System and method for tracking the dilation state of an object

Abstract

Provided herein is a system and method for tracking an expansion state of an object, the expansion state of the object including a kinematic state indicating the position of the object and an extended state indicating one or a combination of the size and orientation of the object. The system includes: at least one sensor configured to detect a scene including a moving object using one or more signal transmissions to generate one or more measurements of the object per transmission; and a processor configured to execute a probability filter that tracks a joint probability of the expansion state of the object estimated by a motion model of the object and a measurement model of the object, wherein the measurement model includes a center-truncated distribution with a truncation interval. The system also includes an output interface configured to output the expansion state of the object.

Description

Technical Field

[0001] The present invention relates generally to automotive object tracking and, more particularly, to systems and methods for tracking an expanded state of an object. Background Art

[0002] The control system used by a vehicle (autonomous or semi-autonomous) predicts safe movements or paths for the vehicle in order to avoid collisions with obstacles such as other vehicles or pedestrians, and the control system also optimizes some criteria associated with the operation of the vehicle. The vehicle's sensors sense the surrounding environment such as road edges, pedestrians and other vehicles. Automotive radar bvar has revealed its role from existing ADAS (Advanced Driver Assistance Systems) to emerging autonomous driving assistance systems. Together with ultrasound, camera and LIDAR sensors, automotive radar assists the task of environmental sensing and understanding in all-weather conditions with affordable cost and scalable production. Specifically, automotive radar provides direct measurement of radial velocity, long operating range, small size in millimeter or sub-terahertz frequency bands, and high spatial resolution.

[0003] The control system of a vehicle tracks the object state of other vehicles (wherein the object state includes the kinematic state) based on automotive radar measurements to control the vehicle. Extended object tracking (EOT) with multiple measurements per scan has shown improved object tracking by enhancing the object state from only the kinematic state to both the kinematic state and the extended state compared to traditional point object tracking that includes only one measurement per scan. The extended state provides the size and orientation of the tracked object. To achieve this, it is necessary to capture the spatial distribution (i.e., how the automotive radar measurements are distributed around the object space) together with the sensor noise. Current methods include a framework of a fixed set of points on a rigid body, which requires an unscalable data association between the fixed set of points and the automotive radar detections even for single object tracking. Spatial models such as contour models and surface models bypass the cumbersome data association steps.

[0004] For automotive radar measurements, the contour model reflects the distribution of measurements along the contour of an object (e.g., a rigid body), and the surface model assumes that the radar measurements are generated from the inner surface of a two-dimensional shape. Examples of contour models include simple rectangular shapes and more general star-convex shapes modeled by random hypersurface models or Gaussian process models. Surface models such as Gaussian-based ellipse and layered Gaussian-based ellipse models are computationally much simpler than contour models that require more degrees of freedom to describe more complex shapes. However, the measurements of the object are affected by noise and only receive reflections from the surface of the object. Therefore, the above models are far from real-world automotive radar measurements, as real-world automotive radar measurements are observed to be distributed around the edges or surfaces of rigid objects with a specific volume.

[0005] Therefore, there is a need for a system and method for tracking the kinematic state and extension state of an object by capturing real-world automotive radar measurements. Summary of the invention

[0006] Some embodiments are directed to a system and method for tracking the expansion state of an object. The expansion state of an object includes a kinematic state indicating the position of the object and an extension state indicating one or a combination of the size and orientation of the object. Some embodiments are based on the recognition that the expansion state of an object can be estimated using a central truncated distribution and a corresponding underlying untruncated Gaussian distribution.

[0007] Some embodiments are based on the goal of tracking an object using automotive radar measurements. To this end, in some embodiments, the object is tracked using point object tracking that receives a single measurement from the object per scan. Point object tracking only provides the kinematic state (position) of the object. In addition, a probabilistic filter with a measurement model of the kinematic state distribution is used to track the object. Some embodiments are based on extended object tracking (EOT), in which multiple objects are tracked and multiple measurements per time step are generated corresponding to each object. The measurements are constructed around the object space. Extended object tracking provides both the kinematic state and the extended state (size and orientation) of the object. The kinematic state and the extended state are collectively referred to as the extended state. The object is tracked using a probabilistic filter with a measurement model of the extended state distribution.

[0008] However, the real-world automotive radar measurement distribution shows that multiple reflections from objects are complex. Due to this complexity, the design of the measurement model becomes complicated. Therefore, the conventional measurement model is only applicable to the kinematic state, not the extended state.

[0009] To this end, in some embodiments, spatial models such as contour models and surface models are used to capture real-world automotive radar measurements. However, the above-mentioned spatial models are inaccurate. Some embodiments are based on the recognition that real-world automotive radar measurements are distributed around the edges or surfaces of objects with a certain volume, which leads to surface volume models. The surface volume model is a balance between the contour model and the surface model, which has more realistic features while keeping the EOT accurate. However, the surface volume model is computationally complex. To this end, some embodiments are based on the goal of formulating a model in which the distribution density appears at the ends rather than the center so that it resembles and captures real-world automotive radar measurements.

[0010] To achieve this, a central truncated distribution is iteratively estimated by a probability filter. The central truncated distribution is used to fit the measurement. The central truncated distribution is based on a truncation interval at the center and provides a smaller probability for measurements at the center of the central truncated distribution within the truncation interval and a larger probability for measurements outside the truncation interval. To this end, some embodiments are based on the recognition that the central truncated distribution can be used to represent real-world measurements.

[0011] The center truncated distribution is a truncation of the underlying untruncated Gaussian distribution according to the truncation interval. The underlying Gaussian distribution is centered at the mean of the distribution, and the variance measures the spread and width of the distribution.

[0012] To this end, some embodiments are based on the goal of estimating a central truncated distribution of fitted measurements and subsequently the mean and variance of an underlying Gaussian distribution corresponding to the estimated central truncated distribution. Some embodiments are based on the recognition that the mean of the underlying Gaussian distribution indicates the position of the object in the expanded state and the variance of the underlying Gaussian distribution indicates the size and orientation of the object in the expanded state. To this end, some embodiments are based on the recognition that using a pair of central truncated distribution and underlying Gaussian distribution, both the kinematic state and the expanded state of the object can be estimated. In addition, this simplifies the parameterization of tracking the expanded state. Furthermore, using a pair of central truncation and underlying Gaussian distribution, the dimensionality of the calculation is reduced.

[0013] Some embodiments are based on the goal of removing noise from a measurement when the measurement is affected by noise. In some embodiments, the probability filter is configured to remove noise from the measurement before evaluating the noise-free measurement source according to a center-truncated Gaussian distribution, so that the probability filter generates a center-truncated distribution that fits the noise-free measurement source. In addition, a truncation interval is determined for the measurement source without noise. According to some embodiments, the measurement model is a hierarchical measurement model that defines probability parameters of hidden measurements of the noise-free source for each measurement.

[0014] To this end, some embodiments are based on the recognition that the hierarchical measurement model essentially captures not only the spatial distribution, i.e., how the automotive radar measurements are spatially distributed around the object, but also the characteristics of the sensor noise. In addition, a Bayesian EOT algorithm is formulated based on the hierarchical measurement model for both the kinematic state and the extended state. In some embodiments, the Bayesian EOT algorithm is developed based on the hierarchical measurement model by recursively predicting the expanded state and updating the expanded state and the truncation interval. The truncation interval is also called the truncation boundary.

[0015] In some embodiments, to update the clipping boundary, the measurement at time step k in global coordinates is converted to a local measurement in the object coordinate system using the updated state estimate from the (t-1)th iteration. k Define density support D kUsing the local measurements aggregated from the scan from time step k-L+1 to time step k, the maximum likelihood estimation is used to update the B k The specified truncation bounds are updated. To this end, the truncation bounds are updated and thus updated truncation bounds are obtained. Using the updated truncation bounds and the measurements at time step k, the kinematic state and the stretch state are updated using the modified random matrix.

[0016] Furthermore, in some embodiments, a control input of a controller of the vehicle is determined using a vehicle model having an extended state with bounded uncertainty, and the vehicle is controlled according to the control input. The vehicle model includes a motion model of an object affected by process noise and a measurement model of the object affected by measurement noise, such that one or a combination of the process noise and the measurement noise bounds the uncertainty of the extended state of the object.

[0017] Thus, one embodiment discloses a system for tracking an expansion state of an object including a kinematic state indicating a position of the object and an extended state indicating one or a combination of a size and orientation of the object, the system comprising: at least one sensor configured to detect a scene including a moving object using one or more signal transmissions to generate one or more measurements of the object; a processor configured to execute a probability filter that tracks a joint probability of the expansion state of the object estimated by a motion model of the object and a measurement model of the object, wherein the measurement model comprises a central truncated distribution having a truncation interval, providing a smaller probability for measurements at the center of the central truncated distribution within the truncation interval, and providing a larger probability for measurements outside the truncation interval, wherein the central truncated distribution is a truncation of an underlying untruncated Gaussian distribution according to the truncation interval, wherein the probability filter is configured to estimate the central truncated distribution of the fitted measurements and generate a mean and variance of the underlying Gaussian distribution corresponding to the central truncated distribution, such that the mean of the underlying Gaussian distribution indicates the position of the object in the expansion state, and the variance of the underlying Gaussian distribution indicates the size and orientation of the object in the expansion state; and an output interface configured to output the expansion state of the object.

[0018] Therefore, another embodiment discloses a method for tracking an expansion state of an object including a kinematic state indicating a position of the object and an extended state indicating one or a combination of a size and an orientation of the object, wherein the method uses a processor connected to a memory storing executable instructions, which executable instructions when executed by the processor perform the steps of the method, the method comprising the following steps: detecting a scene including a moving object by at least one sensor using one or more signal transmissions to generate one or more measurements of the object according to the transmissions; executing a probability filter that tracks a joint probability of the expansion state of the object estimated by a motion model of the object and a measurement model of the object, wherein the measurement model includes a central truncated distribution with a truncation interval, providing a smaller probability for measurements at the center of the central truncated distribution within the truncation interval, and providing a larger probability for measurements outside the truncation interval, wherein the central truncated distribution is a truncation of an underlying untruncated Gaussian distribution according to the truncation interval, wherein the probability filter estimates the central truncated distribution of the fitted measurements and generates a mean and variance of the underlying Gaussian distribution corresponding to the central truncated distribution, so that the mean of the underlying Gaussian distribution indicates the position of the object in the expansion state, and the variance of the underlying Gaussian distribution indicates the size and orientation of the object in the expansion state; and outputting the expansion state of the object via an output interface.

[0019] The presently disclosed embodiments will be further described with reference to the accompanying drawings. The drawings shown are not necessarily to scale, with emphasis instead generally being placed upon illustrating the principles of the presently disclosed embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] [ Figure 1A ] Figure 1A Together, a schematic overview of some principles used by some embodiments for tracking the dilation state of an object is shown.

[0021] [ Figure 1B ] Figure 1B Together, a schematic overview of some principles used by some embodiments for tracking the dilation state of an object is shown.

[0022] [ Figure 1C ] Figure 1C Together, a schematic overview of some principles used by some embodiments for tracking the dilation state of an object is shown.

[0023] [ Figure 2 ] Figure 2 A block diagram of a system for tracking a dilation state of an object is shown in accordance with some implementations.

[0024] [ Figure 3 ] Figure 3 Schematic diagram showing the recursive computation of the posterior density of a dilated state of an object using recursive Bayesian filtering in accordance with some embodiments.

[0025] [ Figure 4 ] Figure 4 Shown are examples of hidden measurement source variables and distributions of observable measurements in accordance with some embodiments.

[0026] [ Figure 5A ] Figure 5A An exemplary cutoff interval adaptation is shown when the front or back of an object faces the sensor in accordance with some embodiments.

[0027] [ Figure 5B ] Figure 5B An exemplary cutoff interval adaptation is shown when the object is oriented sideways relative to the sensor in accordance with some embodiments.

[0028] [ Figure 6 ] Figure 6 A schematic diagram illustrating the expansion state prediction step according to some embodiments.

[0029] [ Fig. 7A ] Fig. 7A A schematic diagram illustrating dilation state update steps according to some embodiments.

[0030] [ Figure 7B ] Figure 7B An exemplary pseudo measurement according to some embodiments is shown.

[0031] [ Figure 7C ] Figure 7C A schematic diagram illustrating pseudo measurement generation, truncation boundary update, and dilation state update according to some embodiments.

[0032] [ Fig. 8A ] Fig. 8A A schematic diagram illustrating a truncation boundary update step according to some embodiments.

[0033] [ Figure 8B ] Figure 8B Filter scan aggregation in an object coordinate system is shown in accordance with some embodiments.

[0034] [ Fig. 9A ] Fig. 9A A simulation of a scenario in which an object moves for 90 time steps during a turn is shown in accordance with some embodiments.

[0035] [ Fig. 9B ] Fig. 9B A performance evaluation graph utilizing an ideal measurement model is shown according to some embodiments.

[0036] [ Fig. 9C ] Fig. 9Cis a table showing the root mean square error (RMSE) of the kinematic state and extension state estimation of the object corresponding to the regular random matrix (RM) and the hierarchical truncated Gaussian random matrix (HTG-RM) using the ideal measurement model.

[0037] [ Fig. 10A ] Fig. 10A A graph showing performance evaluation under model mismatch according to some embodiments is shown.

[0038] [ Fig. 10B ] Fig. 10B is a table showing the RMSE of the kinematic state and extension state estimation of the object corresponding to RM and HTG-RM under model mismatch.

[0039] [ Fig.11A ] Fig.11A A schematic diagram of a vehicle including a controller in communication with a system employing the principles of some embodiments is shown.

[0040] [ Fig. 11B ] Fig. 11B Schematic diagram showing interaction between a controller and a controller of a vehicle according to some embodiments.

[0041] [ Fig. 11C ] Fig. 11C Schematic diagram showing an autonomous or semi-autonomous controlled vehicle using some embodiments to generate control inputs. DETAILED DESCRIPTION

[0042] In the following description, for the purpose of illustration, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it will be apparent to those skilled in the art that the present disclosure may be practiced without these specific details. In other cases, the devices and methods are shown only in block diagram form to avoid obscuring the present disclosure.

[0043] As used in this specification and claims, the terms "for example" and "such as" and the verbs "include," "have," "comprises," and other verb forms thereof, when used in conjunction with a list of one or more components or other items, should each be interpreted as open-ended, meaning that the list should not be viewed as excluding other additional components or items. The term "based on" means based at least in part on. In addition, it will be understood that the phraseology and terminology employed herein are for descriptive purposes and should not be viewed as limiting. Any headings utilized within this description are for convenience only and have no legal or limiting effect.

[0044] Figure 1A , Figure 1B and Figure 1CA schematic overview showing some of the principles used in some embodiments for tracking the expansion state of an object. A sensor 104 (e.g., an automotive radar) is used to track an object (e.g., vehicle 106). In point object tracking 100, a single measurement 108 is received per scan from vehicle 106. Point object tracking provides only the kinematic state (position) of vehicle 106. Additionally, a probabilistic filter with a measurement model having a kinematic state distribution is used to track vehicle 106. In extended object tracking (EOT) 102, multiple measurements 110 are received per scan. The multiple measurements 110 are spatially structured around vehicle 106. Extended object tracking provides the kinematic state and the expansion state (size and orientation) of vehicle 106. The kinematic state and the expansion state are collectively referred to as the expansion state. A probabilistic filter with a measurement model having an expansion state distribution is used to track vehicle 106. However, real-world automotive radar measurement 112 distributions show that multiple reflections from vehicle 106 are complex. Due to this complexity, the design of the measurement model becomes complex. Thus, conventional measurement models are only applicable to the kinematic state and not to the expansion state.

[0045] To this end, in some embodiments, a spatial model 114 such as a contour model 116 and a surface model 118 is used to capture real-world automotive radar measurements 112. However, the above spatial model 114 is inaccurate. Some embodiments are based on the recognition that real-world automotive radar measurements are distributed around the edges or surfaces of an object (vehicle 106) having a specific volume, thereby generating a surface volume model 120. The surface volume model 120 strikes a balance between the contour model 116 and the surface model 118, having more realistic features while maintaining EOT accuracy. However, the surface volume model 120 is computationally complex. To this end, some embodiments are based on the goal of formulating a model (as shown in 122) where the distribution density appears at the ends rather than the center of one or more dimensions, so as to resemble and capture real-world automotive radar measurements 112.

[0046] To achieve this, in some embodiments, a central truncated distribution 124 is estimated. Figure 1C A one-dimensional central truncated distribution 124 with appropriate scaling / normalization and the underlying untruncated Gaussian distribution 132 are shown. The central truncated distribution 124 is based on a truncation interval at the center 126. For example, the truncation interval is given by a < x < b. The central truncated distribution 124 is used to fit the measurements 110. Additionally, the central truncated distribution 124 provides a smaller probability for measurements at the center of the central truncation distribution 126 (i.e., within the truncation interval) and a larger probability for measurements outside the truncation intervals 128, 130. To this end, some embodiments are based on the recognition that the central truncated distribution 124 can be used to represent real-world automotive radar measurements 112.

[0047] This concept can be naturally extended to one or more dimensions. For example, a two-dimensional centrally truncated distribution of the length and width of an object and a three-dimensional centrally truncated distribution of the length, width, and height of an object. For multi-dimensional centrally truncated distributions, the truncated regions can be more complex shapes other than squares or rectangles.

[0048] The central truncated distribution 124 is a truncation of the underlying untruncated Gaussian distribution 132 with appropriate normalization / scaling. The underlying untruncated Gaussian distribution 132 is obtained based on the central truncated distribution. The mean and variance of the central truncated distribution 124 are different from the mean 136 and variance 134 of the underlying untruncated Gaussian distribution 132. In some embodiments, the mean 136 and variance 134 of the underlying untruncated Gaussian distribution 132 can be derived from the mean and variance of the central truncated distribution 124. Therefore, some embodiments are based on the recognition that there is a correlation between the central truncated distribution 124 and the underlying untruncated Gaussian distribution 132. To this end, in some embodiments, the mean 136 and variance 134 of the underlying untruncated Gaussian distribution 132 can be derived from the mean and variance of the central truncated distribution 124.

[0049] Some embodiments are based on the recognition that an underlying untruncated Gaussian distribution 132 can be used for estimation of the expanded state of the vehicle 106. To this end, in some embodiments, a central truncated distribution 124 is fitted to the measurement source, and the mean 136 and variance 134 of the underlying untruncated Gaussian distribution 132 corresponding to the estimated central truncated distribution 124 are iteratively estimated by a probability filter. The underlying untruncated Gaussian distribution 132 is centered at the mean 136 of the distribution, and the variance 134 measures the spread, width, of the distribution. The mean 136 of the underlying untruncated Gaussian distribution 132 indicates the position of the object in the expanded state, and the variance 134 of the underlying Gaussian distribution 132 indicates the size and orientation of the object in the expanded state.

[0050] To this end, some embodiments are based on the realization that using a pair of a centrally truncated distribution and a corresponding underlying untruncated Gaussian distribution, the dilation state of an object can be tracked. Additionally, this simplifies the parameterization of tracking the dilation state. Furthermore, using a pair of centrally truncated and underlying Gaussian distributions, the dimensionality of the calculation is reduced because the underlying Gaussian distribution 132 is represented with fewer parameters than a complex distribution representing the actual measurement.

[0051] Figure 2A block diagram of a system 200 for tracking the expansion state of an object according to some embodiments is shown. The object can be a vehicle, such as (but not limited to) a car, a bicycle, a bus, or a truck. In addition, the vehicle can be an autonomous or semi-autonomous vehicle. The expansion state includes a kinematic state indicating the position of the object and an extended state indicating the size and / or orientation of the object. According to some embodiments, the kinematic state corresponds to the motion parameters of the object, such as speed, acceleration, heading, and turn rate. In some other embodiments, the kinematic state corresponds to the position of the object with its motion parameters. The system 200 may include a sensor 202 or be operatively connected to a group of sensors to detect a scene using one or more signal transmissions to generate one or more measurements of the object per transmission. According to some embodiments, the sensor 202 may be a car radar. In some embodiments, the scene includes a moving object. In some other embodiments, the scene may include one or more objects, which include both moving objects and stationary objects.

[0052] The system 200 may have a plurality of interfaces that connect the system 200 to other systems and devices. For example, a network interface controller (NIC) 214 is adapted to connect the system 200 to a network 216 via a bus 212, and the network 216 connects the system 200 to a set of sensors that are operatively connected. Through the network 216 (wirelessly or by wire), the system 200 receives reflection data of one or more signal transmissions to generate one or more measurements of the object per transmission. Additionally or alternatively, the system 200 includes a control interface 228 configured to send control inputs to the controller 222.

[0053] The system 200 includes a processor 204 configured to execute stored instructions and a memory 206 storing instructions executable by the processor 204. The processor 204 can be a single core processor, a multi-core processor, a computing cluster, or any number of other configurations. The memory 206 can include a random access memory (RAM), a read only memory (ROM), flash memory, or any other suitable memory system. The processor 204 is connected to one or more input devices and output devices via a bus 212. The instructions implement a method for tracking the expansion state of an object.

[0054] To this end, the system 200 includes a motion model 208 and a measurement model 210. In some embodiments, the system 200 includes a probability filter 224. The probability filter 224 is executed by the processor 204. The probability filter iteratively executes the motion model 208 to predict the dilation state and executes the measurement model 210 to update the dilation state of the object predicted by the motion model 208. The execution of the motion model 208 produces a prediction of the dilation state of the object subject to a fixed value of the size of the object and a varying orientation of the object, such that the size of the object is updated only by the measurement model 210, while the orientation of the object is updated by both the motion model 208 and the measurement model 210.

[0055] Some embodiments are based on the recognition that the measurement model 210 includes a central truncated distribution 124 with a truncation interval. In some embodiments, the central truncated distribution 124 is a central truncated Gaussian distribution. In some other embodiments, the central truncated distribution 124 is a central truncated student-t distribution. The central truncated distribution 124 is a truncation of the underlying untruncated Gaussian distribution according to the truncation interval. In some embodiments, the probability filter 224 is configured to estimate the central truncated distribution 124 of the fitting measurement. The measurement model 210 is executed by the probability filter 224 to iteratively update the previous truncation interval determined during the previous iteration of the probability filter to generate a current truncation interval that fits the expansion state predicted by the motion model. In addition, the probability filter 224 updates the expansion state using the measurement model 210 with the central truncated Gaussian distribution of the current truncation interval. According to some embodiments, the probability filter 224 is one or a combination of a Bayesian filter, a Kalman filter, and a particle filter. The Bayesian filter is a general filter that can be used with different types of distributions. The Kalman filter works efficiently with a Gaussian distribution. In some implementations, processor 204 changes the cutoff interval for sensor 202 in response to a change in the orientation of the object.

[0056] In addition, the probability filter 224 is configured to generate a mean and a variance of an underlying Gaussian distribution corresponding to the estimated central truncated Gaussian distribution, such that the mean indicates the position of the object in the expanded state, and the variance indicates the size and orientation of the object in the expanded state. To this end, some embodiments are based on the recognition that the expansion state of the object can be estimated using the estimated central truncated Gaussian distribution and the underlying Gaussian distribution. In some embodiments, the execution of the measurement model 210 outputs a covariance matrix of the fitted measurement. The diagonal elements of the covariance matrix define the size of the object, and the non-diagonal elements of the covariance matrix define the orientation of the object.

[0057] Some embodiments are based on the goal of removing noise from the measurement when the measurement is affected by noise. To this end, in some embodiments, the probability filter 224 is configured to remove noise from the measurement before evaluating the likelihood of the noise-free measurement source according to the center-truncated Gaussian distribution, so that the probability filter 224 generates a center-truncated distribution 124 that fits the noise-free measurement source. In addition, a truncation interval is determined for the measurement source without noise. According to some embodiments, the measurement model 210 is a hierarchical measurement model that defines probability parameters of hidden measurements of noise-free sources for each measurement.

[0058] The system 200 includes a model of a vehicle 226, which includes a motion model 208 of an object affected by process noise and a measurement model 210 of the object affected by measurement noise, such that one or a combination of the process noise and the measurement noise bounds uncertainty in an expanded state of the object. The system 200 is operatively connected to the vehicle. The processor 204 is configured to determine a control input of a controller 222 of the vehicle using the model of the vehicle 226 having an expanded state with bounded uncertainty, and control the vehicle according to the control input.

[0059] In some embodiments, the processor 204 is configured to execute a probability filter 224 that tracks a joint probability of the dilation state of the object estimated by the object's motion model 208 and the object's measurement model 210. The joint probability is a posterior probability conditioned on the dilation state estimated during a previous iteration of the probability filter 224. In addition, the system 200 includes an output interface 220 to output the dilation state of the object. In some embodiments, the output interface 220 is configured to output the dilation state of the object to a controller 222.

[0060] Figure 3 Schematic diagram showing the recursive computation of the posterior density of the dilated state of an object using recursive Bayesian filtering in accordance with some embodiments. The dilated (kinematic and stretched) state is defined as ξ k =[x k ,X k ], a random vector x k ∈R dx represents the kinematic state, X k represents the stretched state. For time step k, the vehicle radar sensor observes n k Measurements

[0061] Assuming that at time k-1 the posterior density 302 is known to be p(ξ k-1 |Z 1:k-1 ), recursive Bayesian filtering begins 300. The posterior density is predicted by performing posterior density prediction 304. In some embodiments, the posterior density is predicted from the Chapman-Kolmogorov equation

[0062] p(ξ k-1 |Z 1:k-1 )=∫p(ξ k-1 |Z 1:k-1) p(ξ k |ξ k-1 )dξ k-1 ...............(1)

[0063] The transfer density p(ξ k |ξ k-1 ) is given by the object motion model. In addition, the predicted posterior density uses the current measurement Z k 308 updates 306 to

[0064] p(ξ k |Z 1:k) ∝p(ξ k |Z 1:k-1 )p(Z k |ξ k ).............(2)

[0065] in is the overall measurement likelihood, Represents the individual spatial distribution. Therefore, the updated posterior density is obtained 312. Since the Bayesian filter is recursive 310, the above steps are iteratively performed until the termination condition is met. In each iteration 310, the posterior density in the next iteration is predicted based on the updated predicted density of the current iteration. For the state update step 306, it includes blocks for scanning and aggregating local measurements 316, truncation boundary updates 318, and expanded state updates 320. It should be noted that the local scanning aggregation step 316 is optional. In addition, if the truncation boundary is known or used to save computational complexity, the online truncation boundary update 318 can also be skipped. To this end, some embodiments are based on the goal of giving all past measurements Z up to time k using Bayesian filtering. 1:k＝ {Z1,···,Z k}, by recursively calculating the posterior density p(ξ k |Z 1:k ) to track the object. In addition, in some embodiments, the posterior density p(ξ k |Z 1:k) Estimate the expansion state ξ with corresponding uncertainty k .

[0066] Hierarchical measurement model

[0067] The measurements 110 of the object are affected by noise and only receive reflections from the surface of the object, therefore, executing the probability filter with the noisy measurements may produce an incorrect estimate of the dilation state and therefore an incorrect object tracking. To this end, a truncation interval is determined for a noise-free measurement source (also referred to as a measurement source) such that the probability filter generates a center-truncated Gaussian distribution that fits the noise-free measurement source. Some embodiments are based on the recognition that the probability filter is configured to remove noise from the measurement before evaluating the likelihood of the noise-free measurement source according to the center-truncated Gaussian distribution.

[0068] In less noisy scenarios, some embodiments are based on the recognition that the probability filter is configured to evaluate the likelihood of noisy measurements according to a stratified center-truncated Gaussian distribution.

[0069] To remove noise from the measurements, some embodiments include the implementation of a hierarchical measurement model that Include hidden measurement source variables In other words, according to some embodiments, the hierarchical measurement model provides the probability parameters of the hidden measurement without noise sources for each measurement. Therefore, mathematically defined as

[0070]

[0071] where H is the kinematic state x k Next, we select the observation matrix of the position component (object center), ρ is the scaling factor, and D k Specify density support, is the normalization factor. In some embodiments, the hidden measurement source variable Also referred to as noise-free measurement source variants. The probability filter replaces the measurement with the hidden measurement when it is executed. Thus, the probability filter generates a center-truncated Gaussian distribution that fits the noise-free measurement source. In some embodiments, the hidden measurement of the noise-free source of each measurement is used to capture features with higher probability around the edges of the object.

[0072] Figure 4 Show hidden measurement source variables Example 400, where the density support is outside rectangle 404. Density support D k It can be any shape. For example, consider a rectangular shape 404 surrounding the center of the object. The rectangular shape 404 consists of four boundaries. Description. In some embodiments, the boundary corresponds to an interval truncated at the center. Truncated Gaussian probability density Centered on the coordinate origin (ρ=0.25, l=4.7, w=1.8, a1=b1=2.14 and a2=b2=0.75).

[0073] Noisy measurements are used to model sensor noise. In some embodiments, the noise-free measurement source is modified with sensor noise. By assuming a conditional distribution that is Gaussian to capture the sensor noise, where R k represents the noise covariance matrix.

[0074] To this end, given the hierarchical measurement model (3), some embodiments are based on the recognition that the resulting measurement likelihood (spatial distribution) can be calculated by integrating over the measurement source variables

[0075]

[0076] The above measurement likelihood (4) leads to the following total measurement likelihood which can be used in (2) of step 306 for updating. Figure 4 Shows the resulting measurement likelihood 402 where R k = diag([0.09, 0.09]). The hierarchical spatial distribution pushes the measurement likelihood away from the center, highly similar to the distribution of real-world automotive radar measurements. Additionally, according to some embodiments, due to self-occlusion, the hierarchical truncation model flexibly describes partially observed radar measurements (e.g., only rarely observed parts of a vehicle).

[0077] Figure 5A Shows an exemplary truncation interval adaptation according to some embodiments when the object faces the sensor 500 with its front 506 or back 502. For example, consider an object that is a vehicle (e.g., vehicle 106) of length "l" 504 and width w 510, and oriented such that its back 502 faces the sensor 500. The sensor 500 obtains measurements corresponding to a local view of the vehicle (i.e., looking from behind). For example, the truncation interval is given by a < x < b. In some embodiments, the truncation interval includes a starting interval that ends at infinity to reflect the orientation of the object relative to the sensor 500, e.g., a < x < ∞. In some other embodiments, the truncation interval includes a starting interval that ends at a maximum value, e.g., a < x < n max . For the above orientation (looking from behind), the truncation interval of the length 504 of the vehicle ends at infinity on the opposite side 506 (front side) of the vehicle relative to the sensor 500. Subsequently, the corresponding probability density 508 is determined. Alternatively, in some embodiments, the truncation interval of the length 504 of the vehicle ends at a maximum value on the opposite side 506 (front side) of the vehicle relative to the sensor 500, and the corresponding probability density can be determined.

[0078] Figure 5B500 according to some embodiments. Figure 5A An object that is the same as the vehicle contemplated in , but oriented laterally relative to the sensor 500. The sensor 500 obtains measurements corresponding to a partial view of the vehicle (i.e., seen from the side). In this case, the truncation interval of the width 510 of the vehicle ends at infinity relative to the sensor on the opposite side 512 of the vehicle. Subsequently, the corresponding probability density 514 is determined. Alternatively, in some embodiments, the truncation interval of the width 510 of the vehicle ends at a maximum value relative to the sensor on the opposite side 512 of the vehicle. To this end, some embodiments are based on the recognition that the hierarchical truncation model flexibly describes not only fully observed radar measurements, but also partially observed radar measurements.

[0079] Extended Object Tracking (EOT) Algorithm

[0080] A Bayesian EOT algorithm is developed based on a hierarchical measurement model for both the kinematic state and the extended state. The Bayesian EOT algorithm is also known as a hierarchical truncated Gaussian random matrix (HTG-RM) algorithm. In some embodiments, the Bayesian EOT algorithm is developed based on a hierarchical measurement model by recursively predicting the dilated state and updating the dilated state and truncation intervals. The truncation intervals are also known as truncation boundaries. Similar to the regular random matrix-based approach, it is assumed that both the predicted and updated dilated state densities share the factorized form of the kinematic state and the extended state.

[0081] p(ξ k |Z 1:k*) ≈p(x k |Z 1:k* )p(X k |Z 1:k* )..............(5)

[0082] =N(x k ;m k|k* ,P k|k* )IW(X k ;v k|k* ,V k|k* ),

[0083] where k * = k-1 for expansion state prediction, k * = k is used for extended state update. In other words, the kinematic state x k is a Gaussian distribution with a predicted / updated mean m k|k* and the covariance matrix P k|k* , and the stretch matrix X k is the inverse Wishart (IW) distribution with v k|k* Degrees of freedom and scaling matrix Vk|k* . Determine the parameters {m,P,v,V} of these associations for prediction k|k-1 and the parameters {m,P,v,V} used for updating k|k The Bayesian EOT algorithm involves recursively predicting the expansion state and updating the expansion state and truncation interval.

[0084] Prediction of expansion status

[0085] Figure 6 Schematic diagram showing the expansion state prediction step 304 according to some embodiments. Given a motion model 600

[0086]

[0087] where g(·) is the kinematic motion model, Q k-1 is the process noise w k-1 The covariance matrix, E x represents the corresponding transformation matrix (e.g., identity matrix or rotation matrix, depending on x k-1 ). Assume that the posterior density p(ξ k-1 |Z 1:k-1 ) shares the same form of (5) and the transition probability of (6), which is determined by the processor 204 for the predicted state density p(ξ k |Z 1:k-1 )602 Calculate the associated parameters {m, P, v, V} k|k-1 . The predicted state density p(ξ k |Z 1:k-1 )'s associated parameters {m,P,v,V} k|k-1 Given as

[0088] m k|k-1 =g(m k-1|k-1 ),

[0089]

[0090]

[0091]

[0092] Where T sis the sampling time and τ is a maneuver-related constant. In some embodiments, the kinematic state prediction 603 in (7a) and (7b) follows the prediction steps of a standard Kalman filter (KF) if g is a linear model, or follows the stretch KF when g is nonlinear. The stretch state prediction 603 is given by (7c) and (7d). In some other embodiments, a Bayesian filter or a particle filter is used instead of a Kalman filter for kinematic state and stretch state prediction. To this end, some embodiments are based on the recognition that a probabilistic filter executed by processor 204 iteratively executes the motion model to predict the expansion state.

[0093] Expansion status update

[0094] Fig. 7A A schematic diagram of an expansion state update step 318 is shown according to some embodiments. Local observation measurements 322 are obtained after optional scan aggregation 316 and truncation boundary update 318. Based on the surface volume distribution of the automotive radar measurement, two sufficient statistics, namely, the sample mean and the sample spread (variance), can be calculated using the regular random matrix method. However, using the regular random matrix method to calculate the sample mean and variance may produce biased estimates for the kinematic state and the extension state of the object.

[0095] In order to correct for these biases, pseudo measurements are developed. In addition, in some embodiments, pseudo measurements are used to calculate sample means and variances. In some embodiments, pseudo measurements are generated 702 by the processor 204 using a hierarchical measurement model. The pseudo measurements are used to calculate sample means and variances. Figure 7B Example pseudo measurements 714 are shown according to some embodiments. The dashed squares represent the truncation boundaries updated according to step 318. Circles 712 represent (possibly aggregated) local observed measurements in object coordinates, and dark dots 714 represent pseudo measurements. The ratio of the number of observed measurements 712 to pseudo measurements 714 is determined by the normalization factor of the truncated Gaussian distribution. k Observational measurements Corresponding to TN Measurement source variable for distribution

[0096] Assume that n c Pseudo-measurement From the complementary measurement likelihood

[0097]

[0098] Corresponding pseudo measurement source variable Where D k ∪D c =R 2 If the number of pseudo samples satisfies The ratio of the source variables is

[0099]

[0100] can be viewed as coming from an underlying Gaussian distribution Therefore, the corresponding joint measurement Is from the distribution As a result of the underlying Gaussian distribution, the kinematic state x k and the stretched state X k Can be obtained through The sample mean and variance give the first- and second-order sufficient statistics to capture 706.

[0101]

[0102]

[0103] in and

[0104] To this end, some embodiments are based on the goal of calculating the sample mean and variance. To calculate the sample mean and variance 706, the processor 204 generates a pseudo measurement. As from of samples, then The object state {x k|k ,X k|k} and truncate boundaries From the previous iteration step. In some embodiments, to avoid and The synthetic sampling of and The sample mean of and its second moment Using two sufficient statistics, the processor 204 calculates 704 the density p(ξ k |Z k )'s associated parameters {m,P,v,V} k|k The updated density p(ξ k |Z k )'s associated parameters {m,P,v,V} k|k Given as

[0105] m k|k =m k|k-1 +Kε,..........(12a)

[0106] P k|k＝ P k|k-1- KH P k|k-1,............(12b)

[0107] v k|k =v k|k-1 +n k ,.............(12c)

[0108]

[0109] Where K = P k|k-1 HS -1 , and Similar to the prediction step, the kinematic state x k The update step 708 is a Kalman filter-like update in (12a) and (12b). In addition, the stretch state update 708 in (12c) and (12d) requires two matrices.

[0110]

[0111]

[0112] They are respectively relative to the centroid of the joint measurement and predicted measured H m k|k-1 (via ε) and joint measurement (via ) are expanded in proportion.

[0113] Figure 7C shows pseudo measurement generation, truncation boundary B according to some embodiments k Schematic diagram of updating and expanding state updates. Get the initial kinematic state x k , stretch state X k and the cutoff boundary B k Given the observed measurements 716 and the predicted kinematic state x k|k-1 , stretch state X k|k-1 and the cutoff boundary B k|k-1 , the pseudo measurement 718 is generated by the processor 204 in iteration 0. In addition, in iteration 0, the pseudo measurement 718 is used to estimate the kinematic state, the dilation state, and the truncation boundary, which are respectively represented as and For this purpose, iteration 0 produces and

[0114] In the next iteration (i.e., iteration 1), based on the previous iteration estimate and and observed measurements 716, pseudo measurements 720 are generated by processor 204. In addition, pseudo measurements 720 are used by processor 204 to estimate the kinematic state, dilation state, and truncation boundary, which are represented as and Thus, the state and truncation boundary estimated in iteration 0 are updated. Similarly, in iteration 2, a pseudo measurement is generated by processor 204 and and Updated to and (Not shown in the figure). The processor 204 performs iterations until a termination condition is met. The termination condition may be predefined. In some embodiments, the termination condition is met when the number of iterations is greater than a threshold.

[0115] Truncation Boundary Update

[0116] Fig. 8A Schematic diagram showing the coordinate transformation 322 from ego vehicle coordinates to object coordinates, the scan aggregation 316 and the online truncation boundary update step 318 according to some embodiments. Given the above updated state ξ k|k =[x k|k ,X k|k ], by making the measurement likelihood Maximize to update the truncation boundary B k , where the individual measurement likelihood Depend on Figure 4 The likelihood described in the description of (4) is given. The measured likelihood is defined as the cumulative density function (CDF) of the standard Gaussian distribution as four boundaries 404 (e.g., B k Specifically, at the tth iteration, the measurement at time step k in the global coordinates is converted to a local measurement in the object coordinate (OC) system by the processor 204 using the updated state estimate from the (t-1)th iteration. The truncation boundary B k Define density support D k Using the scanned aggregated local measurements 316 from time step k-L+1 to time step k, the maximum likelihood (ML) estimate 318 used by processor 204 is used to update the B k To this end, the truncation boundary is updated, thereby obtaining an updated truncation boundary. In addition, in some embodiments, the kinematic state and the extension state are updated by the processor 204 using the HTG-RM using the updated truncation boundary and the measurement at time step k. Some embodiments are based on the recognition that the truncation boundary is accurately estimated using the filtered scan aggregate measurement from the past scan to update the truncation boundary.

[0117] Figure 8BFiltered sweep aggregation 316 in the object coordinate system according to some embodiments is shown. Filtered sweep aggregation is beneficial when automotive radar measurements are sparse and partially visible due to self-occlusion. Measurements 808 of the object 810 at time step k-1 in the global coordinate system are obtained. Similarly, measurements 812, 814 are obtained in the global coordinate system at timestamps k and k+1, respectively. In addition, some embodiments are based on the recognition that given a measurement in the global coordinate system (GC) (denoted by z) and the mean m of the object's kinematic state, the corresponding measurement in OC 816 at iteration t can be obtained as

[0118]

[0119] Where M is the kinematic mean of the available objects m (t-1) Constructed rotation matrix. In addition, All local measurements of the t-th iteration are grouped. At the last T-th iteration, the corresponding local measurements are retained for scanning aggregation. Specifically,

[0120]

[0121] and represents the filtered scan aggregate measurement from time step k. With a sliding window size L, the set of filtered scan aggregate measurements is represented as

[0122] Filtered Scanning Aggregation Measurements and new local measurements Grouped into ML estimate of the cutoff bound at iteration t Given by the following formula

[0123]

[0124] in is of the form (4), which involves the normalization factor and cross-sectional area D k , as function of . The ML estimates of the four truncation boundaries require computing integrals over D, and directly solving (16) may be computationally demanding for online updates. To this end, the scanned aggregate measurements are divided into four clusters using an expectation-maximum algorithm by the processor 204, which effectively decomposes the joint ML boundary update into at most four decoupled ML estimates of the truncation boundaries. The updates of the other three truncation boundaries can be similarly implemented by the processor 204. In the following, for simplicity, the notation of the iteration index t is omitted. It should be noted that the truncation boundary can be set to +∞ when its corresponding measurement set is empty. Let f(y1)=TN(0,Λ 1,1 ,b k,1 ) and f(r1)=(0,R1,1 ) represent density support {y|y>b k,1} is a univariate truncated Gaussian distribution with zero mean and variance R 1,1 The probability density function (PDF) of the Gaussian distribution is . Using the convolution formula, the density of z1=y1+r1 is given by

[0125]

[0126] where φ(·) represents the cumulative density function (CDF) of the standard Gaussian distribution, is the transformation object stretching matrix in OC, ζ 1,1 =Λ 1,1 +R 1,1 . The decomposed ML estimator then measures the set The likelihood of is maximized as

[0127]

[0128] where z1 is given by the x-coordinate of z. This is equivalent to minimizing the following cost function

[0129]

[0130] This can be solved efficiently using standard root-finding algorithms (eg, Halley's method).

[0131] Fig. 9A A simulation of a scenario in which an object moves for 90 time steps during a turn according to some embodiments is shown. The center of rotation of the object coincides with the physical center of the object. In some embodiments, the object is a rectangular object, for example, 4.7 meters long and 1.8 meters wide. The kinematic state of the object is defined as x k =[p k ,v k ,θ k ,ω k ] T ∈R 5 , with a two-dimensional position p k ∈R 2 , Extreme Speed ​​v k , heading / orientation θ k and the turning rate ω k The extended state of the object is determined by the position p k The symmetric positive definite covariance matrix X k Definition. Since the object is a rigid body, its width (w) and length (l) are estimated using the eigenvalue decomposition of the estimated stretched state:

[0132] X k =M(θ k )diag([l2 / 4,w 2 / 4])M T (θ k ),

[0133] Where M(θ k) is the object orientation (θ k ) is the identity matrix of the function.

[0134] In some embodiments, a nearly constant turning rate and extreme velocity motion model is used, where the sampling time T s = 1s and the standard polar and angular acceleration noises are and The transformation function E(·) is a rotation matrix that depends on the turning rate, that is, E(x k )=M(ω k ). In addition, the process of obtaining simulation trajectory.

[0135] Fig. 9B A performance evaluation curve graph with an ideal measurement model according to some embodiments is shown. Consider the ideal case where the automotive radar measurement follows a hierarchical truncated Gaussian model during the simulation trajectory. In addition, in some embodiments, the number of measurements at each time step is obtained from a Poisson distribution with a mean of 8. Fig. 9A Two snapshots of synthetic automotive radar measurements around an object are shown 900, which is a good indicator of realistic radar measurements. As can be seen, most of these radar measurements appear to be around the object edge 902. From 100 Monte Carlo runs, the object tracking performance is compared between a regular random matrix (denoted as RM) and a hierarchical truncated Gaussian random matrix (referred to as HTG-RM) algorithm. Fig. 9B The object tracking performance in terms of localization error (position), object length and width error for a total of 90 time steps using an ideal measurement model is shown. Fig. 9B It is evident that the HTG-RM algorithm outperforms the regularized random matrix approach in several aspects. Specifically, the HTG-RM algorithm provides more consistent estimates of object length and width over time. Furthermore, the corresponding root mean square error (RMSE) of the kinematic and extension state estimates of the object are analyzed.

[0136] Fig. 9C is a table showing the RMSE of the kinematic and extension state estimates of the object corresponding to RM and HTG-RM using the ideal measurement model. The root mean square error of the kinematic and extension state estimates of the object under HTG-RM is significantly smaller than that of the kinematic and extension state estimates of the object under RM. Specifically, HTG-RM produces significantly smaller RMSE in the object length l and width w estimates compared to RM.

[0137] Fig. 10APerformance evaluation under model mismatch according to some embodiments is shown. In real time, no measurement model can perfectly describe real-world automotive radar measurements. To this end, some embodiments are based on the recognition that to evaluate the robustness of the HTG-RM algorithm under model mismatch, a variational radar model of 50 Gaussian mixture components learned from aggregated real-world automotive radar measurements is fit to Fig. 9A Radar measurements are generated during the process. Fig. 10A The object tracking performance in terms of localization error (position), object length and width error for a total of 90 time steps under model mismatch is shown.

[0138] from Fig. 10A Obviously, the HTG-RM algorithm still outperforms the conventional RM method. Fig. 9B The performance of HTG-RM degrades slightly compared to the case of the ideal measurement model in , which shows the robustness of the HTG-RM algorithm on different surface volume measurement models. This is further confirmed by comparing the RMSE of the kinematic and extension state estimates of RM with the RMSE of the kinematic and extension state estimates of HTG-RM.

[0139] Fig. 10B is a table showing the RMSE of the kinematic state and extension state estimation of the object corresponding to RM and HTG-RM under model mismatch. The RMSE of the kinematic state and extension state estimation of the object under HTG-RM is significantly smaller than that of the object under RM. It is obvious from the table that, in particular, the RMSE of the object length and width estimation under HTG-RM is significantly smaller than that of the object length and width estimation under RM.

[0140] Fig.11A A schematic diagram of a vehicle 1100 is shown, which includes a controller 1102 in communication with a system 200 that employs the principles of some embodiments. The vehicle 1100 can be any type of wheeled vehicle, such as a passenger car, a bus, or a rover. In addition, the vehicle 1100 can be an autonomous or semi-autonomous vehicle. For example, some embodiments control the movement of the vehicle 1100. Examples of movement include lateral movement of the vehicle controlled by a steering system 1104 of the vehicle 1100. In one embodiment, the steering system 1104 is controlled by the controller 1102. Additionally or alternatively, the steering system 1104 can be controlled by a driver of the vehicle 1100.

[0141] In some embodiments, the vehicle may include an engine 1110, which may be controlled by the controller 1102 or by other components of the vehicle 1100. In some embodiments, the vehicle may include an electric motor instead of the engine 1110, and may be controlled by the controller 1102 or by other components of the vehicle 1100. The vehicle may also include one or more sensors 1106 to sense the surrounding environment. Examples of sensors 1106 include range finders such as radars. In some embodiments, the vehicle 1100 includes one or more sensors 1108 to sense its current motion parameters and internal states. Examples of one or more sensors 1108 include global positioning systems (GPS), accelerometers, inertial measurement units, gyroscopes, shaft rotation sensors, torque sensors, deflection sensors, pressure sensors, and flow sensors. The sensors provide information to the controller 1102. The vehicle may be equipped with a transceiver 1110 that enables the controller 1102 to communicate with the system 200 of some embodiments through a wired or wireless communication channel. For example, through transceiver 1110 , controller 1102 receives control input from system 200 .

[0142] Fig. 11B Schematic diagram showing the interaction between the controller 1102 and the controller 1112 of the vehicle 1100 according to some embodiments. For example, in some embodiments, the controller 1102 of the vehicle 1100 is a steering control 1114 and a brake / throttle controller 1116 that control the rotation and acceleration of the vehicle 1100. In this case, the controller 1102 outputs control commands to the controllers 1114 and 1116 based on the control input to control the kinematic state of the vehicle. In some embodiments, the controller 1112 also includes a high-level controller, such as a lane keeping assist controller 1118 that further processes the control commands of the controller 1102. In both cases, the controller 1112 uses the output of the controller 1102 (i.e., the control command) to control at least one actuator of the vehicle (e.g., the steering wheel and / or brake of the vehicle) to control the movement of the vehicle.

[0143] Fig. 11C A schematic diagram of an autonomous or semi-autonomous controlled vehicle 1120 using some embodiments to generate control inputs is shown. The controlled vehicle 1120 may be equipped with the system 200. In some embodiments, the controlled vehicle 1120 tracks various obstacles 1122, and then generates control inputs based on the obstacle tracking. In some embodiments, the control inputs include commands specifying values ​​for one or a combination of a steering angle of a wheel of the vehicle and a rotational speed of the wheel, and measurements include values ​​for one or a combination of a rotational rate of the vehicle and an acceleration of the vehicle.

[0144] The generated control inputs are intended to keep the controlled vehicle 1120 within certain boundaries of the road 1124 and to avoid other uncontrolled vehicles (i.e., obstacles 1122 to the controlled vehicle 1120). For example, based on the control inputs, the autonomous or semi-autonomous controlled vehicle 1120 may overtake another vehicle, such as on the left or on the right, or instead stay behind another vehicle within the current lane of the road 1124.

[0145] The following description provides only exemplary embodiments and is not intended to limit the scope, applicability or configuration of the present disclosure. Instead, the following description of exemplary embodiments will provide a feasible description for implementing one or more exemplary embodiments to those skilled in the art. It is contemplated that various changes may be made to the functions and arrangements of the elements without departing from the spirit and scope of the disclosed subject matter set forth in the appended claims.

[0146] Specific details are given in the following description to provide a thorough understanding of the embodiments. However, it will be appreciated by those of ordinary skill in the art that the embodiments may be practiced without these specific details. For example, the systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form to avoid obscuring the embodiments in terms of unnecessary details. In other cases, well-known processes, structures, and techniques may be shown without unnecessary details to avoid obscuring the embodiments. In addition, similar reference numerals and designations in the various drawings indicate similar elements.

[0147] In addition, various embodiments may be described as processes, which are depicted as flow charts, data flow diagrams, structure diagrams, or block diagrams. Although flow charts may describe operations as sequential processes, many operations may be performed in parallel or simultaneously. In addition, the order of operations may be rearranged. A process may terminate when its operations are completed, but may have additional steps that are not discussed or included in the accompanying drawings. In addition, not all operations in any specifically described process may appear in all embodiments. A process may correspond to a method, a function, a program, a subroutine, a subprogram, etc. When a process corresponds to a function, the termination of the function may correspond to the function returning to the calling function or the main function.

[0148] In addition, embodiments of the disclosed subject matter may be implemented at least in part manually or automatically. Manual or automatic implementation may be performed or at least assisted by the use of a machine, hardware, software, firmware, middleware, microcode, hardware description language, or any combination thereof. When implemented in software, firmware, middleware, or microcode, program code or code segments that perform the desired tasks may be stored in a machine-readable medium. A processor may perform the desired tasks.

[0149] In addition, the various methods or processes outlined herein may be encoded as software that can be executed on one or more processors using any of a variety of operating systems or platforms. In addition, such software may be written using any of a variety of suitable programming languages ​​and / or programming or scripting tools, and may also be compiled into executable machine language code or intermediate code that is executed on a framework or virtual machine. Typically, in various embodiments, the functionality of the program modules may be combined or distributed as desired.

[0150] The embodiments of the present disclosure may be embodied as a method, examples of which have been provided. The actions performed as part of the method may be ordered in any suitable manner. Thus, embodiments may be constructed that perform the actions in a different order than shown, which may include performing some actions simultaneously, although shown as sequential actions in the illustrative embodiments.

[0151] Although the present disclosure has been described with reference to certain preferred embodiments, it will be understood that various other adaptations and modifications may be made within the spirit and scope of the present disclosure. Therefore, the aspects of the appended claims cover all such changes and modifications that fall within the true spirit and scope of the present disclosure.

Claims

1. A system for tracking an expanded state of an object, the expanded state of the object comprising a kinematic state indicating a position of the object and an extended state indicating one or a combination of a size and an orientation of the object, the system comprising: at least one sensor configured to detect a scene including a moving object using a plurality of signal transmissions to generate a plurality of measurements of the object per transmission; a processor configured to execute a probability filter that tracks a joint probability of the expanded state of the object estimated by a motion model of the object and a measurement model of the object, wherein the measurement model includes a central truncated distribution with a truncation interval, providing a smaller probability for the measurement at the center of the central truncated distribution within the truncation interval and a larger probability for the measurement outside the truncation interval, wherein the central truncated distribution is a truncation of an underlying untruncated Gaussian distribution according to the truncation interval, wherein the probability filter is configured to estimate the central truncated distribution that fits the measurement and generate a mean and variance of an underlying Gaussian distribution corresponding to the central truncated distribution, such that the mean of the underlying Gaussian distribution indicates a position of the object in the expanded state, and the variance of the underlying Gaussian distribution indicates a size and orientation of the object in the expanded state; and An output interface is configured to output the expansion state of the object.

2. The system according to claim 1, wherein: The probability filter is one or a combination of a Bayesian filter, a Kalman filter, and a particle filter, and wherein the joint probability is a posterior probability conditioned on the dilated state estimated during a previous iteration of the probability filter.

3. The system according to claim 1, wherein: The probability filter iteratively executes the motion model to predict the dilated state and executes the measurement model to update the dilated state predicted by the motion model.

4. The system according to claim 1, wherein: The updating of the extended state includes a sweep aggregation of measurements transformed from global ego-vehicle coordinates to local object coordinates.

5. The system according to claim 3, wherein: within an iteration of the execution of the probability filter, the execution of the measurement model iteratively updates a previous truncation interval determined during a previous iteration of the probability filter to generate a current truncation interval that fits the dilated state predicted by the motion model and updates the dilated state using the measurement model with the central truncation distribution of the current truncation interval, or Therein, the motion model predicts the expansion state of the object subject to a fixed value of the object's size and a changing orientation of the object, such that the object's size is updated only by the measurement model, while the object's orientation is updated by both the motion model and the measurement model.

6. The system according to claim 1, wherein: Execution of the measurement model outputs a covariance matrix that fits the measurements, wherein diagonal elements of the covariance matrix define dimensions of the object, and wherein non-diagonal elements of the covariance matrix define an orientation of the object.

7. The system according to claim 1, wherein: The processor is further configured to change the cutoff interval in response to a change in the orientation of the object relative to the sensor.

8. The system according to claim 1, wherein: The processor is also configured to iteratively execute the probability filter, wherein, for each iteration, the probability filter determines the cutoff interval based on the distance between the clusters of the measurements, orients the axis of the central truncated distribution to connect the clusters of the measurements, generates the central truncated distribution based on the density of the measurements in the clusters, and estimates the mean and variance of the Gaussian distribution underlying the generated central truncated distribution.

9. The system according to claim 1, wherein: The center-truncated distribution is a center-truncated Gaussian distribution.

10. The system according to claim 1, wherein: At least one truncation interval is a start interval that ends at infinity to reflect the orientation of the vehicle relative to the sensor.

11. The system according to claim 9, wherein: A vehicle is oriented laterally relative to the sensor, and the cutoff interval for the width of the vehicle ends at infinity on an opposite side of the vehicle with respect to the sensor.

12. The system according to claim 9, wherein: The vehicle faces the sensor with its front or rear facing, and the cutoff interval for the length of the vehicle ends at infinity on the opposite side of the vehicle with respect to the sensor.

13. The system of claim 1, wherein: The measurement is affected by noise, wherein the truncation interval is determined for a measurement source without noise, and wherein the probability filter is configured to remove noise from the measurement before evaluating the likelihood of the noise-free source of the measurement based on the central truncated distribution, so that the probability filter generates the central truncated distribution that fits the noise-free source of the measurement.

14. The system of claim 1, wherein: The measurement is affected by noise, wherein the truncation interval is determined directly for the measurement, and wherein the probability filter is configured to evaluate the likelihood of the measurement based on a stratified central truncated distribution such that the probability filter generates the stratified central truncated distribution that fits the measurement.

15. The system of claim 12, wherein: The measurement model is a hierarchical measurement model defining, for each of the measurements, probability parameters of a hidden measurement free of noise sources, such that the probabilistic filter replaces the measurements with the hidden measurements when it is executed.

16. An arrangement comprising a system according to claim 1 and a vehicle, the vehicle comprising a controller in communication with the system, wherein: The system further comprises: a memory configured to store a model of the vehicle, the model of the vehicle comprising the motion model of the object affected by process noise and the measurement model of the object affected by measurement noise, such that one or a combination of the process noise and the measurement noise bounds an uncertainty in the expanded state of the object; wherein the processor is configured to determine control inputs of the controller of the vehicle using the model of the vehicle in the extended state with bounded uncertainty, and to control the vehicle according to the control inputs; and Wherein, the vehicle is operatively connected to the system.

17. A method for tracking an expanded state of an object, the expanded state of the object comprising a kinematic state indicating a position of the object and an extended state indicating one or a combination of a size and an orientation of the object, wherein: The method uses a processor coupled to a memory storing executable instructions which, when executed by the processor, perform the steps of the method, the method comprising the steps of: detecting, by at least one sensor, a scene including a moving object using a plurality of signal transmissions to generate a plurality of measurements of the object per transmission; executing a probability filter that tracks a joint probability of the expanded state of the object estimated by a motion model of the object and a measurement model of the object, wherein the measurement model includes a central truncated distribution having a truncation interval, providing a smaller probability for the measurement at the center of the central truncated distribution within the truncation interval and a larger probability for the measurement outside the truncation interval, wherein the central truncated distribution is a truncation of an underlying untruncated Gaussian distribution according to the truncation interval, wherein the probability filter estimates the central truncated distribution that fits the measurement and generates a mean and variance of an underlying Gaussian distribution corresponding to the central truncated distribution, such that the mean of the underlying Gaussian distribution indicates a position of the object in the expanded state, and the variance of the underlying Gaussian distribution indicates a size and orientation of the object in the expanded state; and The expansion state of the object is output via an output interface.

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