Road modeling with integrated gaussian processes

Abstract

This document describes road modeling with integrated Gaussian processes. A road is modeled at a first time instant using at least one Gaussian process regression (GPR). A kernel function is determined based on a set of detected samples received from one or more vehicle systems. Based on the kernel function, a respective mean lateral position associated with a particular longitudinal position is determined for each of the at least one GPR. The respective mean lateral positions of each of the at least one GPR are aggregated to determine a combined lateral position associated with the particular longitudinal position. A road model including the combined lateral position associated with the particular longitudinal position is then output. In this way, a robust and computationally efficient road model can be determined to help improve safety and performance of a vehicle.

Description

Background Technology

[0001] Many modern vehicles include Advanced Driver Assistance Systems (ADAS), which include features such as Adaptive Cruise Control (ACC) and Automatic Emergency Braking (AEB) that can rely on road models to execute correctly. To achieve these features, many vehicles include perception systems that analyze the vehicle's surroundings to create grid-based or parametric road models. However, these models often lack the flexibility to robustly represent road geometry. Furthermore, some road models may be inefficient and unable to process large amounts of data quickly enough to support driving, resulting in output delays in the vehicle's subsystems, which can lead to unsafe or unstable driving behavior. Summary of the Invention

[0002] This document describes road modeling using an ensemble Gaussian process. The road is modeled at the first time step using at least one Gaussian process regression (GPR). A kernel function is determined based on a sample set of detections received from one or more vehicle systems. Based on the kernel function, a corresponding mean lateral position and its uncertainty associated with a specific longitudinal position are determined for each of the at least one GPR. The corresponding mean lateral positions and their uncertainties for each of the at least one GPR are aggregated to determine a combined lateral position associated with the specific longitudinal position. The road model is then output, including the combined lateral position and its uncertainty associated with the specific longitudinal position. In this way, robust and computationally efficient road models can be determined, contributing to improved vehicle safety and performance.

[0003] The aspects described below include: a method for modeling a road using at least one Gaussian Process Representation (GPR) at a first time step. The method begins by determining a kernel function for at least one GPR at the first time step, based on a sample set of detections received from one or more vehicle systems. The kernel function is then used to determine a corresponding average lateral position associated with a specific longitudinal position for each of the at least one GPR, and these corresponding average lateral positions are then aggregated to determine a combined lateral position. A road model including the combined lateral position associated with the specific longitudinal position is then output to aid in the performance of vehicle functions. In this aspect, a system is described that includes at least one processor and a computer-readable storage medium, which, when executed by the at least one processor, configures or enables the processor to perform aspects of road modeling with an integrated Gaussian process as described above. The system can be mounted on a vehicle and is designed to output a road model to aid in the performance of vehicle functions. The system can be configured and implemented as any number of processors or computer-readable storage media. The processor and computer-readable storage medium can be discrete but communication-coupled elements or a single element, such as a system-on-a-chip (SoC).

[0004] This invention provides a simplified concept related to road modeling with integrated Gaussian processes, which is further described in the detailed description and accompanying drawings. This invention is not intended to identify essential features of the claimed subject matter, nor is it intended to define the scope of the claimed subject matter. Attached Figure Description

[0005] The following figures illustrate one or more aspects of road modeling with an integrated Gaussian process in detail in this document. Throughout the figures, the same numbers are generally used to refer to similar features and components:

[0006] Figure 1 An example environment in which road modeling with an integrated Gaussian process can be implemented is shown;

[0007] Figure 2 An example vehicle is shown that implements road modeling with an integrated Gaussian process;

[0008] Figure 3 An example flowchart is shown to implement a road perception system with integrated Gaussian processes for road modeling.

[0009] Figure 4 An example of a detection partitioning module based on road modeling with an integrated Gaussian process is shown;

[0010] Figure 5 An example of a recursive update scheme based on road modeling with an integrated Gaussian process is shown;

[0011] Figure 6 An example implementation of a GPR aggregation module based on road modeling with an integrated Gaussian process is shown;

[0012] Figure 7 Examples of visual detection and trajectory detection are shown;

[0013] Figure 8 An example of a false detection determined based on position and heading data is shown;

[0014] Figure 9 Example road model outputs, including high-confidence and low-confidence thresholds, are shown based on road modeling with an integrated Gaussian process.

[0015] Figure 10 This shows another road modeling output based on road modeling with an integrated Gaussian process;

[0016] Figure 11 An example method for implementing a road perception system with integrated Gaussian processes for road modeling is shown;

[0017] Figure 12 An example method for performing active learning based on road modeling with an integrated Gaussian process is shown; and

[0018] Figure 13 A detailed example method is shown that outputs a road model based on a road model with an integrated Gaussian process. Detailed Implementation

[0019] Overview

[0020] Road perception systems are a crucial technology for advanced driver assistance systems (ADAS). The functions of ADAS, such as adaptive cruise control and automatic emergency braking, often rely on road models to operate correctly. Furthermore, some safety standards require road models to not only model lanes but also determine uncertainties within the model. In many road modeling processes, a road model is created to model the road, determining grid occupancy or a set of parameterized functions. However, these processes often fail to capture the complexities of road geometry, thus hindering the effective implementation of certain vehicle functions within ADAS; they do not provide mechanisms for utilizing data from various sources that could potentially aid in road modeling (e.g., vision systems, radar tracking, and map data).

[0021] In contrast, this document describes computationally efficient and accurate road modeling using integrated Gaussian processes. For example, these techniques can leverage Gaussian process regression (GPR) to efficiently and effectively model roads based on Gaussian processes. Specifically, a partitioned architecture that divides the road modeling problem into multiple smaller road modeling problems can be utilized to increase the overall efficiency of the road model. This efficiency gain is achieved in part by fusing data collected from different sensor systems (e.g., visual, trajectory, and map data). Furthermore, the described techniques allow future measurements to leverage findings from previous models to improve the overall efficiency and accuracy of road modeling.

[0022] Compared to current models, the statistical properties of Gaussian processes allow for the easy and efficient determination of uncertainty from each measurement. As a result, road models operating according to the techniques described in this paper can provide uncertainty values ​​that can be used by the road model itself and downstream components such as trajectory planning to achieve safe and comfortable vehicle operation. The statistical properties of this approach also allow for the tuning of the inputs to the road modeling system to provide accurate results at the cost of minimal computation time. This is particularly important in advanced driver assistance systems, as delayed outputs or inaccurate results can lead to unsafe or uncomfortable driving behaviors that could cause harm to vehicle occupants or surrounding passengers.

[0023] This section describes only some aspects of how the described techniques, apparatus, and systems utilize integrated Gaussian processes to determine road models. Additional details, examples, and implementations of road modeling with integrated Gaussian processes are disclosed herein.

[0024] Example Environment

[0025] Figure 1 An example environment 100 in which road modeling with an integrated Gaussian process can be implemented is shown. In the depicted environment 100, a road perception system 106 is mounted on or integrated into a vehicle 102. The vehicle 102 can travel on a road 120, which may include one or more lanes.

[0026] Although shown as a car, vehicle 102 could represent other types of motorized vehicles (e.g., motorcycles, buses, tractor-trailers, semi-trailer trucks, or construction equipment). Typically, manufacturers can mount the road perception system 106 onto any mobile platform that can travel on road 120.

[0027] In the depicted implementation, a portion of the road perception system 106 is mounted in the rearview mirror of the vehicle 102 to have a field of view of the road 120. The road perception system 106 can project the field of view from any external surface of the vehicle 102. For example, the vehicle manufacturer may integrate at least a portion of the road perception system 106 into a side mirror, bumper, roof, door, windshield, grille, hood, trunk, or any other internal or external location where the field of view includes the road 120. Typically, the vehicle manufacturer may design the location of the road perception system 106 to provide a specific field of view that sufficiently encompasses the road 120 on which the vehicle 102 may travel.

[0028] Vehicle 102 includes one or more sensors 104 to transmit signals to one or more processors of road perception system 106 (not in...). Figure 1 (As shown in the diagram) provides input data. Sensor 104 may include a camera, radar system, Global Positioning System (GPS), Global Navigation Satellite System (GNSS), lidar system, or any combination thereof. The camera may capture still images or videos of road 120. The radar system or lidar system may use electromagnetic signals to detect objects in road 120 or features of road 120. GPS or GNSS may determine the position and / or heading of vehicle 102. Vehicle 102 may include additional sensors to provide input data relating to road 120 and its lanes to road perception system 106. Road perception system 106 may also use vehicle-to-the-world (V2X) or cellular communication technologies to obtain input data from external sources (e.g., nearby vehicles, nearby infrastructure, the Internet).

[0029] Road perception system 106 can estimate the centerline and variance associated with one or more distances along road 120 or lanes. In various respects, the centerline can represent the appropriate path for a vehicle traveling within road 120 or lanes (e.g., the location where the center of the vehicle will travel). Variance can represent the uncertainty associated with a centerline measurement at a specific longitudinal value (e.g., the location along the vehicle's direction of travel). In this way, variance can be determined for each centerline value or at each location along the centerline. Variance can be used to determine the confidence level of the centerline measurement, e.g., high confidence or low confidence. This can include any number of statistical operations or thresholding to determine the confidence level. The variance or confidence level determination at the centerline point can be output along with a road model for the vehicle subsystem to apply. For example, one or more vehicle-based systems 114 can be more trusting when navigating areas predicted by the road model as having high confidence or low variance, but can be more cautious or search for more data when navigating areas with low confidence or high variance.

[0030] The road perception system 106 includes a Gaussian process module 108, an active learning module 110, and an output module 112. The Gaussian process module 108 can utilize multiple Gaussian Process Recognition (GPRs) to perform a Gaussian function and determine the topology of road 120 or lanes. In various aspects, this includes relying on various detections to synthesize multiple GPRs to determine centerline information or other information about road 120 at various points. For example, the Gaussian process module 108 can be used to aggregate detections from different information sources, such as sensor 104 (e.g., radar measurements, visual measurements from a camera system) or prior knowledge (e.g., previous data collected by sensor 104 from a map database). The Gaussian process module 108 can also calculate the uncertainty or quality value associated with each lane segment.

[0031] The active learning module 110 can identify the detections that provide the most information gain to a single GPR or the entire road model. For example, the active learning module 110 can determine that adding a specific detection from the detection pool will maximize the improvement of the GPR, and therefore add that detection to the detections used by the model. In this way, the active learning module 110 can improve the accuracy of the road model with almost no impact on the overall efficiency or speed.

[0032] Output module 112 can control the output of the road model, for example, to send the output to vehicle-based system 114. This may include determining confidence values ​​associated with the elements of the road modeling. In various aspects, output module 112 resolves the determinations of Gaussian process module 108 into a useful road model.

[0033] Vehicle 102 also includes one or more vehicle-based systems 114 that can use data from road perception system 106 to operate vehicle 102 on road 120. Vehicle-based systems 114 may include driver assistance systems 116 and autonomous driving systems 118 (e.g., adaptive cruise control (ACC), automatic emergency braking (AEB), traffic jam assist (TJA), lane centering assist (LCA), and L3 / L4 autonomous driving (L3 / L4) systems on highways). Typically, vehicle-based systems 114 use road perception data provided by road perception system 106 to perform functions. For example, driver assistance system 116 may provide adaptive cruise control and monitor the presence of objects (e.g., objects detected by another system on vehicle 102) in road 120 on which vehicle 102 is traveling. As another example, driver assistance system 116 may provide an alert when vehicle 102 crosses lane markings in the lane on road 120 on which vehicle 102 is traveling.

[0034] The autonomous driving system 118 can move the vehicle 102 to a specific location on the road 120 while avoiding collisions with objects detected by other systems on the vehicle 102 (e.g., radar systems, lidar systems). Road perception data provided by the road perception system 106 can provide information about lane position and lane position uncertainty, enabling the autonomous driving system 118 to perform lane changes or maneuver the vehicle 102.

[0035] Example vehicles

[0036] Figure 2 An example vehicle 102 is shown that implements road modeling with an integrated Gaussian process. The vehicle 102 includes a road perception system 106, which may include one or more processors 202 and a computer-readable storage medium (CRM) 204.

[0037] As a non-limiting example, processor 202 may include a system-on-a-chip (SoC), application processor (AP), central processing unit (CPU), engine control unit (ECU), or graphics processing unit (GPU). Processor 202 may be a single-core or multi-core processor implemented using a homogeneous or heterogeneous core architecture. Processor 202 may include a hardware-based processor implemented as hardware-based logic, circuitry, processing cores, etc. In some aspects, the functionality of processor 202 and other components of the road perception system 106 is provided via an integrated processing, communication, and / or control system (e.g., an SoC) that enables various operations of the vehicle 102 embodying the system.

[0038] The CRM 204 described herein includes any non-transient CRM. CRM 204 may include any suitable memory or storage device that can be used to store device data (not shown) of the road perception system 106, such as random access memory (RAM), static RAM (SRAM), dynamic RAM (DRAM), non-volatile RAM (NVRAM), read-only memory (ROM), or flash memory. CRM 204 may include any combination of volatile or non-volatile memory. Processor 202 may execute any number of computer-executable instructions stored on CRM 204. In some implementations, processor 202 is implemented together with CRM 204, for example, as a system-on-a-chip. In other implementations, processor 202 is external to CRM 204 but communicatively coupled to CRM 204 via a data bus (e.g., bus 218).

[0039] Processor 202 executes computer-executable instructions stored within CRM 204. As an example, processor 202 can execute Gaussian process module 108 to define GPRs, aggregate their models into an accurate model of road 120, and determine the uncertainty associated with the road model. Gaussian process module 108 can determine GPRs that can be used to model the lanes of road 120 by, for example, extracting detections from a high-resolution map stored in CRM 204 and / or tracking them using data from sensor 104. Gaussian process module 108 can also use statistical methods inherent in Gaussian processes to determine the variance associated with the model. Gaussian process module 108 can be divided into sub-modules, each handling different responsibilities of the GPR determination and aggregation process, such as detection partitioning module 206, trained GPR module 208, and GPR aggregation module 210.

[0040] The detection partitioning module 206 can be implemented within CRM 204 and stores computer-executable instructions to be executed by processor 202. When executed by processor 202, the detection partitioning module 206 can allow the detections used to generate the road model to be partitioned into multiple subsets. In an aspect, each GPR can act on a corresponding subset. In some implementations, detections can be partitioned according to certain criteria, such as grouping detections into subsets based on detection type, location, reliability, or any other feasible method.

[0041] Similarly, the trained GPR model 208 can be executed by processor 202 to determine the parameters of one or more GPRs. To define each GPR, the parameters of the kernel function can be determined based on a set of detected samples. In all respects, the set of detected samples is collected from various information sources (e.g., sensor 104 and map information). Once the parameters of the kernel function are determined, each GPR can operate on a specific partition of the detections, as determined by the detection partitioning module 206. The trained GPR model 208 can be executed iteratively, such that the GPR is updated at each subsequent time step for newly collected detections. In this way, the GPR can leverage the findings of previous iterations to reduce complexity while maintaining accuracy in subsequent iterations.

[0042] GPR aggregation module 210 can be implemented in CRM 204, such that when executed by processor 202, processor 202 aggregates multiple GPRs into a single road model. In other words, GPR aggregation module 210 can perform aggregation functions. In various respects, performing this aggregation function not only determines the road model but also determines the uncertainty values ​​associated with the road model. GPR aggregation allows multiple experts to contribute to the final road model, thereby allowing for easy integration of data from various information sources.

[0043] To improve the amount of information gained from including a detection in the detection set, and to enhance the overall efficiency of the road modeling process, processor 202 can execute computer-executable instructions of the active learning module 110 implemented in CRM 204. The active learning module 110 may include an improved query module 212 that determines one or more of the most effective detections to be included in the detection set for a particular iteration. Detections can be queried from a pool of possible detections, and the detection associated with the highest information gain can be selected. In this way, the active learning module 110 can ensure that both accuracy and complexity are enhanced during the road modeling process.

[0044] The road perception system 106, as shown, also includes an output module 112 implemented in CRM 204. Output module 112 can be executed by processor 202 to resolve the determinations of Gaussian process module 108 into a useful road model. For example, output module 112 may include a road model output 214 indicating road information or centerlines determined by aggregated GPR. Output module 112 may also resolve a confidence output 216 indicating the uncertainty associated with road model output 214. Output module 112 may transmit road model output 214 or confidence output 216 to a vehicle-based system interface 222, which facilitates communication between road perception system 106 and vehicle-based system 114. Vehicle-based system interface 222 may control data communication along bus 224 such that road perception data (e.g., road model) is provided from road perception system 106 to vehicle-based system 114 along bus 224.

[0045] The vehicle-based system 114 may include any number of such vehicles. Figure 1 The system described herein. As further non-limiting examples, the vehicle-based system 114 shown in the figure includes an autonomous control system 220-1, a vehicle safety system 220-2, a positioning system 220-3, a multi-sensor tracker 220-4, a vehicle-to-vehicle communication system 220-5, and an occupant interface 220-6. Sensors 104 for providing detection may be maintained by one or more of the vehicle-based systems 114, and sensor data may be provided to the road perception system 106 through the vehicle-based system interface 222. Although not shown, the vehicle-based system interface 222 may include separate interfaces for handling communication with different systems of the vehicle-based system 114; for example, the vehicle-based system interface 222 may include a sensor interface and an autonomous control interface.

[0046] The following describes these and other operations of the Gaussian process module 108, the active learning module 110, the output module 112, and their respective sub-components in more detail.

[0047] Example System

[0048] Figure 3 An example flowchart is shown to implement a road perception system 106 with integrated Gaussian processes for road modeling. The flowchart shows... Figure 1 Example operation of the road perception system 106. The road perception system 106 uses an integrated Gaussian process to determine the road model.

[0049] The road perception system 106 can use various forms of evidence as input 302 received from the vehicle-based system interface 222. As a non-limiting example, input 302 may include a master state 304, visual detection 306, trajectory detection 308, or map detection 310. The master state 304 can identify the current state of the vehicle to determine appropriate measurements to be taken during road modeling. For example, the master state 304 may indicate the vehicle's position, speed, heading, or current destination, allowing the perception system 106 to determine what information is likely most important during road modeling. In various aspects, this may include determining the vehicle's heading so that the road can be modeled in the appropriate relative direction. In some implementations, road modeling can occur at greater distances when the vehicle is traveling at higher speeds, because higher speeds can indicate that a greater distance will be reached faster than if the vehicle were traveling at a slower speed. Typically, any information provided in the master state 304 can be used to determine areas of importance for the perception system 106. Although not shown, input 302 may include prior knowledge, such as previous road modeling information stored in the CRM (e.g., CRM 204) and determined based on previous conditions on the road.

[0050] Input 302 may also include visual detection 306 from a vision detection system. An example of visual detection 306 could be a camera image indicating the lane boundaries of the detected road, from which the centerline can be determined as a point equidistant from each lane boundary. Visual detection 306 can be captured over time by any suitable sensor located inside or outside the vehicle, above or around it. In some implementations, the vision sensor may be mounted to the front of the vehicle (e.g., on the forward-facing portion of a side mirror) to provide sufficient field of view of the lane boundaries.

[0051] Input 302 may also include trajectory detection 308 determined from an appropriate sensor system of the vehicle. For example, trajectory detection 308 may be determined from a radar system or lidar system of the vehicle. The radar system or lidar system may operate on information collected by their respective sensor devices to detect objects in the field of view and create a track that can be used to determine trajectory detection 308. In one example, trajectory detection 308 may be generated from a vehicle traveling at a distance ahead on the same road as the vehicle. In some aspects, the vehicle at a distance ahead may be traveling in the same lane as the vehicle. The track may indicate the path of the vehicle at a distance ahead, and the perception system 106 may use the indicated path as an appropriate path for the vehicle. Thus, by creating trajectory detection 308 from the track, the vehicle can determine information about the road or centerline.

[0052] The perception system 106 may also rely on data in the form of map detection 310 determined from a map of the road or surrounding area. For example, the map may include a high-resolution map included in the CRM 204 of the road perception system 106 or in the memory of the vehicle, a map retrieved from a map or navigation service communicating with the road perception system 106, or a map obtained from a mobile phone or other device communicatively coupled to the road perception system 106. Although not shown, the road perception system 106 may rely on any other suitable measurements, such as data or measurements obtained from sensors located outside the vehicle (e.g., embedded in the road, integrated with signs or markings, located on another vehicle near the vehicle 102).

[0053] The Gaussian process module 108 can then be executed to allocate the road perception system 106 to develop a road model for the road using multiple sources of information and evidence provided by input 302. The detection partitioning module 206 can create one or more subsets from the set of detections provided as input 302. Subsets can be determined from all or a portion of input 302. In some examples, subsets are created by classifying detections based on type, location, reliability, or any other suitable method. Each subset can have a predetermined size that is the same as or different from other subsets. Additionally, each subset can be divided into one or more subsets.

[0054] In some implementations, the active learning module 110 is used to improve the effectiveness of the detections included in each subset. In various aspects, the improvement query module 212 queries the detection pool (e.g., from input 302) and determines the detections that provide the most information gain for the GPR. For example, visual detections 306 can be performed at any point along a portion of a road, as they rely on continuous lane boundaries captured in camera images; therefore, the improvement query module 212 can determine the optimal location of the detections based on how much information will be gained from the detections included in the subset. The active learning module 110 can use various methods to determine the optimal detections. For example, detections can be selected based on the principle of desired improvement or distance from the lower confidence bound. Any detections not selected within one or more subsets can be discarded or retained in input 302 for future iterations. Figure 4 The detection partitioning module is discussed in more detail.

[0055] Once partitioned, each subset can be fed into the trained GPR module 208, where each subset can be acted upon by a separate GPR to determine a separate Gaussian process model. For example, each GPR can be defined by the parameters of the kernel function. Typically, any kernel function can be used to create a road model. The parameters of the kernel function can be defined to maximize the log-marginal likelihood. In some instances, the log-marginal likelihood can be expressed as the sum of the log-marginal likelihoods of each GPR in the GPR set. The GPR can be trained using one of two methods: split training or unified training. In split training, each subset can be used to train a separate GPR. As a result, the set of parameters for the kernel function can be different for each GPR. By partitioning the detections into subsets, the size of each training set can be significantly reduced, thereby reducing the time complexity of training the GPR. In contrast, unified training utilizes a single set of parameters for a kernel function that is common across all GPRs. In unified training, it may be appropriate to express the log-marginal likelihood as the sum of the log-marginal likelihoods of each GPR. In this way, the number of detections used in each GPR can be reduced to a level similar to that used in segmentation training, thus significantly reducing complexity.

[0056] The road perception system 106 can dynamically update the road model and corresponding uncertainties at discrete time intervals. The time interval for information updates can depend on a trade-off between accuracy and computational workload. In some implementations, vehicle-based systems can dynamically change the time interval based on road conditions, driving environment, vehicle speed, and other considerations provided by the master state 304. In some instances, the determined GPR can utilize findings from previous iterations using a previous iteration baseline 312. For example, the previous set of parameters for the kernel function determined in a previous iteration can be used as the baseline (e.g., initial values) for the current iteration. In this way, the accuracy of the GPR can be continuously improved with minimal impact on computational efficiency. Similarly, the current iteration of the GPR can utilize detections captured in previous iterations. As a result, the iterative nature of road modeling with integrated Gaussian processes allows for accurate and computationally efficient road modeling. Figure 5 The trained GPR module 208 is discussed in more detail.

[0057] Each of the GPRs can be aggregated by the GPR aggregation module 210. In all aspects, aggregation occurs through any number of methods, with non-limiting examples including a generalized robust Bayesian committee machine, expert product (PoE), generalized PoE, Bayesian committee machine (BCM), or robust BCM. In some implementations, a generalized robust Bayesian committee machine is used because it converges to the underlying true prediction distribution as the sample size approaches infinity. For each longitudinal location along the road, the aggregated road model can provide lateral values. Furthermore, due to the statistical properties of GPR aggregation, an uncertainty value can be determined for each lateral value provided by the road model. In all aspects, the lateral value can define a point along the centerline of the lane, and an uncertainty value can be associated with that lateral value. Regarding... Figure 6 The GPR aggregation module 210 is described in more detail.

[0058] Road model data, including the modeled centerline or uncertainty, can be provided to output module 112. In some implementations, only the determined values ​​of the road model data are provided to output module 112, and uncertainty is not utilized or provided. In this case, road model output 214 can be generated by output module 112 and can indicate the centerline determined in the current iteration or time interval. In other implementations, uncertainty can be provided along with the road model data. In various aspects, this allows confidence output 216 to be generated along with road model output 214. Each value included in road model output 214 can include uncertainty. In this way, uncertainty values ​​are provided based on the centerline values ​​determined by the road model. Uncertainty values ​​can be determined by any statistical method utilizing standard deviation, various statistical distances, or any other suitable method.

[0059] In another implementation, high and low confidence thresholds are determined based on the road model. The confidence thresholds can be based on statistical distances between corresponding lateral locations determined by various GPRs. For example, high or low confidence thresholds can be based on Mahalanobis or Hausdorff distances between corresponding centerline values ​​of the GPRs (e.g., at the same or similar longitudinal locations). Thus, the road model can be output using values ​​from the road model output 214, based on the high, medium, and low confidence portions determined using confidence output 216.

[0060] The vehicle-based system interface 222 can receive a road model and control the road model to the output of any vehicle-based system. In various respects, the vehicle-based system interface 220 acts as an intermediary between the perception system and the vehicle-based system. As previously discussed, the vehicle-based system can act on the road model provided through the vehicle-based system interface 222 to perform vehicle functions.

[0061] Figure 4 An example of a detection partitioning module 206-1 (e.g., an example of detection partitioning module 206) based on road modeling with an integrated Gaussian process is shown. As shown, a set of detections 402 is provided. These detections 402 can be of various types as described above and include data collected across multiple locations. In this example, the detections are divided into three categories: previous detections 404, trajectory detections 308, and visual detections 306. In some implementations, these can be used as subsets provided to individual GPRs. For example, three GPRs can be used to determine the road model, each GPR acting on a corresponding one of the previous detections 404, trajectory detections 308, and visual detections 306. By partitioning the detections 402 by detection type, the GPRs may be more suitable for processing each detection set, since all detections in the set can be of a similar form. Although a detection set is shown for a specific detection type, there can be any number of partitions to create any number of combinations of sets. Specifically, detection types can be added to or excluded from the set shown in the figure. Furthermore, other partitions independent of detection types are also possible. For example, the detections 402 can be partitioned based on distance from vehicles, detection reliability, or any other method.

[0062] In some implementations, detection 402 can be categorized based on distance from the vehicle. In various respects, this allows the noise values ​​associated with the Gaussian process to vary across different ranges. This can be beneficial because, in general, detection errors can increase with increasing distance from the sensor. Therefore, by classifying detection 402 by distance, the inherent addition of noise in the GPR allows for the accounting of sensor error. In other implementations, heteroscedastic GPR can be used to handle sensor errors varying across distances.

[0063] In the detection partitioning module 206-1, detection 402 is partitioned into subsets, and then these subsets are further partitioned into additional subsets. Specifically, the previously detected detection 404 is partitioned into subsets 406-1 to 406-N, trajectory detection 308 is partitioned into subsets 408-1 to 408-N, and visual detection 306 is partitioned into subsets 410-1 to 410-N. Detection 402 can be recursively partitioned an arbitrary number of times. Additionally, subsets can be partitioned according to different criteria at different levels. For example, detection 402 can first be partitioned into detection types, and then each detection type can be partitioned based on distance, or vice versa. Each subset of detection 402 can have the same or different size as any other subset. In some implementations, each subset includes the same predefined number of subsets. In all respects, not all detections from detection 402 can be used to form subsets. For example, some detections in detection 402 may not have been used during partitioning. Unused detections can be discarded or retained by the road perception system until they can be used in future iterations.

[0064] To improve the effectiveness of including detections in a subset, active learning can be used to determine one or more optimal detections to include from the detection pool. In all aspects, active learning allows the model to include detections that have the greatest impact on improving the accuracy of the road model. Active learning may be particularly advantageous when applied to visual detections 306, as visual detections 306 can be determined at any point along the road. This is because visual detections 306 can provide a polynomial representation of lane markings. Therefore, detections can be determined at any point along the road based on the polynomial representation. Two methods for determining one or more optimal detections from the detection pool are provided. In all aspects, one or more optimal detections are those that provide the most information gain to the model.

[0065] In the first method, one or more optimal detections can be selected based on the principle of desired improvement. In this implementation, detections can be selected such that those that improve the accuracy of GPR are included in a subset. The equation governing the principle of desired improvement can be decomposed as follows:

[0066] EI(x,GRP)=E GRP [max(0,μ GPR(x best )-y(x)]

[0067] Where y(x) is the centerline provided by the polynomial representation of the lane boundary, x is the detected longitudinal value, E is the mean of the Gaussian distribution, and μ GPR (*) is the averaging function given by GPR. In all aspects, maximizing the expected improvement in x value is the optimal longitudinal value for detection.

[0068] In the second method, one or more optimal detections can be selected based on the principle of the lower confidence bound. In this implementation, the detection with the longitudinal value x can be selected to maximize the lower confidence bound as defined in the following equation:

[0069] LCB(x)=2σ GRP (x)-μ GPR (x)

[0070] Where x is the detected vertical value, σ GRP (x) is the standard deviation given by GPR, μ GPR (*) is the averaging function given by GPR. Among all aspects, the x-value that maximizes the lower confidence bound is the best longitudinal value for detection.

[0071] While active learning works particularly well with visual detection 306, it can also be performed on other types of detection. For example, trajectory detection 308 can be used with active learning, and the possible x-values ​​can be limited to the longitudinal position where trajectory detection 308 is performed. Alternatively, trajectory detection 308 can be extrapolated to any value using the heading and position of each of the trajectories in trajectory detection 308. In this case, the possible x-values ​​of one or more optimal detections may not need to be limited, as the detections can be extrapolated to any value. Although trajectory detection 308 is used as an example, this process can be used for any type of detection and is not limited to trajectory detection 308. About Figure 8 The determination of spurious detections (e.g., detection extrapolation) is further described.

[0072] Figure 5 An example of a recursive update scheme based on road modeling with an integrated Gaussian process is shown. The recursive update scheme can be executed by Gaussian process module 208-1 (e.g., an example of Gaussian process module 208). At 504, Gaussian process module 208 receives measurements at time t-1. In various aspects, the measurements include, as... Figure 4The subset of detections detailed in [the document]. At 502, the GPR can be defined based on the measurements received at time t-1. For example, any number of kernel functions known to those skilled in the art can be used to define the GPR capable of determining the road model. The parameters of the kernel function can be determined in one of two ways: segment training or uniform training.

[0073] In split training, each subset of the data can be used to train the standard GPR. The GPR can be partitioned into a standard regression problem, defined as:

[0074] y = f(x) + ε

[0075] Where ε is approximately equal to And σ ε This represents noise. In some implementations, noise can vary based on the uncertainty associated with the sensor data. For example, sensor data or detections located at a greater distance from the vehicle may have greater uncertainty and therefore greater noise values. However, for all detections within a single GPR, the expected noise is equal. Thus, grouping detections according to distance from the vehicle allows for more representative noise values ​​for each GPR.

[0076] Given a training dataset And test input x * Predicted output f * It is represented by a Gaussian distribution. The mean and covariance are given by the following equation:

[0077]

[0078]

[0079] Where k is the kernel function, k * =k(X,x) * ), k ** =k(x * ,x * K = (X, X). Note that the kernel function can be any of many suitable kernel functions. K represents the kernel matrix corresponding to the observed sample set (y). The parameters of the kernel can be trained by maximizing the log-marginal likelihood given by:

[0080]

[0081] In the case of segmented training, each Gaussian Process (GPR) is trained using a separate set of parameters based on a subset of the detections partitioned for that GPR. By partitioning the detections used in each GPR, the size of each kernel matrix is ​​reduced, thereby lowering the time complexity of the operation through a divide-and-conquer strategy. In all respects, this allows the Gaussian process to be suitable for real-time applications, such as road modeling.

[0082] In contrast, unified training uses a single set of parameters. The unified training method can be utilized by introducing the assumption of independence of data subsets. According to this assumption, the log-marginal likelihood can be expressed as the sum of the log-marginal likelihoods of every GPR in the k-th GPR. Specifically, the log-marginal likelihood becomes:

[0083]

[0084] in

[0085]

[0086] Note that by partitioning the kernel matrix into smaller subsets of the k-th GPR, the overall size of the matrix and the number of matrix multiplications are reduced. In this way, unified training using the independence assumption allows for efficient solution of the kernel function's parameters.

[0087] In addition to accuracy and efficiency, road modeling with integrated Gaussian processes allows detections to be partitioned into subsets that are then seamlessly aggregated. As a result, the method provides an inherent ability to perform road modeling using multiple types of sensor data. Furthermore, these techniques allow for the utilization of determinations made at previous time steps in subsequent iterations. At 506, measurements at time t are introduced, and at 508, an updated GPR is determined for time t. In all aspects, subsequent iterations of the GPR can utilize findings from previous iterations. For example, the GPR at time t can utilize the GPR at time t-1 as a baseline. Specifically, the kernel parameters determined at time t-1 can be used as a starting point for determining the kernel parameters at time t. In this way, each iteration can improve the accuracy of the model with minimal loss to runtime complexity. Once the parameters of the kernel function are determined for a specific time, each of the GPRs can be aggregated to produce aggregated values ​​included in the road model.

[0088] Figure 6An example implementation 600 of a GPR aggregation module 210-1 (e.g., an example of GPR aggregation module 210) based on road modeling with an integrated Gaussian process is shown. Example implementation 600 includes a set of detections 604 collected using various information sources. As shown, the detections 604 are partitioned among GPRs 602. Specifically, the detections are partitioned into subsets where GPR 602-1 operates on detections 608-1 and 608-2, GPR 602-2 operates on detections 610-1 and 610-2, and GPR 602-N operates on detections 612-1 and 612-2.

[0089] Each of the GPR 602 models is trained either through unified training or split training. Each GPR 602 model is created based on a corresponding subset of detections provided to the GPR. Once the GPR 602 models are trained, each model can be fed into the GPR aggregation module 210-1 to aggregate the corresponding GPR 602 models. In various aspects, GPR 602 models can be aggregated using any of the following: Expert Product (PoE), Generalized PoE, Bayesian Committee Machine (BCM), Robust BCM, or Generalized Robust BCM. In some implementations, Generalized Robust BCM is used due to its convergence as the number of samples approaches infinity. Generalized Robust BCM can be used to aggregate information from different GPR models. Therefore, the posterior distribution is as follows:

[0090]

[0091] Where D c It is the chief expert with global data allocation, D +k ={D c D k} is a dataset containing the k-th expert and the data assigned to the master expert. β k (x * Allow the k-th expert in x * The contribution at point . For a given vertical value x * The horizontal values ​​can be described by a normal distribution with a mean and a standard deviation:

[0092]

[0093]

[0094]

[0095] Where β k Defined as p c (f * |D c ,x * ) and p +k (f* |x * D +k The difference in entropy between them.

[0096] In various aspects, when GPR 602 is aggregated by executing GPR aggregation module 210-1, road model 606 is determined. Road model data 606 can indicate the centerline of lanes or roads determined by GPR 602. Road model data 606 can be used to determine the road model of a road. In some implementations, the road model includes uncertainty values ​​determined based on the aggregation. In various aspects, the uncertainty values ​​can be determined based on the standard deviation determined during GPR aggregation. As shown, uncertainty can be determined for each point in road model data 606.

[0097] Figure 7 Examples of visual detection 306 and trajectory detection 308 are shown. As shown, a vehicle 102 travels along road 120-1 (e.g., an example of road 120). Several detection types are shown, including visual detection 306 and trajectory detection 308. In one aspect, visual detection 306 is determined based on lane boundaries 702 (e.g., lane boundaries 702-1 and 702-2). In another aspect, visual detection 306-1 (e.g., an example of visual detection 306) is a centerline determined based on lane boundaries 702. The centerline can be determined such that visual detection 306-1 defined along the centerline is equidistant from lane boundaries 702-1 and 702-2. In another aspect, visual detection 306 is recorded.

[0098] Figure 7 The diagram also illustrates trajectory detection 308. In various aspects, trajectory detection 308 is determined based on a radar or lidar system capable of generating a track. In some implementations, trajectory detection 308 may include both location and heading data. For example, the illustrated trajectory detection 308 (e.g., trajectory detection 308-1, trajectory detection 308-2, trajectory detection 308-3, trajectory detection 308-4, and trajectory detection 308-5) includes location data (shown as circles) and heading data (shown as arrows). Typically, the location data of trajectory detection 308 indicates the detected position on road 120-1, while the heading data indicates the direction of travel in that direction. Although shown as including both location and heading data, the detection used to determine the road model may include only location data or only heading data. Furthermore, the depicted detection may be omitted, or additional detections, such as map detection, may be added.

[0099] Figure 8An example of a pseudo-detection 802 determined based on position and heading data is shown. As shown, vehicle 102 travels along road 120-2 (an example of road 120), which is modeled using visual detection 306-2 (an example of visual detection 306) and trajectory detection 308 (e.g., trajectory detection 308-6 and trajectory detection 308-7). In various aspects, trajectory detection 308 includes position data indicated by circles and heading data indicated by arrows. In some implementations, the use of position and heading data can allow extrapolation of pseudo-detections 802 (e.g., pseudo-detections 802-1, pseudo-detections 802-2, pseudo-detections 802-3). For example, pseudo-detections 802 are determined by extending points along the heading from trajectory detection 308-6. Points extended using the heading data of trajectory detection 308-6 become pseudo-detections 802. In some implementations, pseudo-detections 802 can be added to the detection set to be treated like any other detection collected from the sensor system. One advantage of this approach is that additional pseudo-detections 802 can be extrapolated from the last detection located at the farthest distance from vehicle 102. This expands the detection range. Identifying pseudo-detections 802 can be particularly advantageous when using active learning, as it allows extrapolation of detections other than visual detection to determine one or more optimal detections. This relaxes the criteria for determining one or more optimal detections from the detection pool, as pseudo-detections 802 can be created at any point using data from other points.

[0100] The pseudo-detection 802 can also be defined using sine and cosine based on the heading angle with respect to the vertical axis. For example, the position of the pseudo-detection 802 on the horizontal axis can be defined as the lateral position of the previous detection (e.g., trajectory detection 308-6) plus the distance between the pseudo-detection (e.g., pseudo-detection 802-1, pseudo-detection 802-2, pseudo-detection 802-3) and the previous detection multiplied by the sine of the heading angle with respect to the vertical axis. Similarly, the vertical position can be defined as the vertical position of the previous detection (e.g., trajectory detection 308-6) plus the distance between the pseudo-detection (e.g., pseudo-detection 802-1, pseudo-detection 802-2, pseudo-detection 802-3) and the previous detection multiplied by the cosine of the heading angle with respect to the vertical axis.

[0101] In some implementations, heading data is not used to determine pseudo-detection 802. For example, pseudo-detection 802 can be created by adding points along the shortest connection between two subsequent detections (e.g., trajectory detection 308-6 and trajectory detection 308-7). In other aspects, pseudo-detection 802 can be determined by assuming that each subsequent detection is connected by a line. This again allows the detection pool to support more values ​​for active learning. It should also be noted that although described according to trajectory detection 308, pseudo-detection 802 can be determined based on any type of detection.

[0102] Figure 9 An example road model output 900, including high-confidence and low-confidence thresholds, is shown based on road modeling with an integrated Gaussian process. As shown, output 900 includes a high-confidence longitudinal position 902 (rh) and a low-confidence longitudinal position 904 (rl). Vehicle 102 is modeling road 120-3, an example of road 120, and vehicle 102 is traveling on road 120-3. In all aspects, the high-confidence longitudinal position 902 and the low-confidence longitudinal position 904 are divided into three intervals: a high-confidence interval 906, a medium-confidence interval 908, and a low-confidence interval 910. Specifically, the high-confidence interval 906 indicates the interval of the road model reporting the portion from the high-confidence longitudinal position 902 to the vehicle 102 with high accuracy or low uncertainty. The medium-confidence interval 908 is the interval of the road model located between the high-confidence longitudinal position 902 and the low-confidence longitudinal position 904. In some implementations, confidence interval 908 is reported with a certain level of accuracy and uncertainty. Therefore, vehicle 102 may need to further model the medium-confidence interval 908 before crossing road 120-3 at the medium-confidence interval 908. Low-confidence interval 910 may include a portion of the road model that is further away from vehicle 102 than the low-confidence longitudinal location 904. For example, low-confidence interval 910 may correspond to a portion of the road reported with low accuracy and high uncertainty. In some implementations, vehicle 102 may need one or more iterations of road modeling before crossing road 120-3 at the low-confidence interval 910.

[0103] The road modeling output 900 can be determined in several different ways. For example, various statistical distances between detections can be used to determine the high-confidence longitudinal position 902 and the low-confidence longitudinal distance 904. In some implementations, the Hausdorff distance is used to determine the position of the high-confidence longitudinal position 902 such that all detections from various GPRs at longitudinal positions closer to the vehicle 102 than the high-confidence longitudinal position 902 have a Hausdorff distance less than the high-confidence threshold. Furthermore, a low-confidence threshold can be set, and a low-confidence longitudinal position 904 can be determined such that the road model at longitudinal positions closer to the vehicle 102 than the low-confidence longitudinal position 904 has a Hausdorff distance less than the low-confidence threshold. In all respects, the low-confidence threshold and the high-confidence threshold can be any predetermined values. Typically, the low-confidence threshold is higher than the high-confidence threshold because a higher threshold allows for greater measurement uncertainty without exceeding the threshold. In all aspects, the high-confidence longitudinal position 902 and the low-confidence longitudinal position 904 are determined by two factors. First, the consensus score among different sensors. Second, the likelihood of the road model compared to a given road model. Specifically, to determine the high-confidence longitudinal position 902 using the Hausdorff distance, the following equation can be used:

[0104]

[0105] Where C(z) s T is the combination of all comparison pairs from different measurement sources. hh Here, D(r;cz) is the high confidence threshold, and D(r;cz) is the Hausdorff distance. Similarly, the low confidence vertical position 904 can be determined using the Hausdorff distance through the following equation:

[0106]

[0107] Where T l This is the low confidence threshold. Note that high confidence longitudinal position 902 and low confidence longitudinal position 904 can be determined at each time interval in the road modeling process.

[0108] In some implementations, the Mahalanobis distance is used to determine the high-confidence longitudinal position 902 and the low-confidence longitudinal position 904. For example, the high-confidence longitudinal position 902 can be determined using the following equation:

[0109]

[0110] Where z fIt is a fusion measurement given a longitudinal distance r, M0 is the road model, and T hm This is the high-confidence threshold. Similarly, the low-confidence longitudinal location 904 can be determined using the Mahalanobis distance using the following equation:

[0111]

[0112] Where T lm It is a low confidence threshold.

[0113] In some implementations, both Hausdorff distance and Mahalanobis distance can be used. For example, the minimum longitudinal value of each of the above equations can be used to determine the high-confidence longitudinal position 902 and the low-confidence longitudinal position 904. Specifically, the following equation can be used for the high-confidence longitudinal position 902:

[0114]

[0115] Similarly, the following equation can be used for the low-confidence longitudinal position 904:

[0116]

[0117] In all aspects, when using multiple statistical distances (e.g., Hausdorff distance and Mahalanobis distance), the corresponding low confidence threshold and high confidence threshold can be the same or different for the calculations associated with each statistical difference.

[0118] In some implementations, the high-confidence longitudinal position 902 or the low-confidence longitudinal position 904 is not based on statistical distance, but rather on the standard deviation determined in the GPR aggregation. Figure 6 The description details the determination of the standard deviation.

[0119] Figure 10 Another road modeling output 1000 based on road modeling with an integrated Gaussian process is shown. As shown, vehicle 102 is modeling road 120-4 (an example of road 120), and vehicle 102 is traveling on road 120-4. Road modeling output 1000 includes uncertainties 1002 associated with parts of the road model. For example, uncertainty 1002-1 is associated with different parts of the road model compared to uncertainty 1002-2. In some implementations, uncertainty 1002 is based on data generated as part of an aggregation process and... Figure 6 The standard deviation is determined as described in the detailed description. In other implementations, the uncertainty of 1002 is based on... Figure 9 The statistical differences discussed in the text are used to determine this.

[0120] Uncertainty 1002 can be used to influence the behavior of vehicle 102 as it traverses road 120-4. For example, at locations where the road modeling output 1000 of road 120-4 includes a large uncertainty 1002, the vehicle may reduce its speed. Alternatively or additionally, the vehicle may reduce the time interval for iterations used to collect the road model, allowing more information about locations with high uncertainty to be collected before vehicle 102 must traverse that section of road 120-3. Furthermore, vehicle 102 may instruct its driver to perform navigation operations when traversing sections of road 120-3 with high uncertainty 1002. As a result of these operations, providing uncertainty measurements as an element of the road modeling output 1000 can provide more information to vehicle-based systems that rely on the road modeling output 1000, thereby allowing for safer and more comfortable driving behavior.

[0121] Example Method

[0122] Generally, any of the operations described in the methods can be performed, but are not necessarily limited to the order or combination of operations shown herein. Furthermore, any one or more operations can be repeated, combined, or rearranged to provide other operations. For ease of explanation, relative to... Figure 1 The elements describe the methods.

[0123] Figure 11 An example method 1100 for implementing a road perception system with integrated Gaussian processes for road modeling is shown. At 1102, the processor executes computer-readable instructions of Gaussian process module 108 to determine the kernel function of at least one Gaussian Process Recognition (GPR) at a first moment. In various aspects, determining the kernel function includes determining the parameter set of the kernel function of at least one GPR. The kernel parameters can be trained by uniform or partitioned training. Thus, each GPR may have its own kernel parameters, or all GPRs may utilize a single parameter set. In various aspects, each of the GPRs may utilize a different detection set to determine the kernel parameters. In this way, a large problem can be divided into smaller sets of problems, which utilize a divide-and-conquer strategy to maintain computational efficiency.

[0124] At 1104, the processor executes computer-executable instructions of the Gaussian process module 108 to determine the corresponding average lateral position associated with the longitudinal position of each of the at least one GPR. For example, a lateral position value can be determined for a longitudinal position on road 120. Each GPR can operate on a different subset of detections, thus different GPRs can provide different estimates of the average lateral position for a particular longitudinal position. In some implementations, each GPR utilizes a specific type of detection, detections within a specific set of longitudinal ranges, or detections within a specific accuracy range. In this way, easily comparable detections with similar structures can be processed within a single GPR, and aggregation can be performed later to seamlessly process data collected from different sources.

[0125] At 1106, the corresponding average lateral positions of each of at least one GPR are aggregated to determine the combined lateral positions associated with a specific longitudinal position. In various aspects, the Gaussian process module 108 includes computer-executable instructions that, when executed by a processor, enable the processor to perform the aggregation process using any number of statistical procedures, such as a generalized robust Bayesian committee machine, expert product (PoE), generalized PoE, Bayesian committee machine (BCM), or robust BCM. In some implementations, a generalized robust Bayesian committee machine is used because it converges to the underlying true prediction distribution as the sample size approaches infinity. By determining values ​​from multiple GPRs and then aggregating these values, a road model can be determined from multiple sensor sources while maintaining accuracy and computational efficiency. Furthermore, the aggregation can provide a statistical method for determining the uncertainty associated with each lateral value corresponding to a specific longitudinal value. Thus, the road model can include both the values ​​associated with the road model and the uncertainties associated with those values.

[0126] At 1108, the road model of road 120 at the first moment is output by output module 112. In some implementations, the road model is output to vehicle-based system 114 to assist in the execution of vehicle functions, such as autonomous or assisted driving functions. In some implementations, the road model of road 120 includes a combined lateral position and uncertainty associated with the longitudinal position. In other implementations, only the combined lateral position associated with the longitudinal position along road 120 is output. In some implementations, the road model includes multiple lateral positions, each associated with multiple longitudinal positions along road 120, to adequately model road 120.

[0127] Figure 12An example method 1200 for performing active learning based on road modeling with an integrated Gaussian process is illustrated. In each aspect, active learning is performed by executing computer-executable instructions of an active learning module 110. In each aspect, at 1202, one or more optimal detections are determined from the detection pool. In some implementations, active learning is utilized prior to subsequent iterations of the road modeling process. Alternatively or additionally, active learning can be used to classify detections into subsets during the first iteration. Typically, one or more optimal detections correspond to the detections that provide the most information gain. Specifically, one or more optimal detections can be determined using principles of desired improvement or principles of lower confidence bounds. Active learning can ensure that the detections added to the dataset are the most useful, thereby maintaining or improving accuracy and computational efficiency.

[0128] At time 1204, at least one kernel function for the GPR is determined at the second time step. In various implementations, the kernel function is determined using kernel parameters based on a subset determined through active learning at time 1202. In some implementations, the kernel function at the second time step can be determined using kernel parameters determined at the first time step. In this way, the GPR can be iteratively used to continuously update the road model in subsequent time steps. For example, kernel function parameters determined in previous iterations can serve as a baseline in subsequent iterations. Furthermore, detections from previous iterations can be used to determine kernel parameters for subsequent iterations. In this way, the accuracy of the road model can continue to improve with minimal regression to computational efficiency.

[0129] At 1206, the updated corresponding average lateral position associated with the longitudinal position of each GPR is determined. In each aspect, the updated corresponding average lateral position is based on a kernel function defined by kernel parameters determined at the second time step. At 1208, the updated corresponding average lateral positions associated with the longitudinal positions are aggregated to produce an updated combined lateral position associated with the longitudinal positions. In each aspect, the road model represents the combined lateral position associated with the corresponding longitudinal position. The aggregation may again include determining the uncertainty associated with each lateral position. At 1210, the road model of road 120 at the second time step is output by executing output module 112. In each aspect, the road model is output to the vehicle-based system 114 of vehicle 102 and includes more or more accurate information about road 120 when compared with the road model at the first time step. In some implementations, the road model includes the combined lateral position and associated uncertainty.

[0130] Figure 13A detailed example method 1108 is shown, which outputs a road model based on a road model with an integrated Gaussian process. In each aspect, method 1108 is executed by executing computer-executable instructions of output module 112. At 1302, the lateral positions of each GPR are compared. In each aspect, the comparison includes determining the distinct statistical differences between the GPRs. Method 1108 may optionally continue to 1304, 1306, or both.

[0131] At position 1304, the high-confidence longitudinal position is defined as the minimum longitudinal position, where the Hausdorff distance between at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the high-confidence threshold. In all respects, the high-confidence threshold is defined as any value that depends on the application. For example, the high-confidence threshold can be lower when higher confidence is desired or a high safety factor is to be achieved. Alternatively, or instead of the high-confidence longitudinal position, the low-confidence longitudinal position is defined as the minimum longitudinal position, where the Hausdorff distance between at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the low-confidence threshold. Typically, the low-confidence threshold is higher than the high-confidence threshold because higher confidence allows for greater uncertainty without exceeding the threshold.

[0132] At 1306, the high-confidence longitudinal position is determined as the minimum longitudinal position, wherein the Mahalanobis distance between at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the high-confidence threshold. In all respects, the high-confidence threshold is defined as any value dependent on the application and may differ from the high-confidence threshold defined at 1304. Similar to the operation performed at 1304, the low-confidence longitudinal position can be determined as the minimum longitudinal position, wherein the Mahalanobis distance between at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the low-confidence threshold. Again, the low-confidence threshold may be the same as or different from the low-confidence threshold at 1304.

[0133] In the implementation of both operations at position 1304 and position 1306, the minimum low-confidence vertical position or the minimum high-confidence vertical position can be determined. In all respects, this is accomplished by performing a minimum operation between the positions determined at positions 1304 and 1306.

[0134] At point 1308, the road model of the road at the first moment is output, which includes a combined lateral position associated with the longitudinal position or the high-confidence longitudinal position. In some implementations, the road model may include a low-confidence longitudinal position. Thus, the road model may include a high-confidence portion, a medium-confidence portion, and a low-confidence portion, which are respectively defined as the portion of the road model from vehicle 102 to the high-confidence longitudinal position, the portion from the high-confidence longitudinal position to the low-confidence longitudinal position, and the portion from the low-confidence longitudinal position to any further longitudinal position from vehicle 102. In this way, the disclosed road modeling with integrated Gaussian processes allows the output to include accurate values ​​of road models with associated uncertainties.

[0135] Additional examples

[0136] Example 1. A method comprising: modeling a road at a first time using at least one Gaussian process regression (GPR), the modeling comprising: determining a kernel function of at least one GPR based on a sample set of detections received from one or more vehicle systems at the first time; determining a corresponding mean lateral position of each of the at least one GPR, the corresponding mean lateral position being associated with a specific longitudinal position, based on the kernel function at the first time; aggregating the corresponding mean lateral positions of each of the at least one GPR to determine a combined lateral position associated with the specific longitudinal position; and outputting a road model of the road at the first time, the road model including the combined lateral position associated with the specific longitudinal position.

[0137] Example 2. The method as described in any of the preceding examples, wherein determining the combined lateral position associated with a particular longitudinal position comprises: determining the variance associated with the longitudinal position; and outputting a road model of the road at a first moment further comprising the variance associated with the longitudinal position.

[0138] Example 3. The method as described in any of the preceding examples further includes: modeling a road at a second time using at least one Gaussian process regression (GPR), the modeling comprising: determining a kernel function of at least one GPR at the second time based on an updated detection set received from one or more vehicle systems and a kernel function at a first time; determining an updated corresponding mean lateral position of each of the at least one GPR based on the kernel function at the second time, the updated corresponding mean lateral position being associated with a longitudinal position of the at least one GPR; aggregating the updated corresponding mean lateral positions of each of the at least one GPR to determine an updated combined lateral position associated with the longitudinal position; and outputting a road model of the road at the second time, the road model including the updated combined lateral position associated with the longitudinal position.

[0139] Example 4. The method as described in any of the preceding examples, wherein the method further comprises: for at least one GPR, determining one or more optimal detections from a detection pool, each detection in the detection pool including a longitudinal position and a lateral position, the one or more optimal detections corresponding to the detection that provides the most information gain, wherein the one or more optimal detections from the detection pool are included in the sample set of detections.

[0140] Example 5. The method as described in any of the preceding examples, wherein the detection that provides the most information gain comprises: determining the longitudinal position that causes the largest change in the corresponding average lateral position of at least one GPR, the corresponding average lateral position being associated with the longitudinal position.

[0141] Example 6. The method as described in any of the preceding examples, wherein the detection that provides the most information gain comprises: determining the longitudinal position with the maximum lower confidence limit based on the corresponding average lateral position associated with the longitudinal position and the corresponding variance associated with the longitudinal position.

[0142] Example 7. The method as described in any of the preceding examples, wherein the kernel function for determining at least one GPR at a first moment includes determining the kernel parameters that result in the maximum log-marginal likelihood.

[0143] Example 8. The method as described in any of the preceding examples, wherein the kernel function for determining at least one GPR at a first moment comprises: dividing the detected sample set into one or more detection subsets; and determining kernel parameters that result in the maximum sum of each log-marginal likelihood associated with each of the one or more detection subsets.

[0144] Example 9. The method as described in any of the preceding examples, wherein dividing the detected sample set into one or more detection subsets is based on the detection type.

[0145] Example 10. The method as described in any of the preceding examples, wherein the kernel function for determining at least one GPR at a first moment is further based on Gaussian noise values.

[0146] Example 11. The method as described in any of the preceding examples, wherein aggregating the corresponding average lateral positions of each of at least one GPR to determine the combined lateral positions associated with a particular longitudinal position comprises using at least one of the following: a generalized robust Bayesian committee machine; an expert product; a generalized expert product; a Bayesian committee machine; or a robust Bayesian committee machine.

[0147] Example 12. The method as described in any of the preceding examples, wherein outputting a road model at a first moment includes outputting the road model to a vehicle-based system to assist the vehicle-based system in performing vehicle functions.

[0148] Example 13. The method as described in any of the preceding examples, wherein the sample set to be detected includes position data and heading data.

[0149] Example 14. The method as described in any of the preceding examples, wherein at least one detection in the sample set of detections is received from a vision detection system of a vehicle and is based on the visual detection of lane boundaries on the detected road.

[0150] Example 15. The method as described in any of the preceding examples, wherein at least one detection in the sample set being detected is a trajectory detection received from the radar system of the vehicle, and is based on radar tracking determined by the radar system.

[0151] Example 16. The method as described in any of the preceding examples, wherein at least one detection in the sample set is a trajectory detection received from a mapping system of a vehicle and based on a road map of the road.

[0152] Example 17. The method as described in any of the preceding examples, wherein the sample set to be detected includes multiple detection types.

[0153] Example 18. The method as described in any of the preceding examples, wherein the output road model at a first time step comprises: for each pair of GPRs in at least one GPR, comparing the average lateral position associated with the longitudinal position; determining a high-confidence longitudinal position, wherein each comparison of the average lateral position associated with a longitudinal position smaller than the high-confidence longitudinal position is less than a high-confidence threshold, wherein determining the high-confidence longitudinal position comprises: determining a minimum longitudinal position, wherein the Hausdorff distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the high-confidence threshold; or determining a minimum longitudinal position, wherein the Mahalanobis distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the high-confidence threshold; and outputting a combined lateral position associated with the longitudinal position at the longitudinal position smaller than the high-confidence longitudinal position as the high-confidence position.

[0154] Example 19. The method as described in any of the preceding examples, wherein the road model of the output road at a first time further comprises: determining a low-confidence longitudinal position, wherein each comparison of the lateral positions associated with a longitudinal position smaller than the low-confidence longitudinal position is less than a low-confidence threshold, wherein determining the low-confidence longitudinal position comprises: determining a minimum longitudinal position, wherein the Hausdorff distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the low-confidence threshold; or determining a minimum longitudinal position, wherein the Mahalanobis distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the low-confidence threshold; and outputting a combined lateral position associated with longitudinal positions at longitudinal positions smaller than the low-confidence longitudinal position and longitudinal positions greater than or equal to the high-confidence longitudinal position as a medium-confidence position; and outputting a combined lateral position associated with longitudinal positions at longitudinal positions greater than or equal to the low-confidence longitudinal position as a low-confidence position.

[0155] Example 20. A method comprising: modeling a road using at least one Gaussian process regression (GPR), the modeling comprising: for a GPR in at least one GPR, determining one or more best detections from a detection pool, each detection in the detection pool including a longitudinal position and a lateral position, the one or more best detections corresponding to the maximum information gain; using the GPR in at least one GPR and the one or more best detections, determining a corresponding average lateral position associated with the longitudinal position; using an aggregation function, determining a combined lateral position associated with the longitudinal position, the combined lateral position being based at least on the corresponding average lateral position determined using the one or more best detections; and outputting a road model of the road, the road model including the combined lateral position associated with the longitudinal position.

[0156] Example 21. The method as described in any of the preceding examples, wherein the detection associated with the maximum information gain comprises: determining the longitudinal position as the largest change in the corresponding average lateral position that results in at least one GPR, the corresponding average lateral position being associated with the longitudinal position.

[0157] Example 22. The method as described in any of the preceding examples, wherein the detection associated with the maximum information gain comprises: determining the longitudinal position with the maximum lower confidence limit based on the corresponding average lateral position associated with the longitudinal position and the corresponding variance associated with the longitudinal position.

[0158] Example 23. A system comprising: at least one processor configured to model a road at a first time using at least one Gaussian process regression (GPR), the at least one processor being configured to model the road at the first time by: determining a kernel function of one or more GPRs based on a sample set of detections received from one or more vehicle systems; determining a corresponding mean lateral position of each of the one or more GPRs based on the kernel function, the corresponding mean lateral position being associated with a longitudinal position; aggregating the corresponding mean lateral positions of each of the at least one GPR to determine a combined lateral position associated with the longitudinal position; and outputting a road model of the road at the first time, the road model including the combined lateral position associated with the longitudinal position.

[0159] Example 24. A system as described in any of the preceding examples, wherein at least one processor is configured to: determine a combined lateral position associated with the longitudinal position by determining the variance associated with the longitudinal position; and output a road model of the road at a first moment to include the variance associated with the longitudinal position.

[0160] Example 25. A system as described in any of the preceding examples, wherein at least one processor is further configured to: model a road at a second time step using at least one Gaussian process regression (GPR), the at least one processor being configured to model the road at the second time step by: determining a kernel function of at least one GPR at the second time step based on an updated detection set received from one or more vehicle systems and a kernel function at a first time step; determining an updated corresponding mean lateral position of each of the at least one GPRs based on the kernel function at the second time step, the updated corresponding mean lateral position being associated with a longitudinal position of at least one GPR; aggregating the updated corresponding mean lateral positions of each of the at least one GPRs to determine an updated combined lateral position associated with the longitudinal position; and outputting a road model of the road at the second time step, the road model including the updated combined lateral position associated with the longitudinal position.

[0161] Example 26. A system as described in any of the preceding examples, wherein at least one processor is further configured to: for at least one GPR, determine one or more optimal detections from a detection pool, each detection in the detection pool including a longitudinal position and a lateral position, the one or more optimal detections corresponding to the detection that provides the most information gain; and include the one or more optimal detections from the detection pool in a sample set of said detections.

[0162] Example 27. A system as described in any of the preceding examples, wherein at least one processor is further configured to aggregate the respective average lateral positions of each of at least one GPR to determine a combined lateral position associated with a longitudinal position, comprising using at least one of the following: a generalized robust Bayesian committee machine; an expert product; a generalized expert product; a Bayesian committee machine; or a robust Bayesian committee machine.

[0163] Example 28. A system as described in any of the preceding examples, wherein at least one processor is further configured to output a road model of the road at a first time step by: for each pair of GPRs in at least one GPR, comparing the average lateral position associated with the longitudinal position; determining a high-confidence longitudinal position, wherein each comparison of the average lateral position associated with a longitudinal position smaller than the high-confidence longitudinal position is less than a high-confidence threshold, wherein at least one processor is configured to determine the high-confidence longitudinal position by: determining a minimum longitudinal position, wherein the Hausdorff distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the high-confidence threshold; or determining a minimum longitudinal position, wherein the Mahalanobis distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the high-confidence threshold; and outputting a combined lateral position associated with the longitudinal position at the longitudinal position smaller than the high-confidence longitudinal position as the high-confidence position.

[0164] Example 29. A system as described in any of the preceding examples, wherein at least one processor is further configured to output a road model of a road at a first time step by: determining a low-confidence longitudinal position, wherein each comparison of lateral positions associated with a longitudinal position smaller than the low-confidence longitudinal position is less than a low-confidence threshold, wherein at least one processor is configured to determine the low-confidence longitudinal position by: determining a minimum longitudinal position, wherein the Hausdorff distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the low-confidence threshold; or determining a minimum longitudinal position, wherein the Mahalanobis distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the low-confidence threshold; and outputting a combined lateral position associated with longitudinal positions at longitudinal positions smaller than the low-confidence longitudinal position and longitudinal positions greater than or equal to the high-confidence longitudinal position as a medium-confidence position; and outputting a combined lateral position associated with longitudinal positions at longitudinal positions greater than or equal to the low-confidence longitudinal position as a low-confidence position.

[0165] Example 30. A system as described in any of the preceding examples, wherein: the system is mounted on a vehicle; and at least one processor is configured to: in response to an output road model at a first moment, execute the road model at the first moment to perform the functions of the vehicle.

[0166] Example 31. A system comprising a processor configured to perform a method of any of the preceding examples.

[0167] Example 32. A system comprising means for performing a method of any of the preceding examples.

[0168] Example 33. A non-transient computer-readable storage medium comprising instructions that, when executed, cause a processor to perform a method of any of the preceding examples.

[0169] Conclusion

[0170] While various embodiments of the present disclosure have been described in the foregoing description and illustrated in the accompanying drawings, it should be understood that the present disclosure is not limited thereto, but can be practiced in various ways within the scope of the following claims. It will be apparent from the foregoing description that various modifications can be made without departing from the spirit and scope of the present disclosure as defined by the following claims.

[0171] Unless the context explicitly states otherwise, the use of "or" and grammatically related terms indicates an unrestricted, non-exclusive alternative. As used herein, the phrase referring to "at least one" of a list of items means any combination of those items, including a single member. As an example, "at least one of a, b, or c" is intended to cover: a, b, c, ab, ac, bc, and abc, as well as any combination with multiple identical elements (e.g., aa, aaa, aab, aac, abb, acc, bb, bbb, bbc, cc, and ccc, or any other ordering of a, b, and c).

Claims

1. A method for road modeling, the method comprising: The road is modeled at the first time step using multiple Gaussian process regressions (GPR) in the following manner: Based on a sample set of detections received from one or more vehicle systems, the kernel function of each of the plurality of GPRs is determined at the first moment; Based on the kernel function at the first moment, the corresponding average lateral position of each of the plurality of GPRs is determined, and the corresponding average lateral position is associated with a specific longitudinal position. Aggregate the respective average lateral positions of each of the plurality of GPRs to determine a combined lateral position associated with the specific longitudinal position; and Output the road model of the road at the first time point, the road model including the combined lateral position associated with the specific longitudinal position; and The road is modeled at the second time step using the multiple GPRs in the following manner: For each of the plurality of GPRs, an optimal detection from the detection pool is determined, each detection in the detection pool including a longitudinal position and a lateral position. The optimal detection is included in the sample set of the detections and corresponds to the detection that provides the most information gain, wherein the detection that provides the most information gain includes: The longitudinal position is determined as the one that causes the maximum change in the corresponding average lateral position of the plurality of GPRs, the corresponding average lateral position being associated with the longitudinal position; or The longitudinal position with the maximum lower confidence limit is determined based on the corresponding average lateral position associated with the longitudinal position and the corresponding variance associated with the longitudinal position. For each of the plurality of GPRs, the kernel function of each of the plurality of GPRs at the second time time is determined based on the updated detection set received from one or more vehicle systems, the best detection, and the kernel function of each of the plurality of GPRs at the first time time. Based on the kernel function at the second time point, an updated corresponding average lateral position of each of the plurality of GPRs is determined, the updated corresponding average lateral position being associated with the longitudinal position of each of the plurality of GPRs. Aggregate the updated average lateral position of each of the plurality of GPRs to determine an updated combined lateral position associated with the longitudinal position; and Output the updated road model of the road at the second time point, the updated road model including the updated combined lateral position associated with the longitudinal position.

2. The method as described in claim 1, characterized in that, Determining the combined lateral position associated with the specific longitudinal position includes: Determine the variance associated with the longitudinal position; and The road model output at the first moment further includes the variance associated with the longitudinal position.

3. The method as described in claim 1, characterized in that, Determining the kernel function for each of the plurality of GPRs at the first moment includes determining the kernel parameters that result in the maximum log-marginal likelihood.

4. The method as described in claim 1, characterized in that, The kernel function for determining each of the plurality of GPRs at the first moment includes: The sample set to be detected is divided into one or more detection subsets; and Determine the kernel parameter that results in the maximum sum of each log-marginal likelihood associated with each of the one or more detection subsets.

5. The method as described in claim 4, characterized in that, Dividing the sample set of the detection into one or more detection subsets is based on the detection type.

6. The method as described in claim 1, characterized in that, The kernel function of each of the plurality of GPRs is determined at the first moment based on the Gaussian noise value.

7. The method as described in claim 1, characterized in that, Aggregating the respective average lateral positions of each of the plurality of GPRs to determine the combined lateral position associated with the particular longitudinal position includes using at least one of the following: Generalized Robust Bayesian Committee Machine; Expert product; Generalized expert product; Bayesian committee machine; or Robust Bayesian committee machine.

8. The method as described in claim 1, characterized in that, Outputting the road model at the first moment includes outputting the road model to a vehicle-based system to help the vehicle-based system perform vehicle functions.

9. The method as described in claim 1, characterized in that, The sample set for detection includes location data and heading data.

10. The method as described in claim 1, characterized in that, At least one detection in the sample set of the detection is received from the visual detection system of the vehicle and is based on the visual detection of lane boundaries on the road.

11. The method as described in claim 1, characterized in that, At least one detection in the sample set of the detection is a trajectory detection received from the radar system of the vehicle, and is based on radar tracking determined by the radar system.

12. The method as described in claim 1, characterized in that, At least one detection in the sample set of the detection is a map detection received from the mapping system of the vehicle and based on the road map of the road.

13. The method as described in claim 1, characterized in that, The sample set for testing includes multiple test types.

14. The method as described in claim 1, characterized in that, The road model output at the first time step includes: For each pair of GPRs among the plurality of GPRs, a comparison will be made with the average lateral position associated with the longitudinal position; The high-confidence vertical position is determined using the following method: Determine a minimum longitudinal position, wherein the Hausdorff distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to a high confidence threshold, which is a predetermined value; or Determine a minimum longitudinal position, wherein the Mahalanobis distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the high confidence threshold; and Output the road model of the road at the first time point, the road model of the road at the first time point including the combined lateral position associated with the high confidence longitudinal position.

15. The method as described in claim 14, characterized in that, The output of the road model at the first time step further includes: The low-confidence vertical location is determined using the following method: Determine a minimum longitudinal position, wherein the Hausdorff distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to a low confidence threshold, the low confidence threshold being another predetermined value greater than the high confidence threshold; or Determine a minimum longitudinal position, wherein the Mahalanobis distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the low confidence threshold; and Output the road model of the road at the first time step, the road model of the road at the first time step including the combined lateral position associated with the low confidence longitudinal position.

16. A method for road modeling, the method comprising: Roads are modeled using multiple Gaussian process regressions (GPRs), the modeling process including: For each of the multiple GPRs, the optimal detection from the detection pool is determined, where each detection in the detection pool includes a longitudinal position and a lateral position, and the optimal detection corresponds to the maximum information gain. Using the GPR from the plurality of GPRs and the best detection, a corresponding average lateral position associated with the longitudinal position is determined; Using an aggregation function, a combined lateral position associated with the longitudinal position is determined, the combined lateral position being based at least on the corresponding average lateral position determined using the optimal detection; and Output the road model of the road, the road model including the combined lateral position associated with the longitudinal position.

17. The method as described in claim 16, characterized in that, The detection associated with the maximum information gain includes: The longitudinal position is determined as the one that causes the largest change in the corresponding average lateral position of the plurality of GPRs, the corresponding average lateral position being associated with the longitudinal position.

18. The method as described in claim 16, characterized in that, The detection associated with the maximum information gain includes: The longitudinal position with the maximum lower confidence limit is determined based on the corresponding average lateral position associated with the longitudinal position and the corresponding variance associated with the longitudinal position.

19. A system for road modeling, the system comprising: At least one processor, said at least one processor being configured to: The road is modeled at the first time step using multiple Gaussian process regressions (GPRs), and the at least one processor is configured to model the road at the first time step in the following manner: Based on a sample set of detections received from one or more vehicle systems, the kernel function of each of the plurality of GPRs is determined at the first moment; Based on the kernel function, the corresponding average lateral position of each of the plurality of GPRs is determined, and the corresponding average lateral position is associated with the longitudinal position. Aggregate the respective average lateral positions of each of the plurality of GPRs to determine a combined lateral position associated with the longitudinal position; and Output the road model of the road at the first time moment, the road model including the combined lateral position associated with the longitudinal position; and The road is modeled using the multiple GPRs at a second time step, and the at least one processor is configured to model the road at the second time step in the following manner: For each of the plurality of GPRs, an optimal detection from the detection pool is determined, each detection in the detection pool including a longitudinal position and a lateral position. The optimal detection is included within the sample set of the detections and corresponds to the detection that provides the most information gain, wherein the detection that provides the most information gain includes: The longitudinal position is determined as the one that causes the maximum change in the corresponding average lateral position of the plurality of GPRs, the corresponding average lateral position being associated with the longitudinal position; or The The longitudinal position with the maximum lower confidence limit is determined based on the corresponding average lateral position associated with the longitudinal position and the corresponding variance associated with the longitudinal position. For each of the plurality of GPRs, the kernel function of each of the plurality of GPRs at the second time time is determined based on the updated detection set received from one or more vehicle systems, the best detection, and the kernel function of each of the plurality of GPRs at the first time time. Based on the kernel function at the second time point, an updated corresponding average lateral position of each of the plurality of GPRs is determined, the updated corresponding average lateral position being associated with the longitudinal position of each of the plurality of GPRs. Aggregate the updated average lateral position of each of the plurality of GPRs to determine an updated combined lateral position associated with the longitudinal position; and Output the updated road model of the road at the second time point, the updated road model including the updated combined lateral position associated with the longitudinal position.

20. The system as described in claim 19, characterized in that, The at least one processor is configured to: The combined lateral position associated with the longitudinal position is determined by determining the variance associated with the longitudinal position; and Output the road model of the road at the first time point, including the variance associated with the longitudinal position.

21. The system as described in claim 19, characterized in that, The at least one processor is further configured to aggregate the respective average lateral position of each of the plurality of GPRs to determine the combined lateral position associated with the longitudinal position by using at least one of the following: Generalized Robust Bayesian Committee Machine; Expert product; Generalized expert product; Bayesian committee machine; or Robust Bayesian committee machine.

22. The system as described in claim 19, characterized in that, The at least one processor is further configured to output the road model of the road at the first time step in the following manner: For each pair of GPRs among the plurality of GPRs, a comparison will be made with the average lateral position associated with the longitudinal position; The high-confidence vertical position is determined using the following method: Determine a minimum longitudinal position, wherein the Hausdorff distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to a high confidence threshold, which is a predetermined value; or Determine a minimum longitudinal position, wherein the Mahalanobis distance between the average lateral positions of at least a pair of GPRs at the minimum longitudinal position is greater than or equal to the high confidence threshold; as well as Output the road model of the road at the first time point, the road model of the road at the first time point including the combined lateral position associated with the high confidence longitudinal position.

23. The system as described in claim 22, characterized in that, The at least one processor is further configured to output the road model of the road at the first time step in the following manner: The low-confidence vertical location is determined using the following method: Determine a minimum longitudinal position, wherein the Hausdorff distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to a low confidence threshold, the low confidence threshold being another predetermined value greater than the high confidence threshold; or Determine a minimum longitudinal position, wherein the Mahalanobis distance between the average lateral positions of at least one pair of GPRs at the minimum longitudinal position is greater than or equal to the low confidence threshold; and Output the road model of the road at the first time step, the road model of the road at the first time step including the combined lateral position associated with the low confidence longitudinal position.

24. The system as described in claim 19, characterized in that: The system is installed on the vehicle; and The at least one processor is configured to: In response to outputting the road model of the road at the first moment, the road model of the road at the first moment is executed to perform the function of the vehicle.

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