Multi-parameter collaborative optimization method and system for four-dimensional gaussian sputter reconstruction

Abstract

The disclosure provides a multi-parameter collaborative optimization method and system for four-dimensional Gaussian sputtering reconstruction, relating to the technical field of data processing. The method comprises: obtaining trajectory optimization loss items, external parameter calibration loss items and positioning optimization loss items corresponding to trajectory parameter sets, sensor external parameter sets and self-vehicle positioning parameters respectively, and determining a trajectory smoothing regularization term according to the change amount of adjacent frame pose parameters; weighting and summing each loss item and the trajectory smoothing regularization term according to the corresponding weight coefficient to obtain a global unified loss function; aggregating the three types of parameters into a single parameter vector, performing back propagation on the global unified loss function through a single optimizer, and synchronously updating the single parameter vector according to the obtained gradient; dynamically adjusting the weight coefficient according to the gradient convergence state of the parameters corresponding to each loss item; and outputting the converged three types of parameters to a four-dimensional Gaussian sputtering model for dynamic scene reconstruction.

Description

Technical Field

[0001] This disclosure relates to the field of data processing technology, and more specifically, to a multi-parameter collaborative optimization method and system for four-dimensional Gaussian sputtering reconstruction. Background Technology

[0002] In 4D Gaussian Splatting (4DGS) dynamic scene reconstruction for autonomous driving scenarios, three types of parameters—vehicle trajectory, multi-sensor external participation in vehicle localization, and others—must all be kept accurate to ensure the consistency of the dynamic scene over time. Related technologies typically assign these three types of parameters to different modules, using independent loss functions and optimizers for step-by-step or alternating optimization, assuming that each module is independent of the others.

[0003] However, the three types of parameters mentioned above share the same four-dimensional Gaussian scene representation and are highly coupled: trajectory parameters determine the deformation of the dynamic Gaussian over time, extrinsic parameters determine the projection relationship of sensor observations, and positioning parameters determine the vehicle's position in the global coordinate system. Residual errors in one type of parameter can be propagated to other parameters through the shared scene representation, and subsequent optimization may disrupt the converged results, making it difficult to maintain consistency among the three types of parameters. Furthermore, the different dimensions and convergence speeds of the various loss terms mean that fixed weights can easily lead to over-updating of some parameters and under-updating of others; when trajectory parameters are optimized independently frame by frame, abrupt pose changes can easily occur due to the lack of constraints from adjacent frames. Therefore, existing methods struggle to achieve synchronous convergence of the three types of parameters, easily causing sensor projection misalignment, vehicle positioning drift, and jittery changes in vehicle trajectory, thereby disrupting the temporal consistency of dynamic scene reconstruction. Summary of the Invention

[0004] The purpose of this disclosure is to provide a multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction, a multi-parameter collaborative optimization system for four-dimensional Gaussian sputtering reconstruction, an electronic device, and a computer-readable storage medium. It can improve the multi-parameter collaborative convergence capability and the temporal consistency of dynamic scene reconstruction by constructing a globally unified loss function and updating the trajectory parameters, sensor extrinsic parameters, and vehicle positioning parameters synchronously with a single optimizer, while dynamically adjusting the weight coefficients according to the gradient convergence state.

[0005] Other features and advantages of this disclosure will become apparent from the following detailed description, or may be learned in part from practice of this disclosure.

[0006] According to a first aspect of the present disclosure, a multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction is provided, comprising: obtaining a trajectory optimization loss term, an extrinsic parameter calibration loss term, a positioning optimization loss term, and a trajectory smoothing regularization term constraining the temporal continuity of the trajectory; wherein, the trajectory optimization loss term corresponds to the set of trajectory parameters to be optimized, the extrinsic parameter calibration loss term corresponds to the set of sensor extrinsic parameters to be optimized, the positioning optimization loss term corresponds to the vehicle positioning parameters to be optimized, and the trajectory smoothing regularization term is obtained based on the change in pose parameters of adjacent frames in the trajectory parameter set; the trajectory optimization loss term, the extrinsic parameter calibration loss term, the positioning optimization loss term, and the trajectory smoothing regularization term are weighted and summed according to their respective weight coefficients to obtain a globally unified loss. The function aggregates the trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters into a single parameter vector; it performs backpropagation on a globally unified loss function using a single optimizer, and synchronously updates the trajectory parameters, extrinsic parameters, and vehicle positioning parameters in the single parameter vector based on the gradient obtained from backpropagation; during the synchronous update process, it dynamically adjusts the weight coefficients corresponding to each loss term based on the gradient convergence state of the parameters corresponding to each loss term; wherein, the trajectory optimization loss term and the trajectory smoothing regularization term correspond to the trajectory parameter set; and it outputs the synchronously updated converged trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters to a four-dimensional Gaussian sputtering model for dynamic scene reconstruction using the four-dimensional Gaussian sputtering model.

[0007] According to a second aspect of the present disclosure, a multi-parameter collaborative optimization system for four-dimensional Gaussian sputtering reconstruction is provided. The system includes: a loss acquisition module for acquiring a trajectory optimization loss term, an extrinsic parameter calibration loss term, a positioning optimization loss term, and a trajectory smoothing regularization term constraining the temporal continuity of the trajectory; wherein the trajectory optimization loss term corresponds to a set of trajectory parameters to be optimized, the extrinsic parameter calibration loss term corresponds to a set of sensor extrinsic parameters to be optimized, the positioning optimization loss term corresponds to vehicle positioning parameters to be optimized, and the trajectory smoothing regularization term is obtained based on the change in pose parameters of adjacent frames in the trajectory parameter set; a loss fusion module for weighted summation of the trajectory optimization loss term, the extrinsic parameter calibration loss term, the positioning optimization loss term, and the trajectory smoothing regularization term according to their respective weight coefficients to obtain a globally unified loss function; and a parameter aggregation module. The system comprises: a trajectory parameter set, a sensor extrinsic parameter set, and vehicle positioning parameters aggregated into a single parameter vector; a synchronization update module, used to backpropagate the global unified loss function using a single optimizer and synchronously update the trajectory parameters, extrinsic parameters, and vehicle positioning parameters in the single parameter vector based on the gradient obtained from the backpropagation; a weight adjustment module, used to dynamically adjust the weight coefficients corresponding to each loss term during the synchronization update process based on the gradient convergence state of the parameters corresponding to each loss term; wherein the trajectory optimization loss term and the trajectory smoothing regularization term correspond to the trajectory parameter set; and a parameter output module, used to output the synchronously updated converged trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters to a four-dimensional Gaussian sputtering model for dynamic scene reconstruction of the four-dimensional Gaussian sputtering model.

[0008] According to a third aspect of the present disclosure, an electronic device is provided, comprising: a processor; and a memory storing computer-readable instructions that, when executed by the processor, implement the multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction as described in the first aspect.

[0009] According to a fourth aspect of the present disclosure, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction as described in the first aspect.

[0010] The technical solutions provided in this disclosure can include the following beneficial effects: According to the multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction in this example embodiment, on the one hand, since the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term are weighted and fused into a globally unified loss function, the three types of parameters can be collaboratively optimized under the same loss metric, thereby reducing conflicts between different optimization objectives. On the other hand, since the trajectory parameters, sensor extrinsic parameters, and vehicle localization parameters are aggregated into a single parameter vector and backpropagation and synchronous updates are performed through a single optimizer, the gradient generated by the globally unified loss can simultaneously act on the three types of parameters, thereby reducing repeated perturbations of existing convergence results by step-by-step optimization and improving the synchronous convergence capability of the three types of parameters. Furthermore, since the weight coefficients corresponding to each loss term are dynamically adjusted according to the gradient convergence state of the parameters corresponding to each loss term, and both the trajectory optimization loss term and the trajectory smoothing regularization term participate in the weight adjustment based on the gradient convergence state of the trajectory parameter set, the optimization contribution of each loss term can change with the convergence process, thereby avoiding over-updating or under-updating of some parameters and improving the balance and stability of the joint optimization process. On the other hand, since the trajectory smoothing regularization term is obtained based on the changes in pose parameters between adjacent frames and participates in the optimization of the global unified loss, excessive pose changes between adjacent frames can be constrained, thereby reducing trajectory jitter and jumps and improving the temporal continuity of the vehicle's motion trajectory. In addition, since the converged trajectory parameters, sensor extrinsic parameters, and vehicle localization parameters are synchronously updated and jointly output to the four-dimensional Gaussian sputtering model, dynamic scene reconstruction can be performed based on the three types of parameters that are coordinated with each other. This reduces sensor projection misalignment, vehicle position drift, and trajectory temporal discontinuity, and improves the consistency of dynamic scene reconstruction.

[0011] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0012] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0013] Figure 1 The schematic diagram illustrates a multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to some embodiments of the present disclosure.

[0014] Figure 2 The illustration shows a schematic diagram of a multi-parameter collaborative optimization overall architecture according to some embodiments of the present disclosure.

[0015] Figure 3 The illustration shows a schematic diagram of the construction of a globally uniform loss function according to some embodiments of the present disclosure.

[0016] Figure 4 A flowchart illustrating the dynamic adjustment of weighting coefficients according to some embodiments of the present disclosure is shown.

[0017] Figure 5 A schematic diagram illustrating the periodic update control flow of weight coefficients according to some embodiments of the present disclosure is shown.

[0018] Figure 6 The schematic diagram illustrates the structure of a multi-parameter collaborative optimization system for four-dimensional Gaussian sputtering reconstruction according to some embodiments of the present disclosure.

[0019] Figure 7 The schematic diagram illustrates the structural schematic of a computer system of an electronic device according to some embodiments of the present disclosure.

[0020] In the accompanying drawings, the same or corresponding reference numerals indicate the same or corresponding parts. Detailed Implementation

[0021] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this specification. Rather, they are merely examples of systems and methods consistent with some aspects of this specification as detailed in the appended claims.

[0022] The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of this specification. The singular forms “a,” “the,” and “the” as used in this specification and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0023] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be more thorough and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art.

[0024] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a thorough understanding of embodiments of this disclosure. However, those skilled in the art will recognize that the technical solutions of this disclosure can be practiced without one or more of the specific details, or other methods, components, systems, steps, etc., can be employed. In other instances, well-known methods, systems, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of this disclosure.

[0025] Furthermore, the accompanying drawings are for illustrative purposes only and are not necessarily drawn to scale. The block diagrams shown in the drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor systems and / or microcontroller systems.

[0026] With the development of autonomous driving perception and dynamic scene modeling technologies, four-dimensional Gaussian sputtering technology has been gradually applied to the reconstruction of dynamic scenes for autonomous driving due to its high scene representation and rendering efficiency. Four-dimensional Gaussian sputtering introduces a time dimension into the three-dimensional Gaussian scene representation to model the changes of vehicles, pedestrians, and road environment over time, thereby obtaining a dynamic scene representation with temporal information.

[0027] In the process of four-dimensional Gaussian sputtering reconstruction in autonomous driving scenarios, it is usually necessary to optimize the vehicle trajectory, multi-sensor extrinsic parameters, and vehicle localization parameters. Trajectory parameters describe the deformation relationship of the dynamic Gaussian over time, sensor extrinsic parameters describe the projection relationship between different sensor observation data and the scene representation, and vehicle localization parameters describe the vehicle's pose in the global coordinate system. The accuracy of these three types of parameters collectively affects the dynamic scene reconstruction result.

[0028] Related technologies typically employ separate trajectory optimization, extrinsic parameter calibration, and localization optimization modules for different parameters. Each module uses an independent loss function and optimizer, updating the corresponding parameters through step-by-step or alternating optimization. For example, some schemes can jointly optimize camera extrinsic parameters and 3D Gaussian scene representation, some can alternately optimize camera pose and scene parameters, and others can jointly optimize neural scene representation based on multi-sensor extrinsic parameters. Furthermore, in the field of multi-task learning, there are general methods that adjust the weights of multiple loss terms based on uncertainty or gradient information. However, the above schemes usually only jointly process some parameters or belong to a general loss weighting framework that does not distinguish between specific applications, making them difficult to directly apply to the collaborative optimization of vehicle trajectory, sensor extrinsic parameters, and vehicle localization parameters.

[0029] Because trajectory parameters, sensor extrinsic parameters, and vehicle localization parameters share the same four-dimensional Gaussian scene representation and are mutually coupled, when using step-by-step or alternating optimization, the residual error of one type of parameter may be propagated to other parameters through the scene representation. Subsequent updates to other parameters may then alter the reconstruction results corresponding to the already optimized parameters, making it difficult for the three types of parameters to converge synchronously. Furthermore, the dimensions and convergence speed of the loss terms corresponding to different parameters may differ. Using fixed weights or manually setting weights can easily lead to some parameters being over-updated while others are under-updated.

[0030] Furthermore, when optimizing vehicle trajectory frame by frame, related technologies often lack explicit correlation between poses of adjacent frames. When pose parameters of individual frames shift significantly, discontinuous changes can easily occur between adjacent frames, resulting in jitter or jumps in the vehicle trajectory on the time axis.

[0031] Therefore, in the process of reconstructing dynamic scenes using four-dimensional Gaussian sputtering, related technologies are prone to problems such as sensor projection misalignment, vehicle positioning drift, and discontinuous vehicle trajectory, which in turn affect the temporal consistency of the dynamic scene reconstruction results.

[0032] To address all or part of the technical problems in the aforementioned related technologies, this disclosure provides a multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction. This method can be used to implement a multi-parameter collaborative optimization system for four-dimensional Gaussian sputtering reconstruction. Figure 1 The schematic diagram illustrates a multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to some embodiments of the present disclosure. Reference Figure 1 As shown, the multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction may include the following steps: Step S101: Obtain the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term that constrains the temporal continuity of the trajectory; wherein, the trajectory optimization loss term corresponds to the set of trajectory parameters to be optimized, the extrinsic parameter calibration loss term corresponds to the set of sensor extrinsic parameters to be optimized, the localization optimization loss term corresponds to the vehicle localization parameters to be optimized, and the trajectory smoothing regularization term is obtained based on the change in pose parameters of adjacent frames in the trajectory parameter set; Step S102: The trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term are weighted and summed according to their respective weight coefficients to obtain a globally unified loss function; Step S103: Aggregate the trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters into a single parameter vector; Step S104: Backpropagate the global unified loss function using a single optimizer, and update the trajectory parameters, extrinsic parameters, and vehicle localization parameters in the single parameter vector synchronously based on the gradient obtained from the backpropagation. Step S105: During the synchronous update process, the weight coefficients corresponding to each loss term are dynamically adjusted according to the gradient convergence state of the parameters corresponding to each loss term; wherein, the trajectory optimization loss term and the trajectory smoothing regularization term correspond to the trajectory parameter set. Step S106: The synchronized updated converged trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters are output to the four-dimensional Gaussian sputtering model for dynamic scene reconstruction.

[0033] According to the multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction in this example embodiment, on the one hand, since the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term are weighted and fused into a globally unified loss function, the three types of parameters can be collaboratively optimized under the same loss metric, thereby reducing conflicts between different optimization objectives. On the other hand, since the trajectory parameters, sensor extrinsic parameters, and vehicle localization parameters are aggregated into a single parameter vector and backpropagation and synchronous updates are performed through a single optimizer, the gradient generated by the globally unified loss can simultaneously act on the three types of parameters, thereby reducing repeated perturbations of existing convergence results by step-by-step optimization and improving the synchronous convergence capability of the three types of parameters. Furthermore, since the weight coefficients corresponding to each loss term are dynamically adjusted according to the gradient convergence state of the parameters corresponding to each loss term, and both the trajectory optimization loss term and the trajectory smoothing regularization term participate in the weight adjustment based on the gradient convergence state of the trajectory parameter set, the optimization contribution of each loss term can change with the convergence process, thereby avoiding over-updating or under-updating of some parameters and improving the balance and stability of the joint optimization process. On the other hand, since the trajectory smoothing regularization term is obtained based on the changes in pose parameters between adjacent frames and participates in the optimization of the global unified loss, excessive pose changes between adjacent frames can be constrained, thereby reducing trajectory jitter and jumps and improving the temporal continuity of the vehicle's motion trajectory. In addition, since the converged trajectory parameters, sensor extrinsic parameters, and vehicle localization parameters are synchronously updated and jointly output to the four-dimensional Gaussian sputtering model, dynamic scene reconstruction can be performed based on the three types of parameters that are coordinated with each other. This reduces sensor projection misalignment, vehicle position drift, and trajectory temporal discontinuity, and improves the consistency of dynamic scene reconstruction.

[0034] The multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction in this example embodiment will be further explained below.

[0035] In step S101, the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term constraining the temporal continuity of the trajectory are obtained; wherein, the trajectory optimization loss term corresponds to the set of trajectory parameters to be optimized, the extrinsic parameter calibration loss term corresponds to the set of sensor extrinsic parameters to be optimized, the localization optimization loss term corresponds to the vehicle localization parameters to be optimized, and the trajectory smoothing regularization term is obtained based on the change in pose parameters of adjacent frames in the trajectory parameter set.

[0036] The trajectory optimization loss term represents the loss amount used to evaluate the degree of difference between the trajectory parameter set and the expected vehicle motion trajectory. The trajectory parameter set can represent a set of parameters used to describe the pose state of the vehicle or dynamic scene object at multiple time points. The extrinsic parameter calibration loss term represents the loss amount used to evaluate the degree of difference between the sensor extrinsic parameter set and the sensor observation projection relationship. The sensor extrinsic parameter set can represent a set of parameters used to describe the transformation relationship between different sensor coordinate systems. The localization optimization loss term represents the loss amount used to evaluate the degree of difference between the vehicle's localization parameters and the vehicle's actual pose. The vehicle's localization parameters can represent parameters used to describe the vehicle's position and attitude in the global coordinate system. The trajectory smoothing regularization term represents a regularization amount used to constrain the degree of change in pose parameters between adjacent frames.

[0037] For example, corresponding loss terms can be obtained from the trajectory optimization module, extrinsic parameter calibration module, and localization optimization module, respectively, and trajectory smoothing regularization terms can be determined based on the variation relationship between pose parameters of adjacent frames in the trajectory parameter set. Since loss terms associated with the three types of parameters to be optimized and trajectory temporal constraints are obtained simultaneously, a loss basis can be provided for the unified optimization of the three types of parameters in the future, and the unconstrained changes of trajectory parameters in the time series can be reduced.

[0038] In step S102, the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term are weighted and summed according to their respective weight coefficients to obtain a global unified loss function.

[0039] The weighting coefficients can be represented by coefficients used to adjust the contribution of the corresponding loss term to the overall optimization objective. The global unified loss function can be represented by an objective function composed of multiple loss terms, used to uniformly evaluate the overall optimization state of trajectory parameters, sensor extrinsic parameters, and vehicle positioning parameters.

[0040] Specifically, corresponding weight coefficients can be configured for the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term. Each loss term is then combined with its corresponding weight coefficient, and the results are summarized to form a globally unified loss function. Since the four loss terms are incorporated into the same loss metric framework, it reduces objective conflicts arising from different parameters being updated based on independent optimization objectives, and improves the coordination between the optimization objectives of the three types of parameters.

[0041] In step S103, the trajectory parameter set, the sensor extrinsic parameter set, and the vehicle positioning parameters are aggregated into a single parameter vector.

[0042] Among them, a single parameter vector can represent a data structure that uniformly carries trajectory parameters, sensor extrinsic parameters, and vehicle positioning parameters according to a preset arrangement. Parameter aggregation can represent the processing procedure of organizing multiple types of parameters to be optimized, which were originally stored or managed separately, into the same parameter space to be optimized.

[0043] Specifically, the three types of parameters—trajectory parameters, sensor extrinsic parameters, and vehicle positioning parameters—can be organized into a unified parameter representation according to a preset order, and the correspondence between each parameter segment in a single parameter vector and its corresponding parameter type can be recorded. By incorporating the three types of parameters into the same parameter vector, a unified data foundation can be provided for subsequent calculation and updating of the three types of parameters using the same optimization process, avoiding the three types of parameters entering different optimization processes separately.

[0044] In step S104, a single optimizer is used to backpropagate the global unified loss function, and the trajectory parameters, extrinsic parameters, and vehicle positioning parameters in the single parameter vector are updated synchronously based on the gradient obtained from the backpropagation.

[0045] In this context, a single optimizer can represent an optimization tool that manages and updates various parameters in a single parameter vector during the same optimization process. Backpropagation can represent the process of calculating the gradients of each parameter to be optimized by working backwards along the parameter computation relationship based on a globally unified loss function. The gradient can represent the direction and degree of change of the globally unified loss function relative to the corresponding parameter. Synchronous update can represent performing the same round of updates on the three types of parameters based on the gradients obtained in the same backpropagation.

[0046] Specifically, a globally unified loss function can be used as the starting point for backpropagation to obtain its gradients relative to trajectory parameters, sensor extrinsic parameters, and vehicle localization parameters. Then, a single optimizer adjusts the corresponding parameters in the single parameter vector based on each gradient. Since the three types of parameters are updated synchronously based on the gradients generated by the same globally unified loss function, the repeated perturbations of previous optimization results by subsequent parameter updates during the step-by-step optimization process can be reduced, which is conducive to the convergence of the three types of parameters to a mutually coordinated state.

[0047] In step S105, during the synchronous update process, the weight coefficients corresponding to each loss term are dynamically adjusted according to the gradient convergence state of the parameters corresponding to each loss term; wherein, the trajectory optimization loss term and the trajectory smoothing regularization term correspond to the trajectory parameter set.

[0048] The gradient convergence state represents the stability or convergence progress of the gradient of the corresponding parameter as it changes during the optimization process. Dynamic adjustment indicates that the weight coefficients are changed according to the current optimization state, rather than using fixed values ​​throughout the optimization process. The parameters corresponding to each loss term include: the trajectory optimization loss term and trajectory smoothing regularization term correspond to the trajectory parameter set; the extrinsic parameter calibration loss term corresponds to the sensor extrinsic parameter set; and the positioning optimization loss term corresponds to the vehicle positioning parameters.

[0049] Specifically, during parameter synchronization updates, the gradients of the trajectory optimization loss term with respect to the trajectory parameter set, the extrinsic parameter calibration loss term with respect to the sensor extrinsic parameter set, the localization optimization loss term with respect to the vehicle localization parameters, and the trajectory smoothing regularization term with respect to the trajectory parameter set can be statistically analyzed separately. The weight coefficients of the corresponding loss terms are then adjusted based on the gradient convergence state of their respective parameters. Since the weight coefficients for the four loss terms are adjusted according to the gradient convergence state of their corresponding parameters, this process can compensate for differences in gradient magnitude between different loss terms, preventing loss terms with smaller gradient magnitudes from being masked by other loss terms in the globally unified loss function.

[0050] In step S106, the synchronously updated converged trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters are output to the four-dimensional Gaussian sputtering model for dynamic scene reconstruction.

[0051] Among them, the four-dimensional Gaussian sputtering model can represent a model that uses Gaussian primitives with spatial and temporal attributes to represent and render dynamic scenes. Synchronous update convergence can represent the state in which trajectory parameters, sensor extrinsic parameters, and vehicle positioning parameters reach a preset convergence condition after multiple rounds of synchronous updates. Dynamic scene reconstruction can represent the process of restoring the spatial structure of a scene and its temporal changes based on scene information from multiple time points.

[0052] Specifically, the three types of parameters that have reached convergence can be used as input parameters for the four-dimensional Gaussian sputtering model, enabling the model to perform dynamic scene representation and reconstruction based on the updated trajectory relationship, sensor observation relationship, and vehicle pose relationship. Since the three types of parameters are simultaneously optimized under a globally unified loss constraint and then input into the four-dimensional Gaussian sputtering model, the inconsistency between the trajectory, sensor projection relationship, and vehicle localization relationship can be reduced, thus improving the temporal consistency of the dynamic scene reconstruction results.

[0053] The following is a detailed explanation of the contents of steps S101 to S106.

[0054] The overall architecture for multi-parameter collaborative optimization in this disclosure can be found in [reference]. Figure 2 .like Figure 2 As shown, the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term are input into the adaptive weight coefficient module. The adaptive weight coefficient module adjusts the weight coefficients corresponding to each loss term based on the gradient convergence state of the parameters corresponding to each loss term, and then performs a weighted fusion of the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term based on the adjusted weight coefficients to obtain a globally unified loss function.

[0055] The global unified loss function is further input into a single optimizer. The single optimizer performs backpropagation on the global unified loss function to obtain the gradients of the trajectory parameter set, the sensor extrinsic parameter set, and the vehicle localization parameters. In the same parameter update, the trajectory parameter set, the sensor extrinsic parameter set, and the vehicle localization parameters are updated synchronously, so that the three types of parameters are adjusted collaboratively under the constraint of the same global unified loss function.

[0056] The synchronously updated trajectory parameter set, sensor extrinsic parameter set, and vehicle localization parameters are output to the four-dimensional Gaussian sputtering model. Specifically, the trajectory parameter set is used to update the temporal variation relationships in the four-dimensional Gaussian sputtering model, the sensor extrinsic parameter set is used to update the projection relationships between each sensor observation and the scene representation, and the vehicle localization parameters are used to update the vehicle's pose relationship in the global coordinate system.

[0057] The four-dimensional Gaussian sputtering model is re-rendered based on the synchronously updated three types of parameters. Following the parameter feedback / re-rendering path, the re-rendering results are fed back to the loss term acquisition side for recalculating the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term. Subsequently, the adaptive weight coefficient module readjusts the weight coefficients corresponding to each loss term, and the single optimizer synchronously updates the three types of parameters again. This forms an iterative optimization closed loop between loss term acquisition, weight adjustment, global unified loss function construction, parameter synchronous update, and model re-rendering.

[0058] In some embodiments, the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term are weighted and summed according to their respective weight coefficients to obtain a globally unified loss function, which may include: The first step is to multiply the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term by their respective weight coefficients.

[0059] The second step is to sum the results of each multiplication to obtain a globally unified loss function.

[0060] For example, the globally unified loss function can be expressed as: in, Represents a globally uniform loss function. This represents the trajectory optimization loss term. This indicates the external parameter calibration loss item. This represents the positioning optimization loss term. This represents the trajectory smoothing regularization term; , , and These represent the weight coefficients corresponding to the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term, respectively.

[0061] Each weight coefficient can satisfy the following normalization constraint: in, This represents the preset total weight coefficient, and its value is a fixed value greater than zero.

[0062] Specifically, in each iteration, the current values ​​of the four loss terms can be obtained, each loss term is multiplied by its corresponding weight coefficient, and the four products are summed. In this way, the optimization objectives corresponding to the trajectory parameters, sensor extrinsic parameters, and vehicle positioning parameters, as well as the trajectory temporal continuity constraints, are incorporated into the same loss metric framework. Since all loss terms together constitute a globally unified loss function, it can reduce the objective conflicts that arise when different parameters are optimized using independent loss functions, and improve the coordination between the optimization objectives of the three types of parameters.

[0063] For example, the process of constructing a globally unified loss function can be found in [reference needed]. Figure 3 .like Figure 3 As shown, the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term are input into the weighted summation stage. In the weighted summation stage, each loss term is multiplied by its corresponding weight coefficient, and the results of the multiplications are accumulated to obtain the globally unified loss function.

[0064] The trajectory optimization loss term, extrinsic parameter calibration loss term, and positioning optimization loss term characterize the optimization states corresponding to the trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters, respectively. The trajectory smoothing regularization term constrains the pose changes between adjacent frames in the trajectory parameter set. By incorporating these four terms into a globally unified loss function, the optimization objectives of the three types of parameters and the trajectory temporal continuity constraints can participate in subsequent parameter updates under the same loss metric.

[0065] In some embodiments, the weighting coefficients satisfy normalization constraints, which may include: The original weight values ​​corresponding to each weight coefficient are normalized so that the sum of the weight coefficients obtained after normalization is 1.

[0066] Here, the original weight values ​​can represent intermediate weight values ​​determined according to preset configurations or the current optimization state, which have not yet undergone normalization. Normalization can refer to the process of scaling the original weight values ​​according to their relative magnitudes.

[0067] The original weights corresponding to the four loss terms can be expressed as follows: , , and For example, normalization can be performed according to the proportion of each original weight value in the sum of the original weight values: After normalization, the weight coefficients satisfy: The above-described normalization method is merely an example; other normalization methods that ensure the sum of all weight coefficients equals 1 can also be used. Because the weight coefficients are converted to a uniform numerical scale, the impact of changes in the overall magnitude of the original weight values ​​on the numerical range of the globally uniform loss function can be reduced.

[0068] In a further embodiment, normalizing the original weight values ​​may include: Apply the Softmax function to each original weight value to obtain the weight coefficients that sum to 1.

[0069] For example, the four weighting coefficients can be expressed as follows: in, This represents an exponential function with the natural constant as its base. The Softmax function can convert raw weight values ​​of arbitrary real numbers into positive weight coefficients while preserving the relative magnitudes of different raw weight values. This facilitates the differentiated configuration of each loss term's contribution to the globally unified loss function according to its optimization state.

[0070] In some embodiments, the trajectory smoothing regularization term is obtained based on the change in pose parameters between adjacent frames in the trajectory parameter set, and may include: The first step is to calculate the second-order difference based on the pose parameters of three consecutive frames in the trajectory parameter set. The second-order difference represents the acceleration of the pose transformation between adjacent frames.

[0071] The second-order difference can represent the difference between two adjacent pose changes. The acceleration of pose changes between adjacent frames can represent the degree of change in pose change between consecutive frames, and is not limited to the actual acceleration of the vehicle in physical space.

[0072] For example, the set of trajectory parameters in the current iteration can be represented as ,in, Indicates the first Frame pose parameters Indicates the frame number. This represents the total number of frames corresponding to the trajectory parameter set.

[0073] For the Frame, First Frame and the The frame can be calculated using the following formula: The second-order difference of the pose corresponding to the frame: in, Indicates the first The second-order difference of the pose corresponding to the frame The range of values ​​is .

[0074] The second step is to obtain the trajectory smoothing regularization term based on the sum of the squares of the moduli of the second-order differences corresponding to each frame.

[0075] Specifically, the square of the magnitude of the second-order difference of the pose corresponding to each intermediate frame can be calculated separately, and the results can be accumulated: in, This represents the magnitude of the vector or pose difference component. The larger the second-order pose difference, the less smooth the pose change between consecutive frames, and the larger the corresponding trajectory smoothing regularization term. Since the trajectory smoothing regularization term can increase the global uniform loss under abrupt trajectory changes, its participation in parameter updates can suppress excessive pose shifts in individual frames and improve the temporal continuity of the vehicle's trajectory.

[0076] In a further embodiment, the pose parameters include translational and rotational components. Calculating the second-order difference based on the pose parameters of three consecutive frames from the trajectory parameter set can include: The first step is to calculate the second-order difference of the translation components in the vector space for three consecutive frames, thus obtaining the translation second-order difference.

[0077] The translation component can represent the vehicle's position component in the preset coordinate system. For the... The frame, the second-order difference of translation, can be expressed as: in, Indicates the first The translation vector of the frame. Indicates the first The second-order difference of the translation corresponding to the frame.

[0078] The second step is to calculate the second-order difference of the rotation components of three consecutive frames in the tangent space of the rotation group to obtain the rotation second-order difference.

[0079] The rotation group can be represented as a nonlinear parameter space consisting of three-dimensional rotation transformations. The tangent space of the rotation group can be represented as a linear space used to describe the rotation increments in vector form within the local neighborhood of the rotation group.

[0080] Specifically, we can first calculate the first... Frame to the Relative rotation of frames and the first Frame to the The relative rotations of the frames are then mapped to the tangent space of the rotation group, and the difference between them is calculated: in, Indicates the first The rotation component of the frame, express inverse transform, This represents the logarithmic mapping from the three-dimensional rotation group to its corresponding tangent space. Indicates the first The second-order difference of the rotation corresponding to the frame.

[0081] The third step is to perform a weighted summation of the squares of the magnitudes of the translational second-order difference and the rotational second-order difference according to the rotation term weights, so as to obtain the second-order difference evaluation results for three consecutive frames.

[0082] Based on the second-order difference evaluation results of each frame, the trajectory smoothing regularization term can be obtained according to the following formula: in, This represents the smoothing coefficient, used to adjust the overall strength of the trajectory smoothing constraint; This represents the rotation term weight, used to adjust the contribution of the rotation second-order difference relative to the translation second-order difference.

[0083] For example, It can be set to 0.01. It can be set to 0.5. The above values ​​are for illustrative purposes only and do not constitute a limitation on the embodiments of this disclosure.

[0084] After calculating the trajectory smoothing regularization term, it can be compared with the corresponding weighting coefficients. The components are multiplied and then incorporated into a globally unified loss function. Since the translation and rotation components are calculated using second-order differences in spaces that are compatible with their parameter properties, both vehicle position and attitude changes can be constrained simultaneously, and unreasonable rotation calculation results caused by directly performing linear differences on the rotation matrix can be avoided.

[0085] In some embodiments, aggregating the trajectory parameter set, the sensor extrinsic parameter set, and the vehicle positioning parameters into a single parameter vector may include: The trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters are concatenated to obtain a single parameter vector to be optimized. This single parameter vector simultaneously carries the trajectory parameters, extrinsic parameters, and vehicle positioning parameters.

[0086] Among them, splicing can represent the process of organizing different parameter sets into the same parameter structure in a preset parameter arrangement order.

[0087] For example, a single parameter vector can be represented as: in, Represents a single-parameter vector. This represents the sub-vector of parameters corresponding to the set of trajectory parameters. This represents a sub-vector of parameters corresponding to the set of sensor extrinsic parameters. This represents the parameter subvector corresponding to the vehicle's positioning parameters.

[0088] Specifically, the starting and ending positions of each parameter sub-vector within a single parameter vector, as well as the parameter dimension, can be recorded. After obtaining the gradient corresponding to a single parameter vector, different gradient components can be mapped to their respective parameter sub-vectors according to the aforementioned positional relationships. Since the three types of parameters are incorporated into the same parameter structure to be optimized, a data foundation can be provided for a single optimizer to uniformly manage the gradients and update states of the three types of parameters.

[0089] In some embodiments, backpropagation of a global uniform loss function is performed using a single optimizer, and the trajectory parameters, extrinsic parameters, and vehicle localization parameters in a single parameter vector are synchronously updated based on the gradient obtained from the backpropagation. This may include: The first step is to perform a backpropagation on the global unified loss function to obtain the gradients of the global unified loss function with respect to the trajectory parameters, extrinsic parameters, and vehicle localization parameters.

[0090] Specifically, gradient backpropagation can be performed along the computational relationships between the global unified loss function and the four loss terms, as well as between each loss term and its corresponding parameter to be optimized, to obtain: in, , and The gradients of the global uniform loss function with respect to the trajectory parameters, extrinsic parameters, and vehicle localization parameters are represented in that order. This represents the gradient calculation operator.

[0091] The second step involves using a single optimizer to synchronously update the trajectory parameters, extrinsic parameters, and vehicle positioning parameters in the same parameter update cycle, based on the gradients of the trajectory parameters, extrinsic parameters, and vehicle positioning parameters.

[0092] A single parameter update can represent a single optimizer updating the three types of parameters based on the gradients obtained in the same round of backpropagation, before calculating the next round of the global unified loss function. The single optimizer can aggregate the three types of gradients into a gradient vector according to their arrangement in the single parameter vector, and adjust the corresponding parameter segments in the single parameter vector accordingly.

[0093] Since the gradients corresponding to the three types of parameters are all obtained by the same global unified loss function through one backpropagation and are updated in the same round, the time difference caused by updating different parameters in sequence can be reduced, and the optimization results of the parameters updated later can be avoided from being repeatedly destroyed by the parameters updated earlier.

[0094] In a further embodiment, the single optimizer can be the Adam optimizer.

[0095] The Adam optimizer can represent an optimizer that adaptively determines parameter update amounts based on gradient-based first-moment and second-moment estimation. When initializing the Adam optimizer, a single parameter vector can be registered as a whole as the object to be optimized.

[0096] For example, the parameter update process of the Adam optimizer can be represented as: in, Indicates the current iteration number. and They represent the first Single parameter vector before and after the update. Indicates the first The aggregated gradient vector obtained from the next iteration. This represents the first moment estimate of the gradient. This represents the second-order moment estimate of the gradient. and These represent the first-order moment estimate and the second-order moment estimate after bias correction, respectively. This represents the first-order moment attenuation coefficient. This represents the second-order moment attenuation coefficient. Indicates the learning rate. This indicates a small optimizer used to improve numerical stability.

[0097] For example, It can be set to , It can be set to 0.9. It can be set to 0.999. It can be set to The values ​​mentioned above are for illustrative purposes only.

[0098] Because the Adam optimizer can adjust the update magnitude of different parameters based on the first and second moments of the gradient of each parameter, it can improve the stability of the synchronous update process even when the numerical scales or gradient magnitudes of the three types of parameters are different.

[0099] In some embodiments, during the synchronous update process, the values ​​of each weight coefficient are dynamically adjusted based on the gradient convergence state of the parameters corresponding to the trajectory optimization loss term, extrinsic parameter calibration loss term, and localization optimization loss term. This may include: The first step is to calculate the gradient statistics of the parameters corresponding to each loss term according to the set iteration period.

[0100] The set iteration period represents the number of parameter updates between two adjacent weight adjustments. Gradient statistics represent statistical results reflecting the magnitude or change state of the gradient of the corresponding parameter. The convergence state monitor acquires the gradient of the parameters corresponding to each loss term after each backpropagation, and, upon reaching the set iteration period, calculates the gradient statistics of the parameters corresponding to the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term, respectively. The trajectory optimization loss term and trajectory smoothing regularization term correspond to the trajectory parameter set, the extrinsic parameter calibration loss term corresponds to the sensor extrinsic parameter set, and the localization optimization loss term corresponds to the vehicle localization parameters.

[0101] The second step is to adjust the corresponding weight coefficients based on the gradient statistics, and keep the weight coefficients unchanged between two adjacent adjustments.

[0102] Specifically, when the weight adjustment time is reached, a new weight coefficient can be determined based on the gradient statistics in the current iteration cycle; after the adjustment is completed, the weight coefficient determined in this iteration cycle is used continuously until the weight adjustment time is reached again.

[0103] The dynamic adjustment process of the weighting coefficients can be found in [reference needed]. Figure 4 .like Figure 4 As shown, firstly, in step S201, gradient statistics are calculated according to the set iteration cycle. Specifically, in each iteration cycle, the gradients of the parameters corresponding to the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term are collected, and when the weight adjustment time is reached, the gradients in the current iteration cycle are statistically analyzed to obtain gradient statistics that reflect the current convergence state.

[0104] Subsequently, in step S202, the original weight values ​​are determined according to the gradient convergence state. Specifically, the relative gradient magnitude corresponding to each loss term can be determined based on the gradient statistics of the parameters corresponding to each loss term. Then, according to the principle that the original weight value is inversely proportional to the relative gradient magnitude, the original weight value corresponding to each loss term is calculated respectively, so that the original weight value of different loss terms can reflect their current optimization state.

[0105] Next, in step S203, the original weight values ​​are normalized. Specifically, a normalization method can be applied to each original weight value to convert it into an adjusted weight coefficient, so that each weight coefficient meets the preset normalization constraint, thereby facilitating the subsequent construction of the global unified loss function according to a unified scale for each loss term.

[0106] Finally, in step S204, the adjusted weight coefficients are obtained and remain unchanged between adjacent adjustments. That is, after the weight adjustment is completed in the current iteration cycle, the weight coefficients obtained in this adjustment are continuously used in the weighted summation of each loss term until the next new weight adjustment time is reached. Figure 4 The processing shown can adjust the weight coefficients periodically and keep them stable within the period, thereby reducing the disturbance caused by frequent weight changes to the global unified loss function and parameter update process.

[0107] For example, 50 iterations can be set as an iteration cycle, with the weight coefficients updated sequentially at the 50th, 100th, and 150th iterations. Between two weight adjustments, the weight coefficients remain unchanged. Because the weight coefficients are updated periodically, rather than changing frequently with each iteration, the interference of weight fluctuations on the global uniform loss function and the direction of parameter updates can be reduced.

[0108] The periodic update control process for the weighting coefficients can be found in [reference needed]. Figure 5 .like Figure 5 As shown, in step S301, the mean and variance of the gradients of the parameters corresponding to each loss term are statistically analyzed according to the set iteration period to obtain the gradient statistical results of the parameters corresponding to each loss term in the current iteration period.

[0109] Subsequently, in step S302, based on the gradient statistics obtained in step S301, the original weight values ​​corresponding to each loss term are calculated according to the principle of inverse proportionality to the gradient magnitude. The smaller the relative gradient magnitude, the larger the corresponding original weight value; the larger the relative gradient magnitude, the smaller the corresponding original weight value.

[0110] Next, in step S303, Softmax normalization is applied to each original weight value to obtain each weight coefficient that sums to 1, and the normalized weight coefficients are used to weight the corresponding loss terms.

[0111] Next, in step S304, it is determined whether the update cycle has been reached. If the update cycle has been reached, return to step S301, recalculate the mean and variance of the gradients of the parameters corresponding to each loss term in the new iteration cycle, and recalculate each weight coefficient; if the update cycle has not been reached, execute step S305, and keep each weight coefficient unchanged in the current cycle.

[0112] After step S305, parameter synchronization updates continue, and steps S301 to S304 are executed again when the next update cycle is reached. This allows for updating each weight coefficient according to the set iteration cycle and maintaining the stability of each weight coefficient between adjacent updates, reducing the disturbance caused by frequent changes in weight coefficients to the global unified loss function and parameter update process.

[0113] In a further embodiment, the gradient statistics include the mean and variance of the gradient of the corresponding parameters. Adjusting the corresponding weight coefficients based on each gradient statistic may include: The first step is to determine the relative gradient magnitude of each loss term based on the mean of the gradients of the parameters corresponding to the trajectory optimization loss term, the extrinsic parameter calibration loss term, the localization optimization loss term, and the trajectory smoothing regularization term.

[0114] For example, the relative gradient magnitude corresponding to the trajectory optimization loss term can be expressed as: The relative gradient magnitude corresponding to the extrinsic calibration loss term can be expressed as: The relative gradient magnitude corresponding to the localization optimization loss term can be expressed as: The relative gradient magnitude corresponding to the trajectory smoothing regularization term can be expressed as: in, , , and The terms represent the relative gradient magnitudes of the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term, respectively. This indicates the calculation of the mean. This indicates taking the absolute value of each component in the gradient.

[0115] The variance of the gradient of the corresponding parameter can be determined by the following formula: in, Used to indicate trajectory optimization loss term, extrinsic parameter calibration loss term, positioning optimization loss term, or trajectory smoothing regularization term. Indicates the first The variance of the gradient of the parameters corresponding to each loss term. This indicates variance calculation.

[0116] The gradient mean reflects the overall magnitude of the gradient generated by the corresponding loss term within the current iteration period, while the gradient variance reflects the degree of gradient fluctuation. When the gradient mean decreases and the gradient variance tends to stabilize, it indicates that the corresponding parameters are gradually approaching a stable state.

[0117] The second step is to calculate the original weight value corresponding to each loss term, based on the principle that the original weight value is inversely proportional to the relative gradient magnitude.

[0118] The third step is to normalize the original weight values ​​to obtain the adjusted weight coefficients, so that the parameters corresponding to the loss terms with relatively small gradient magnitudes obtain larger weight coefficients.

[0119] Since loss terms with relatively small gradient magnitudes correspond to larger original weight values, their contribution to the global unified loss function can be increased in subsequent iterations, reducing the situation where a certain loss term is masked by other loss terms for a long time due to differences in the gradient magnitudes of different parameters.

[0120] In a further embodiment, calculating the original weight value corresponding to each loss term according to the principle that the original weight value is inversely proportional to the relative gradient magnitude can include: For any loss term, the proportional constant is divided by the sum of the relative gradient magnitude of the loss term and a preset small quantity to obtain the original weight value corresponding to the loss term.

[0121] For example, the original weight values ​​corresponding to the three loss terms can be determined according to the following formula: in, , , and These represent the original weight values ​​corresponding to the trajectory optimization loss term, the extrinsic parameter calibration loss term, the localization optimization loss term, and the trajectory smoothing regularization term, respectively. This represents the scaling constant, used to control the overall numerical scale of the original weight values; This indicates a preset small amount, used to prevent the denominator from being zero when the relative gradient magnitude is zero.

[0122] For example, It can be set to When the relative gradient magnitude is small, the corresponding original weight value increases; when the relative gradient magnitude is large, the corresponding original weight value decreases. After obtaining the original weight values, the aforementioned normalization process can be used to obtain the weight coefficients corresponding to the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term, respectively.

[0123] By adding a pre-defined small amount to the denominator, the validity of the original weight value calculation can be maintained even if a certain relative gradient magnitude is close to zero, thus improving the numerical stability of the weight adjustment process.

[0124] In some embodiments, before the synchronization update begins, the weight coefficients can be initialized to equal values.

[0125] Specifically, when sufficient historical gradient data reflecting the gradient convergence state is not yet available, the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term can be made to have the same contribution ratio in the early stages of optimization.

[0126] For example, it can be set as follows: Since the initial values ​​of the four weight coefficients are equal, the optimization will not favor any loss term in the early stage, which can provide a relatively balanced initial condition for adjusting the weight coefficients according to the gradient convergence state in the later stage.

[0127] In some embodiments, synchronously updating the converged trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters and outputting them to the four-dimensional Gaussian sputtering model may include: The first step is to synchronize the trajectory parameter set to the temporal deformation field of the four-dimensional Gaussian sputtering model.

[0128] The temporal deformation field can represent the model portion used to describe the relationship between the position, orientation, or other spatial properties of Gaussian elements and time. After synchronizing the trajectory parameter set to the temporal deformation field, the four-dimensional Gaussian sputtering model can determine the dynamic scene deformation relationship at different times based on the updated trajectory parameters.

[0129] The second step is to synchronize the sensor extrinsic parameter set to the projection matrix of each sensor.

[0130] The projection matrix represents the matrix used to project observation data from the sensor coordinate system onto the target coordinate system or the imaging plane. The projection matrices of each sensor can be updated based on the rotation and translation parameters in the sensor's extrinsic parameter set, allowing each sensor's observations to participate in dynamic scene reconstruction according to the updated coordinate transformation relationship.

[0131] The third step is to synchronize the vehicle's positioning parameters to the vehicle's pose representation in the global coordinate system.

[0132] The vehicle pose representation can be a data structure used to record the vehicle's position and orientation in the global coordinate system. By synchronizing the vehicle's localization parameters, the overall pose of the vehicle and its sensors in the global scene can be determined.

[0133] Since the three types of parameters are synchronized to the model parts in the four-dimensional Gaussian sputtering model that correspond to their physical meanings, the temporal deformation of the scene, the sensor projection relationship, and the global pose of the vehicle can be kept coordinated.

[0134] In some embodiments, after outputting the synchronously updated trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters to the four-dimensional Gaussian sputtering model, the method may further include: The four-dimensional Gaussian sputtering model is triggered to re-render using the synchronized trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters. The re-rendered results are then fed back to calculate the trajectory optimization loss term, extrinsic parameter calibration loss term, and positioning optimization loss term for the next iteration.

[0135] Among them, re-rendering can refer to the process of the four-dimensional Gaussian sputtering model regenerating the scene image and corresponding scene representation of the target viewpoint or target time based on the current parameters.

[0136] Specifically, after each parameter update, the current trajectory parameter set can be periodically synchronized to the temporal deformation field, the current sensor extrinsic parameter set can be periodically synchronized to the projection matrix of each sensor, and the current vehicle positioning parameters can be periodically synchronized to the vehicle pose representation. Subsequently, the four-dimensional Gaussian sputtering model is triggered to perform the next round of rendering.

[0137] The trajectory optimization module can recalculate the trajectory optimization loss term based on the re-rendered results and trajectory-related geometric information; the extrinsic parameter calibration module can recalculate the extrinsic parameter calibration loss term based on the geometric relationship between the re-rendered results and multi-sensor observations; and the localization optimization module can recalculate the localization optimization loss term based on the re-rendered results and the vehicle's pose relationship in the global coordinate system. It can also recalculate the trajectory smoothing regularization term based on the updated trajectory parameter set.

[0138] In a complete iteration, the following processes can be performed sequentially: obtain the loss terms calculated by the three external modules and calculate the trajectory smoothing regularization term; calculate the global unified loss function; perform a backpropagation on the global unified loss function; synchronously update the single parameter vector through the Adam optimizer; adjust the weight coefficients when the set iteration period is reached; synchronize the updated parameters to the four-dimensional Gaussian sputtering model and re-render.

[0139] The above process can be repeated until the global unified loss function reaches the preset convergence condition or the maximum number of iterations is reached. For example, when the decrease in the global unified loss function is less than [a certain value] in 200 consecutive iterations... At this point, it can be determined that the synchronous update has converged; or, the update can be stopped when the number of iterations reaches 10,000. The above values ​​are for illustrative purposes only and do not constitute a limitation.

[0140] Since the re-rendering results can reflect the actual impact of the current three types of parameters on the dynamic scene reconstruction results and are fed back to the next loss calculation, an optimization closed loop can be formed between parameter updates, model synchronization, re-rendering, loss calculation and further updates.

[0141] In other embodiments, the weight coefficients are dynamically adjusted based on the gradient convergence state of the parameters corresponding to the trajectory optimization loss term, extrinsic parameter calibration loss term, and localization optimization loss term. This can also be achieved using a strategy based on uncertain parameters, including: The first step is to configure uncertainty parameters for the trajectory optimization loss term, the extrinsic parameter calibration loss term, and the positioning optimization loss term, respectively.

[0142] Among them, the uncertainty parameter can represent the fluctuation level, reliability, or optimization difficulty of the corresponding loss term in the current optimization stage. The uncertainty parameters corresponding to the trajectory optimization loss term, extrinsic parameter calibration loss term, and positioning optimization loss term can be expressed as follows: , and .

[0143] The second step is to determine the original weight value of the corresponding loss term based on each uncertainty parameter. The original weight value is inversely proportional to the square of the corresponding uncertainty parameter.

[0144] For example, the original weight values ​​can be determined according to the following formula: The third step is to normalize the original weight values ​​to obtain the adjusted weight coefficients.

[0145] In this implementation, loss terms with higher uncertainty correspond to smaller original weight values, while loss terms with lower uncertainty correspond to larger original weight values. Because this implementation can adjust the optimization contribution of each loss term based on the difference in uncertainty, it is suitable for scenarios where different loss terms have significantly different degrees of volatility or reliability.

[0146] In one extended implementation, uncertainty parameters can also be configured for the trajectory smoothing regularization term. And determine its original weight value according to the following formula: in, This represents the uncertainty parameter corresponding to the trajectory smoothing regularization term. Therefore, a unified uncertainty estimation method can be used to determine the original weight values ​​of the four loss terms and then normalize them.

[0147] In other embodiments, in application scenarios where computing resources are limited or the requirements for trajectory smoothness are low, the weight coefficients corresponding to the trajectory smoothing regularization term can be set to zero, and the trajectory optimization loss term, extrinsic parameter calibration loss term, and localization optimization loss term can be weighted and summed according to their respective weight coefficients to obtain a globally unified loss function.

[0148] At this point, you can set: The globally unified loss function can be simplified to: By setting the weight coefficients corresponding to the trajectory smoothing regularization term to zero, the computational overhead incurred by the trajectory smoothing regularization term participating in the calculation of the global unified loss function and backpropagation can be omitted. This implementation no longer provides explicit second-order difference constraints on the trajectory, but can still perform collaborative optimization of trajectory parameters, sensor extrinsic parameters, and vehicle positioning parameters through unified weighting of the three types of loss terms and synchronous updating of the three types of parameters.

[0149] In other embodiments, while maintaining a single optimizer, the participation of various parameters in synchronous updates can be controlled according to different optimization stages, including: The first step is to fix the external parameters in the early optimization stage and update the trajectory parameters and vehicle positioning parameters simultaneously.

[0150] Here, fixing the extrinsic parameters means preserving the current values ​​of the sensor extrinsic parameters, preventing a single optimizer from modifying the sensor extrinsic parameters based on their gradients in the current stage. For example, these values ​​can be fixed in the first 1000 iterations. Update only and .

[0151] The second step is to remove the fixation of external parameters during the mid-term optimization stage and simultaneously update the trajectory parameters, external parameters, and vehicle positioning parameters.

[0152] For example, between the 1000th and 5000th iterations, all three types of parameters can participate in backpropagation and parameter updates. At this point, the single optimizer synchronously updates the single parameter vector based on the gradients of the three types of parameters using the globally unified loss function.

[0153] The third step is to reduce the learning rate of the single optimizer in the later stage of optimization and to fine-tune the trajectory parameters, extrinsic parameters, and vehicle positioning parameters.

[0154] Fine-tuning can refer to adjusting the three types of parameters with smaller update increments compared to the earlier and middle stages. For example, after the 5000th iteration, the learning rate could be adjusted from... Reduced to And continue to update the three types of parameters synchronously.

[0155] Since the sensor extrinsic parameters are fixed in the early stage of optimization to ensure relatively accurate initial estimates, the instability caused by the simultaneous large changes of multiple parameters in the early stage of optimization can be reduced. After the fixation is removed in the middle stage, the three types of parameters can be adjusted in a coordinated manner under the same global unified loss function. In the later stage, reducing the learning rate can reduce parameter oscillations when approaching the convergence state.

[0156] In some embodiments, the trajectory optimization loss term, the extrinsic parameter calibration loss term, and the positioning optimization loss term are calculated by the external trajectory optimization module, the extrinsic parameter calibration module, and the positioning optimization module, respectively, and then input.

[0157] The external modules can represent functional modules that are independent of the global unified loss function construction, single parameter vector formation, and synchronous update process, and calculate loss terms according to corresponding evaluation rules. This embodiment of the disclosure can call the loss calculation interfaces provided by each external module to obtain the corresponding loss terms, without limiting the specific parameterization methods used within each external module.

[0158] The trajectory optimization loss term measures the consistency of pose transformations between adjacent frames and the geometric consistency between the trajectory and the reconstructed scene. The trajectory optimization module can calculate the trajectory optimization loss term based on the pose relationships between adjacent frames and the geometric correspondence between trajectory-related objects and the reconstructed scene.

[0159] The extrinsic calibration loss term is used to measure the geometric consistency of multi-sensor extrinsic parameters under a four-dimensional Gaussian sputtering model. The extrinsic calibration module can calculate the extrinsic calibration loss term based on the alignment degree of different sensor observations in a shared four-dimensional Gaussian scene representation. This extrinsic calibration loss term serves as a component input to a globally unified loss function, and the specific feature alignment method or loss construction method within it is not limited in the embodiments of this disclosure.

[0160] The localization optimization loss term measures the consistency of the vehicle's localization parameters in the global coordinate system. The localization optimization module can calculate the localization optimization loss term based on the spatial alignment between the vehicle's localization results and the four-dimensional Gaussian scene representation.

[0161] Since the three types of loss terms retain the evaluation meanings corresponding to trajectory optimization, external parameter calibration, and vehicle localization respectively, and are jointly input into the globally unified loss function, it is possible to implement unified coordination of the three types of parameters while retaining the professional evaluation capabilities of each external module.

[0162] In a further embodiment, the trajectory optimization loss term does not include pixel-level photometric loss, but includes adjacent frame pose transformation consistency loss and reprojection error loss.

[0163] Among these, pixel-level photometric loss can represent the loss determined based on the brightness or color difference of corresponding pixels in the rendered image and the observed image. Adjacent frame pose transformation consistency loss can represent the difference between the pose transformation and the expected motion relationship between adjacent frames. Reprojection error loss can represent the difference between the projected position and the corresponding observed position after projecting scene points, feature points, or other geometric objects onto the observation plane according to the current trajectory parameters.

[0164] The consistency loss of pose transformation between adjacent frames can be expressed as: The reprojection error loss can be expressed as For example, the trajectory optimization loss term can be determined according to the following formula: in, This represents the combination coefficients corresponding to the consistency loss of pose transformation between adjacent frames. These represent the combination coefficients corresponding to the reprojection error loss. The two combination coefficients mentioned above can be preset according to different loss ranges or evaluation requirements.

[0165] Specifically, the trajectory optimization module can obtain the pose transformation consistency loss between adjacent frames based on the deviation between the relative pose transformation and the reference motion relationship between consecutive frames; it can also obtain the reprojection error loss based on the deviation between the reprojection position of the trajectory-related geometric object and the corresponding observation position, and combine the two into a trajectory optimization loss term.

[0166] Since the trajectory optimization loss term is determined based on pose relationship and reprojection geometry, without introducing pixel-level photometric differences, the trajectory optimization in this embodiment can be kept within the geometric consistency constraint and maintain the technical boundary with other optimization schemes based on pixel-level photometric errors.

[0167] Furthermore, in the exemplary embodiments of this disclosure, a multi-parameter collaborative optimization system for four-dimensional Gaussian sputtering reconstruction is also provided. (Refer to...) Figure 6 As shown, the multi-parameter collaborative optimization system 600 for four-dimensional Gaussian sputtering reconstruction includes: a loss acquisition module 610, a loss fusion module 620, a parameter aggregation module 630, a synchronization update module 640, a weight adjustment module 650, and a parameter output module 660. Wherein: The loss acquisition module 610 can be used to acquire trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term constraining the temporal continuity of the trajectory; wherein, the trajectory optimization loss term corresponds to the set of trajectory parameters to be optimized, the extrinsic parameter calibration loss term corresponds to the set of sensor extrinsic parameters to be optimized, the localization optimization loss term corresponds to the vehicle localization parameters to be optimized, and the trajectory smoothing regularization term is obtained based on the change in pose parameters of adjacent frames in the trajectory parameter set; The loss fusion module 620 can be used to weight and sum the trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term and trajectory smoothing regularization term according to their respective weight coefficients to obtain a globally unified loss function. The parameter aggregation module 630 can be used to aggregate the trajectory parameter set, the sensor extrinsic parameter set, and the vehicle positioning parameters into a single parameter vector; The synchronous update module 640 can be used to backpropagate the global unified loss function with a single optimizer, and synchronously update the trajectory parameters, extrinsic parameters and vehicle localization parameters in the single parameter vector based on the gradient obtained from the backpropagation. The weight adjustment module 650 can be used to dynamically adjust the weight coefficients corresponding to each loss term according to the gradient convergence state of the parameters corresponding to each loss term during the synchronous update process; wherein, the trajectory optimization loss term and the trajectory smoothing regularization term correspond to the trajectory parameter set; The parameter output module 660 can be used to output the synchronously updated converged trajectory parameter set, sensor extrinsic parameter set and vehicle positioning parameters to the four-dimensional Gaussian sputtering model for dynamic scene reconstruction of the four-dimensional Gaussian sputtering model.

[0168] Furthermore, in an exemplary embodiment of this disclosure, an electronic device capable of implementing the above-described multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction is also provided.

[0169] Those skilled in the art will understand that various aspects of this disclosure can be implemented as a system, method, or program product. Therefore, various aspects of this disclosure can be embodied in the following forms: a completely hardware embodiment, a completely software embodiment (including firmware, microcode, etc.), or an embodiment combining hardware and software aspects, collectively referred to herein as a "circuit," "module," or "system."

[0170] The following reference Figure 7 To describe an electronic device 700 according to such an embodiment of the present disclosure. Figure 7 The electronic device 700 shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments disclosed herein.

[0171] like Figure 7 As shown, the electronic device 700 is manifested in the form of a general-purpose computing device. The components of the electronic device 700 may include, but are not limited to: at least one processing unit 710, at least one storage unit 720, a bus 730 connecting different system components (including storage unit 720 and processing unit 710), and a display unit 740.

[0172] The storage unit stores program code that can be executed by the processing unit 710, causing the processing unit 710 to perform the steps described in the "Detailed Description" section of this specification according to various exemplary embodiments of this disclosure. The storage unit 720 may include a readable medium in the form of a volatile storage unit, such as a random access memory (RAM) unit 721 and / or a cache memory unit 722, and may further include a read-only memory unit (ROM) unit 723.

[0173] The storage unit 720 may also include a program / utility 724 having a set (at least one) of program modules 725, including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0174] Bus 730 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the various bus structures.

[0175] Electronic device 700 can also communicate with one or more external devices 770 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 700, and / or with any device that enables electronic device 700 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 750. Furthermore, electronic device 700 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 760. As shown, network adapter 760 communicates with other modules of electronic device 700 via bus 730. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 700, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0176] Through the description of the above embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal system, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0177] In exemplary embodiments of this disclosure, a computer-readable storage medium is also provided, on which a program product capable of implementing the methods described above is stored. In some possible embodiments, various aspects of this disclosure may also be implemented as a program product including program code, which, when the program product is run on a terminal device, causes the terminal device to perform the steps according to various exemplary embodiments of this disclosure described in the "Detailed Description" section above.

[0178] The program product for implementing the above-described multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to embodiments of this disclosure can be a portable compact disk read-only memory (CD-ROM) and include program code, and can run on a terminal device, such as a personal computer. However, the program product of this disclosure is not limited thereto. In this document, the readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, system, or device.

[0179] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or any combination thereof. More specific examples (a non-exhaustive list) of readable storage media include: electrical connections with one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0180] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, system, or device.

[0181] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0182] Program code for performing the operations of this disclosure can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0183] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of this disclosure and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0184] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, touch terminal, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0185] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the claims.

[0186] It should be understood that this disclosure is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this disclosure is limited only by the appended claims.

Claims

1. A multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction, characterized in that, The method includes: The trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term constraining the temporal continuity of the trajectory are obtained. Among them, the trajectory optimization loss term corresponds to the set of trajectory parameters to be optimized, the extrinsic parameter calibration loss term corresponds to the set of sensor extrinsic parameters to be optimized, the localization optimization loss term corresponds to the vehicle localization parameters to be optimized, and the trajectory smoothing regularization term is obtained based on the change in pose parameters of adjacent frames in the trajectory parameter set. The trajectory optimization loss term, extrinsic parameter calibration loss term, localization optimization loss term, and trajectory smoothing regularization term are weighted and summed according to their respective weight coefficients to obtain a globally unified loss function. The trajectory parameter set, sensor extrinsic parameter set, and vehicle positioning parameters are aggregated into a single parameter vector; A single optimizer is used to backpropagate the global unified loss function, and the trajectory parameters, extrinsic parameters, and vehicle localization parameters in the single parameter vector are updated synchronously based on the gradient obtained from the backpropagation. During the synchronous update process, the weight coefficients corresponding to each loss term are dynamically adjusted according to the gradient convergence state of the parameters corresponding to each loss term; wherein, the trajectory optimization loss term and the trajectory smoothing regularization term correspond to the trajectory parameter set. The synchronized updated set of trajectory parameters, sensor extrinsic parameters, and vehicle positioning parameters are output to the four-dimensional Gaussian sputtering model for dynamic scene reconstruction.

2. The multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to claim 1, characterized in that, The step of weighting and summing the trajectory optimization loss term, the extrinsic parameter calibration loss term, the positioning optimization loss term, and the trajectory smoothing regularization term according to their respective weight coefficients to obtain a globally unified loss function includes: The trajectory optimization loss term, the extrinsic parameter calibration loss term, the positioning optimization loss term, and the trajectory smoothing regularization term are multiplied by their respective weight coefficients, and the results of the multiplications are summed to obtain the global unified loss function. Each of the weight coefficients satisfies the normalization constraint, and the sum of the weight coefficients is a constant.

3. The multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to claim 2, characterized in that, The weight coefficients satisfy normalization constraints, including: The original weight values ​​corresponding to each of the weight coefficients are normalized so that the sum of the weight coefficients obtained after normalization is 1.

4. The multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to claim 1, characterized in that, The trajectory smoothing regularization term is obtained based on the change in pose parameters between adjacent frames in the trajectory parameter set, including: The second-order difference is calculated based on the pose parameters of three consecutive frames in the trajectory parameter set. The second-order difference represents the acceleration of pose transformation between adjacent frames. The trajectory smoothing regularization term is obtained by summing the squares of the moduli of the second-order differences corresponding to each frame.

5. The multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to claim 4, characterized in that, The pose parameters include translation and rotation components. The calculation of the second-order difference based on the pose parameters of three consecutive frames in the trajectory parameter set includes: The translation components of three consecutive frames are used to calculate the second-order difference in vector space to obtain the translation second-order difference; The rotation components of three consecutive frames are calculated in the tangent space of the rotation group to obtain the rotation second-order difference; According to the rotation term weights, the squares of the modulus of the translation second-order difference and the squares of the modulus of the rotation second-order difference are weighted and summed to obtain the second-order difference corresponding to the three consecutive frames.

6. The multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to claim 1, characterized in that, The step of aggregating the trajectory parameter set, the sensor extrinsic parameter set, and the vehicle positioning parameters into a single parameter vector includes: The trajectory parameter set, the sensor extrinsic parameter set, and the vehicle positioning parameters are concatenated to obtain a parameter vector to be optimized. The parameter vector simultaneously carries the trajectory parameters, the extrinsic parameters, and the vehicle positioning parameters.

7. The multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to claim 1 or 6, characterized in that, The step of backpropagating the global unified loss function using a single optimizer and synchronously updating the trajectory parameters, extrinsic parameters, and vehicle localization parameters in the single parameter vector based on the gradient obtained from the backpropagation includes: Perform a backpropagation on the global unified loss function to obtain the gradients of the global unified loss function with respect to the trajectory parameters, the extrinsic parameters, and the vehicle localization parameters, respectively; The single optimizer synchronously updates the trajectory parameters, extrinsic parameters, and vehicle positioning parameters in the same parameter update based on the gradients of the trajectory parameters, extrinsic parameters, and vehicle positioning parameters.

8. The multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to claim 1, characterized in that, During the synchronous update process, the weight coefficients corresponding to each loss term are dynamically adjusted based on the gradient convergence state of the parameters corresponding to each loss term, including: According to the set iteration period, the gradient statistics of the parameters corresponding to each loss term are calculated. The corresponding weight coefficients are adjusted according to the gradient statistics, and the weight coefficients are kept unchanged between two adjacent adjustments.

9. The multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction according to claim 8, characterized in that, The gradient statistics include the mean and variance of the gradient of the corresponding parameter, and adjusting the corresponding weight coefficients according to each gradient statistic includes: The relative gradient magnitude of each loss term is determined based on the mean of the gradients of the parameters corresponding to the trajectory optimization loss term, the extrinsic parameter calibration loss term, the positioning optimization loss term, and the trajectory smoothing regularization term. Calculate the original weight value corresponding to each loss term according to the principle that the original weight value is inversely proportional to the relative gradient magnitude; The original weight values ​​are normalized to obtain the adjusted weight coefficients, so that the parameters corresponding to the loss terms with smaller gradient magnitudes obtain larger weight coefficients.

10. A multi-parameter collaborative optimization system for four-dimensional Gaussian sputtering reconstruction, used to implement the multi-parameter collaborative optimization method for four-dimensional Gaussian sputtering reconstruction as described in any one of claims 1 to 9, characterized in that, The system includes: The loss acquisition module is used to acquire trajectory optimization loss term, extrinsic parameter calibration loss term, positioning optimization loss term, and trajectory smoothing regularization term constraining the temporal continuity of the trajectory; wherein, the trajectory optimization loss term corresponds to the set of trajectory parameters to be optimized, the extrinsic parameter calibration loss term corresponds to the set of sensor extrinsic parameters to be optimized, the positioning optimization loss term corresponds to the vehicle positioning parameters to be optimized, and the trajectory smoothing regularization term is obtained based on the change in pose parameters of adjacent frames in the trajectory parameter set; The loss fusion module is used to weight and sum the trajectory optimization loss term, the extrinsic parameter calibration loss term, the positioning optimization loss term, and the trajectory smoothing regularization term according to their respective weight coefficients to obtain a globally unified loss function. The parameter aggregation module is used to aggregate the trajectory parameter set, the sensor extrinsic parameter set, and the vehicle positioning parameters into a single parameter vector. The synchronous update module is used to backpropagate the global unified loss function with a single optimizer, and to synchronously update the trajectory parameters, extrinsic parameters and vehicle positioning parameters in the single parameter vector based on the gradient obtained from the backpropagation. The weight adjustment module is used to dynamically adjust the weight coefficients corresponding to each loss term according to the gradient convergence state of the parameters corresponding to each loss term during the synchronous update process; wherein, the trajectory optimization loss term and the trajectory smoothing regularization term correspond to the trajectory parameter set. The parameter output module is used to output the synchronously updated converged trajectory parameter set, the sensor extrinsic parameter set, and the vehicle positioning parameters to the four-dimensional Gaussian sputtering model for dynamic scene reconstruction of the four-dimensional Gaussian sputtering model.

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