is based on The principle is to use the mean and standard deviation of the spatial average perturbation of the first 100 frames as a benchmark, remove the basic noise fluctuations, and use them as the trigger point for the adaptive learning rate to start decreasing.

[0097] In an offline benchmark test scenario, localized smoke interference of known concentration is introduced into a standard environment, and the pixel perturbation estimates of the smoke-polluted area and the normal view area are statistically analyzed. Fixed bias constant Set as follows:

[0098] ,

[0099] in, It is a fixed bias constant. This is the normal disturbance threshold. This setting is used to isolate small global fluctuations and ensure that densification pause is not triggered when the global disturbance is small.

[0100] Proportional adjustment coefficient Adjustments are made according to the following constraints, when the perturbation value of a pixel in the polluted area... Reaching the global perturbation mean of When the value is greater than or equal to the specified value, the pixel should satisfy the following condition:

[0101] ,

[0102] At this point, the position gradient cutoff trigger rate of the Gaussian unit in the contaminated area needs to reach [a certain threshold]. The above, and at the same time, the false freezing rate in normal areas must be lower than By adjusting the scaling factor This enables dynamic topology gating thresholds. It can accurately encompass polluted areas and selectively pause the densification of Gaussian elements in polluted areas, thus completing a complete closed-loop process from environmental degradation perception to adaptive adjustment of mapping parameters.

Claims

1. A three-dimensional Gaussian splash adaptive reconstruction method based on an extended state observer, characterized in that, Includes the following steps: Step 1: Obtain the uncertainty metric and rendering residuals output from the 3D Gaussian splash simultaneous localization and mapping backend. The uncertainty metric includes the pixel-wise uncertainty variance. The rendering residual includes pixel-by-pixel photometric error, with the pixel-by-pixel uncertainty variance. Using the system state variables, rendering residuals as input variables, and environmental degradation disturbances as extended state variables, a Gaussian uncertain discrete-time state-space equation is constructed. Step 2: Based on the state-space equation, design a pixel-by-pixel expanded state observer, introduce a nonlinear error feedback function to distinguish between high-frequency measurement noise and low-frequency environmental degradation signals, and dynamically estimate the uncertainty variance of each pixel to obtain a pixel-by-pixel estimate. The environmental degradation perturbation of each pixel is estimated online to obtain the pixel-by-pixel perturbation estimate. ; Step 3: Using the pixel-by-pixel estimated value Construct adaptive pixel weights for the rendering loss function, and apply them to the pixel-by-pixel perturbation estimate. Spatial aggregation yields global degradation indices. ,by Adaptive modulation of Gaussian parameters optimizes the learning rate when the absolute value of the pixel-by-pixel perturbation estimate is... Exceeding the dynamic topology gating threshold The corresponding region's Gaussian densification operation is paused when the time is triggered, realizing a joint closed-loop compensation of weight adaptation, learning rate adaptation, and densification gating.

2. The three-dimensional Gaussian splash adaptive reconstruction method based on an extended state observer according to claim 1, characterized in that, The construction of the Gaussian uncertainty discrete-time state-space equation described in step 1 is carried out according to the following steps: Step 1.1: Place the first Uncertainty variance at each pixel Defined as system state variables Expansion state quantity For the first Environmental disturbances at each pixel affect the uncertainty variance. Systematic perturbations caused by evolution, observable inputs For the first The pixel-by-pixel photometric error between the rendered image and the input image at each pixel; Step 1.2: Construct the first The discrete-time state-space equation for each pixel is given by the following formula: ， ， ， in, It is about controlling the gain. It is the inter-frame time step. It is the first The pixel in the first Uncertainty variance of frames It is the first The pixel in the first Frame environmental perturbation state variables. It is the first The pixel in the first Uncertainty variance of frames It is the first The pixel in the first Frame environmental perturbation state variables. It's rendering residuals. These are noisy observations. It is observation noise. Satisfying the slowly varying perturbation assumption, within extremely short time steps between adjacent frames. Within this range, the rate of change of environmental disturbances is extremely small, thus approximating the slowly varying disturbance assumption; Step 1.3: Adjust the control gain The initial frame calibration is performed, and its control gain expression is as follows: ， in, It is about controlling the gain. It is the variance of the initial frame mean uncertainty. It is the mean of the rendering residuals of the initial frame.

3. The three-dimensional Gaussian splash adaptive reconstruction method based on an extended state observer according to claim 1, characterized in that, The design of the pixel-by-pixel expansion state observer described in step 2 is implemented according to the following steps: Step 2.1: Based on the discrete-time state-space equation established in Step 1, a second-order linear extended state observer is independently designed for each pixel. The prediction step is calculated using the estimated value and input of the previous frame. The prediction step incorporates the dynamic estimated value and rendering residual of the previous frame to achieve forward extrapolation of the state variables and unknown environmental disturbances in the current frame in the temporal domain. Prior estimation of the uncertainty variance and environmental disturbances of the current frame is performed. The expression for the prediction step is as follows: ， ， in, It is the first The pixel in the first The predicted value of the uncertainty variance of the frame. It is the first The pixel in the first The predicted environmental disturbance value of the frame. It is the first The pixel in the first The dynamic estimate of the uncertainty variance of the frame. It is the first The pixel in the first Frame-by-pixel perturbation estimate, It is the first The pixel in the first Frame rendering residual input, It is about controlling the gain. It is the inter-frame time step; Step 2.2: Obtain the first The pixel in the first Uncertainty variance observations of frames The observation error between the predicted value and the actual observed value is calculated, and its expression is as follows: ， in, It is the first The pixel in the first Frame observation error, It is the first The pixel in the first The predicted value of the uncertainty variance of the frame. It is the first The pixel in the first The noisy observations of the frame, i.e., observations with noisy uncertainty variance; Step 2.3: Based on the observation error, the state of the prediction step is corrected by feedback to complete the update step of the pixel-by-pixel expansion state observer. The update step achieves nonlinear filtering of high-frequency measurement noise and real-time dynamic correction of low-frequency environmental degradation disturbances by substituting the deviation between the predicted state and the actual observation value into a nonlinear continuous function, thus obtaining the final dynamic estimate. The expression of the update step is as follows: ， ， in, It is the first The pixel in the first The pixel-by-pixel estimate output after frame update. It is the first The pixel in the first The pixel-by-pixel perturbation estimate output after frame update. It is the first The pixel in the first The predicted value of the uncertainty variance of the frame. It is the first The pixel in the first The predicted environmental disturbance value of the frame. It is the first The pixel in the first Frame observation error, , These are the observer feedback gain matrix coefficients. It is a nonlinear continuous function used to suppress high-frequency measurement noise and extract low-frequency environmental disturbances. , and It is the adjustment parameter of the nonlinear continuous function. It is a linear interval threshold; The nonlinear continuous function The mathematical expression is as follows: ， in, It is a nonlinear continuous function. This is the input error value. It is a non-linear factor. It is a linear interval threshold. It is a symbolic function, and this function is... It exhibits linear scaling within the interval, used to suppress high-frequency measurement noise. It exhibits a nonlinear power function within the interval, which is used to amplify low-frequency environmental degradation signals and achieve adaptive separation of high-frequency noise and low-frequency disturbances.

4. The three-dimensional Gaussian splash adaptive reconstruction method based on an extended state observer according to claim 1, characterized in that, The step 3 described using the pixel-by-pixel estimated value Construct adaptive pixel weights for the rendering loss function, and apply them to the pixel-by-pixel perturbation estimate. Spatial aggregation yields global degradation indices. ,by Adaptive modulation of Gaussian parameters optimizes the learning rate when the absolute value of the pixel-by-pixel perturbation estimate is... Exceeding the dynamic topology gating threshold When the corresponding region's Gaussian densification operation is paused, the following steps are implemented: Step 3.1: Perform loop closure compensation from the weight dimension, using the updated uncertainty variance as a pixel-by-pixel estimate. For input, construct an exponential spatial adaptive weight allocation function, whose adaptive weight expression is as follows: ， in, It is the first The pixel in the first Adaptive weighting of frames It is the attenuation coefficient. It is the first The pixel in the first Pixel-by-pixel estimates of the frame; Step 3.2: Perform closed-loop compensation from the learning rate dimension, estimating the pixel-by-pixel perturbation value for all valid pixels in the current frame. The absolute value is taken and global average spatial aggregation is performed to calculate the global degradation index. Furthermore, a dynamic learning rate modulation function based on a global degradation index is constructed, and the specific implementation steps are as follows: ， ， ， in, It is the first Global degradation metrics for frames. It is the total number of pixels. It is the first The pixel in the first Frame-by-pixel perturbation estimate, It is the first Adaptive learning rate of frames, It is the minimum learning rate scaling factor. It is the base learning rate. It is the minimum learning rate limit. It is a smoothing adjustment factor. This is the normal perturbation threshold; when the global degradation index... Exceeding the threshold At that time, learning rate It adaptively decreases as the disturbance increases; Step 3.3: Perform closed-loop compensation from the density dimension, and calculate the dynamic topology gating threshold based on the global degradation index of the current frame. In the 3D Gaussian compaction control process, each pixel is traversed until... At that time, the extracted projection covers the first The set of 3D Gaussian element indices on each pixel is given. The positional gradient accumulation of the 3D Gaussian elements in the set is forcibly truncated, and their cloning and splitting operations are frozen. The dynamic topology gating threshold expression is as follows: ， in, It is the first Frame dynamic topology gating threshold, It is the proportional adjustment coefficient. It is the first Global degradation metrics for frames. It is a fixed bias constant.

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