A method for velocity inference and trajectory reconstruction of unobserved vehicles in a connected environment

Abstract

The present invention discloses a method for speed inference and trajectory reconstruction of unobserved vehicles in a networked environment, the method comprising: obtaining trajectory data of intelligent networked vehicles and observed manually driven vehicles in mixed traffic flows, and arranging these records in chronological order. Searching for the inflection point of the speed change of the intelligent networked vehicle and estimating the shock wave velocity. Calculating the impact of congestion disturbance and free flow disturbance on the speed of any point in space respectively, and inferring the speed value of the full-time and space coordinate point. Based on the observed trajectory data of manually driven vehicles, the position intervals of the preceding unobserved vehicles are divided, and candidate positions of the unobserved vehicles are generated. A full-time and space vehicle trajectory reconstruction model is established, the optimal position of the unobserved vehicle at each time section is inferred, and the trajectory sequence of the unobserved vehicle is reconstructed. The method designed by the present invention improves the accuracy of speed and position estimation, and has important practical value for improving urban traffic perception and control capabilities.

Description

Technical Field

[0001] The present invention relates to the field of traffic perception and big data analysis, and in particular to a method for inferring the speed and reconstructing the trajectory of unobserved vehicles in a networked environment. Background Art

[0002] Against the backdrop of rapid urbanization and economic development, traffic congestion has become a common problem in many cities around the world. Traffic congestion not only affects urban efficiency and reduces residents' quality of life, but also leads to serious environmental pollution and energy waste.

[0003] Vehicle trajectories contain all traffic flow-related information at the spatiotemporal level, supporting traffic management and application measures such as traffic flow modeling and simulation, traffic conflict analysis, and congestion identification. With breakthroughs in vehicle-to-vehicle (V2X) and communication technologies, intelligent connected vehicles (ICVs) equipped with high-precision positioning systems, high-definition cameras, radar, and other environmental perception sensors can be considered new mobile detectors, recording their complete microscopic trajectories and the positions of surrounding vehicles with centimeter-level accuracy. However, due to the low penetration rate of ICVs and their limited detection range, the trajectory data they collect is significantly fragmented and incomplete. Therefore, it remains difficult to fully capture vehicle trajectories across all spatiotemporal dimensions, posing significant challenges for refined traffic control. Against this backdrop, vehicle trajectory reconstruction technology has become a hot topic in the field of traffic perception, leveraging existing detection data to develop effective models or algorithms to obtain a complete picture of traffic flow.

[0004] Current trajectory reconstruction technologies can be roughly divided into two categories: the first category is based on data-driven methods, which include interpolation and machine learning methods. They aim to use known partial trajectory data to reconstruct trajectories and ensure the continuity of speed in time and space. However, this type of method is sensitive to the density of detection data. When the spatial density of detectors is low, traditional interpolation methods will reduce the continuity and accuracy of the reconstruction results. The second category is model-based methods. Because they incorporate the influence of traffic flow operation patterns, this method is more robust to traffic congestion and transition states than data-driven methods, and can reconstruct vehicle trajectories with higher accuracy in some complex dynamic traffic scenarios.

[0005] In general, existing technologies fail to fully utilize data collected from intelligent connected vehicles, often using fixed empirical values ​​to set shock wave velocity parameters, making the reconstruction process difficult to ensure robustness. Furthermore, they lack consideration of vehicle following behavior during the reconstruction process, significantly impacting the applicability of the reconstructed trajectory. This novel vehicle trajectory reconstruction method considers the characteristics of sampled data from intelligent connected vehicles and proposes a velocity inference and trajectory reconstruction method for unobserved vehicles. By minimizing the difference between the estimated and actual positions of observed vehicles, it calculates the optimal position of the preceding unobserved vehicles. Summary of the Invention

[0006] The purpose of this invention is to provide a method for inferring the speed and reconstructing the trajectories of unobserved vehicles in a connected environment. Using expressways as the research object, a full-time and space-time vehicle trajectory reconstruction model is established. The optimal position of unobserved vehicles at each time section is inferred, and a trajectory sequence of unobserved vehicles is reconstructed to improve the accuracy of vehicle speed and position estimation.

[0007] To achieve the above functions, the present invention designs a method for estimating the speed and reconstructing the trajectory of unobserved vehicles in a connected environment. For each vehicle on the target road section, the following steps S1 to S5 are executed to complete the inference of the unobserved vehicle trajectory:

[0008] Step S1: Acquire the driving records of intelligent connected vehicles and manually driven vehicles observed by intelligent connected vehicles in the mixed traffic flow on the target road section, including vehicle trajectory data, and extract the vehicle ID, time, location, speed, and acceleration, and arrange the driving records of each vehicle in chronological order;

[0009] Step S2: Based on the driving records of each vehicle, searching for the inflection point of the speed change of the intelligent connected vehicle and calculating the shock wave velocity;

[0010] Step S3: Calculate the speed of the manually driven vehicle at any point on the target road section under the influence of congested flow disturbance and free flow disturbance respectively, and the speed of the manually driven vehicle at any point on the target road section under the combined influence of congested flow disturbance and free flow disturbance; in order to infer the speed values ​​of all time and space coordinate points;

[0011] Step S4: Based on the trajectory data of the manually driven vehicle observed by the intelligent connected vehicle, the position intervals of the previously unobserved vehicles are divided to generate candidate positions of the unobserved vehicles;

[0012] Step S5: Establish a full-time and space vehicle trajectory reconstruction model. Based on the candidate positions of the unobserved vehicles and the speed of the vehicle at any point on the target road section, infer the optimal position of the unobserved vehicles at each time section, and obtain the complete trajectory sequence of the unobserved vehicles through iterative reconstruction.

[0013] Beneficial effects: Compared with the prior art, the advantages of the present invention include:

[0014] This method deeply mines the fragmented trajectory information detected by intelligent connected vehicles and recalibrates the shock wave velocity using the vehicle's own motion trajectory, helping to more accurately approximate real-world traffic dynamics and providing critical prior information for inferring position. Simultaneously, a full-time and spatiotemporal vehicle trajectory reconstruction model is established based on the principles of a car-following model. By minimizing the deviation between the estimated and measured positions of observed vehicles, the most likely position of each undetected vehicle is inferred. This proposed method for inferring and reconstructing the speed of unobserved vehicles in a connected environment improves the accuracy of speed and position estimation, and has important practical value for enhancing urban traffic perception and control capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a flow chart of a method for inferring the speed and reconstructing the trajectory of an unobserved vehicle in a connected environment according to an embodiment of the present invention;

[0016] Figure 2 is a schematic diagram of shock wave velocity identification provided according to an embodiment of the present invention;

[0017] Figure 3 is a schematic diagram of the principle of space coordinate point velocity estimation provided by an embodiment of the present invention;

[0018] Figure 4 is a schematic diagram of generating candidate positions of unobserved vehicles according to an embodiment of the present invention;

[0019] Figure 5 2 is a schematic diagram of estimating the optimal position of an unobserved vehicle according to an embodiment of the present invention. DETAILED DESCRIPTION

[0020] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0021] The embodiment of the present invention provides a method for inferring the speed and reconstructing the trajectory of an unobserved vehicle in a networked environment, referring to Figure 1 For each vehicle on the target road section, execute the following steps S1 to S5 to complete the inference of the unobserved vehicle trajectory:

[0022] Step S1: Acquire the driving records of intelligent connected vehicles and manually driven vehicles observed by intelligent connected vehicles in the mixed traffic flow on the target road section, including vehicle trajectory data, and extract the vehicle ID, time, location, speed, and acceleration, and arrange the driving records of each vehicle in chronological order;

[0023] The specific method of step S1 is as follows:

[0024] For intelligent connected vehicles, the complete trajectory data of the vehicle is obtained from the data packets received by the vehicle communication module of the intelligent connected vehicle, and the vehicle ID, time, location, speed, and acceleration are extracted;

[0025] For manually driven vehicles, due to limited detection range and low penetration rate, only some manually driven vehicles can be observed by intelligent connected vehicles. Therefore, all recorded trajectory data fragments of manually driven vehicles are retrieved from the data packet, and the license plate number is used as the vehicle ID. For the same vehicle ID, all driving information related to the vehicle in the data packet is extracted, including timestamp, position, speed and acceleration, and sorted by timestamp to ensure the time series consistency of the data.

[0026] Step S2: Based on the driving records of each vehicle, searching for the inflection point of the speed change of the intelligent connected vehicle and calculating the shock wave velocity;

[0027] The specific steps of step S2 are as follows:

[0028] Step S2.1: For a pair of adjacent CAVs in the same lane h and CAV f , from the first timestamp to the last timestamp, set the sliding time window m to 5s, that is, from t1 to t5, t2 to t6, t3 to t7, ..., t I-4 ~t i Step by step, calculate the velocity standard deviation σ in each time window m m :

[0029]

[0030] Among them, v i is the velocity of the trajectory point of the intelligent connected vehicle, μ m is the vehicle speed v in the time window i The average value of

[0031] If σ m >2.5, then it is considered that v i is the inflection point of the speed change of the intelligent connected vehicle;

[0032] Step S2.2: Schematic diagram for shock wave velocity identification Figure 2 , assuming intelligent connected vehicle CAV h and CAV f The positions of the inflection points are x hi and x fi , and the corresponding times are t hi and t fi , the shock wave velocity is calculated as follows:

[0033]

[0034] Where c cong is the shock wave velocity.

[0035] Step S3: Calculate the speed of the manually driven vehicle at any point on the target road section under the influence of congested flow disturbance and free flow disturbance respectively, and the speed of the manually driven vehicle at any point on the target road section under the combined influence of congested flow disturbance and free flow disturbance; in order to infer the speed values ​​of all time and space coordinate points;

[0036] Reference diagram of the principle of spatial coordinate point velocity estimation Figure 3 , the specific steps of step S3 are as follows:

[0037] Step S3.1: For any spatial point coordinate (x, t) on the target road section, the speed of the manually driven vehicle spatial coordinate point observed by the intelligent connected vehicle is known to be v d (x, t), then the kernel density function under free flow state is Expressed as:

[0038]

[0039] Among them, φ is the kernel function; x i is the spatial coordinate point of the manually driven vehicle observed by the intelligent connected vehicle, t i is the speed of the spatial coordinate point of the manually driven vehicle observed by the intelligent connected vehicle, c free It is the disturbance velocity in the free flow state. Since the value does not change much, it is taken as 70km / h based on experience.

[0040] The speed v of the manually driven vehicle at point (x, t) under the influence of free flow disturbance is free (x, t) is calculated as follows:

[0041]

[0042] Step S3.2: For any spatial point coordinate (x, t) on the target road section, the speed of the manually driven vehicle spatial coordinate point observed by the intelligent connected vehicle is known to be v d (x, t), then the kernel density function under congestion flow state is Expressed as:

[0043]

[0044] Among them, c cong is the shock wave velocity; calculated in step S2;

[0045] Under the influence of congestion flow disturbance, the speed v of the manually driven vehicle at point (x, t) is cong (x, t) is calculated as follows:

[0046]

[0047] Step S3.3: For any spatial point coordinate (x, t) on the target road segment, considering the superposition of congestion flow disturbance and free flow disturbance, the speed v(x, t) of the manually driven vehicle is calculated as follows:

[0048] v(x,t)=ω(x,t)·v free (x,t)+(1-ω(x,t))·v cong (x,t)

[0049] Among them, ω(x, t) is an adaptive weight function that depends on the congestion level of each observation point at point (x, t), as shown in the following formula:

[0050]

[0051] Where, is the speed threshold between the free flow state and the congested flow state, which is 50 km / h according to experience; Δv is the transition width between the free flow and congested flow state, which is 10 km / h according to experience.

[0052] The kernel functions in step S3.1 and step S3.2 are specifically as follows:

[0053]

[0054] Where σ is the spatial smoothing width, which is empirically taken as 1 km; τ is the temporal smoothing width, which is empirically taken as 30 s.

[0055] Step S4: Based on the trajectory data of the manually driven vehicle observed by the intelligent connected vehicle, the position intervals of the previously unobserved vehicles are divided to generate candidate positions of the unobserved vehicles;

[0056] Schematic diagram of unobserved vehicle candidate position generation Figure 4 , the specific steps of step S4 are as follows:

[0057] Step S4.1: For a pair of adjacent CAVs in the same lane h and CAV f , defining intelligent connected vehicles (CAVs) h The last observable human-driven vehicle within the detection range is V h,I , Intelligent Connected Vehicle (CAV) f The first observable human-driven vehicle within the detection range is V f,1 , the vehicle body length is l, and the static safety distance between vehicles is s0; since the time from T0 to T e Moment, Vh,I and V f,1 The vehicles between them cannot be observed. Assuming that there are at most N unobserved vehicles, N is calculated as follows:

[0058]

[0059] Where x h,I 、x f,1 They are respectively manually driven vehicles V h,I 、V f,1 location;

[0060] Step S4.2: For each time segment, all unobserved vehicles V u,J Candidate position x′ u,J Should be in the vehicle V h,I With V f,1 Within a reasonable range between, no vehicle V is observed u,J The candidate position interval is calculated by the following formula:

[0061] x f,1 +s0+l≤x u,J ≤x h,I -(N-1)·(s0+l)

[0062] Step S5: Establish a full-time and space vehicle trajectory reconstruction model. Based on the candidate positions of the unobserved vehicles and the speed of the vehicle at any point on the target road section, infer the optimal position of the unobserved vehicles at each time section, and obtain the complete trajectory sequence of the unobserved vehicles through iterative reconstruction.

[0063] Schematic diagram of optimal position inference for unobserved vehicles Figure 5 , the specific steps of step S5 are as follows:

[0064] Step S5.1: For unobserved vehicles V u,J Different candidate positions x′ u,J , calculate the unobserved vehicle V u,J With the observable vehicle V f,1 The distance difference Δs; through step S3, it can be known that the unobserved vehicle V u,J Speed ​​v u,J , based on the unobserved vehicle V u,J Speed ​​v u,J , calculate the unobserved vehicle V u,J With the observable vehicle V f,1 The speed difference Δv;

[0065] Step S5.2: Calculate different candidate positions x′ u,J Generate an observable vehicle V f,1 The acceleration value is expressed as:

[0066]

[0067] Among them, v f,1 (t) is the observable vehicle V f,1 The speed, v max is the free stream velocity, γ is the acceleration factor, and its value is usually between 1 and 5. is the observable vehicle V f,1 The expected spacing is calculated as follows:

[0068]

[0069] Where S min is the safety distance, H is the safe headway, b is the comfortable deceleration, a max is the maximum acceleration;

[0070] Since the observable vehicle V f,1 From T0 to T e Position x at time f,1 (t) and velocity v f,1 (t) is known, calculate the observable vehicle V f,1 The position at the next time step is:

[0071]

[0072] Step S5.3: Establish a trajectory reconstruction model to solve the unobserved vehicle V at each moment u,J The optimal position of is as follows:

[0073]

[0074] Step S5.4: Reconstruct CAV f The last unobserved vehicle V u,J The trajectory of the unobserved vehicle V is reconstructed by iteratively executing steps S3 to S5, using its trajectory sequence as a reference. u,J The front car V u,J-1 Until the reconstructed trajectory is consistent with the intelligent connected vehicle CAV h The detected trajectories intersect to reconstruct the trajectory of the unobserved vehicle in all time and space.

[0075] The following is an application example of the method designed by the present invention:

[0076] The target road section in this example is Shenzhen Airport South Road in Bao'an Hangcheng Subdistrict, Bao'an District, Shenzhen. The study section is the elevated section of the city expressway running from west to east. The section is approximately 2 kilometers long with a speed limit of 80 km / h. The statistical information of the traffic state variables is shown in Table 1:

[0077] Table 1 Traffic status information

[0078]

[0079] In this example, a certain proportion of IDM vehicles are randomly distributed on the road at a penetration rate of 6%. IDM vehicles extract real-time information such as the speed and position of the detected vehicles from the trajectory data detected in the current lane and adjacent lanes. Before applying the trajectory reconstruction method, the parameters of the car-following model for human-driven vehicles and IDM vehicles are calibrated. The relevant IDM car-following model parameters are shown in Table 2:

[0080] Table 2 Model parameter values

[0081]

[0082] Based on the dataset and input parameters, the trajectory reconstruction algorithm of the present invention reconstructs the trajectories of all vehicles on the road section. The mean absolute error (MAE) is used to evaluate the reconstruction accuracy. The trajectory reconstruction results are verified using both the traditional model and the method of the present invention. The estimated error for each vehicle i is defined as the difference between the estimated trajectory and the observed trajectory:

[0083]

[0084] in, represents the estimated position of the jth trajectory point of vehicle i at time t, x i (t) represents the observed position of the jth trajectory point of vehicle i at time t. J represents the total number of trajectory points reconstructed by vehicle i. The larger the error, the greater the deviation between the true value and the estimated value.

[0085] Using the above formula, the velocity estimation errors for the traditional model and the proposed method are 2.48 m / s and 1.13 m / s, respectively. This demonstrates the superiority of the proposed method in reducing velocity estimation bias. The position estimation errors for the two algorithms are shown in Table 3. It can be seen that the maximum, average, and minimum errors for the proposed method are reduced by 39.37%, 26.21%, and 48.37%, respectively, compared to those for the traditional algorithm. This demonstrates that the proposed trajectory reconstruction algorithm is more accurate and reliable, providing more reliable data support for traffic management and planning.

[0086] Table 3 Comparison of trajectory reconstruction results between the present invention and the traditional method

[0087]

[0088] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.

Claims

1. A method for inferring the speed and reconstructing the trajectory of an unobserved vehicle in a connected environment, characterized by: For each vehicle on the target road section, execute the following steps S1 to S5 to complete the inference of the unobserved vehicle trajectory: Step S1: Acquire the driving records of intelligent connected vehicles and manually driven vehicles observed by intelligent connected vehicles in the mixed traffic flow on the target road section, including vehicle trajectory data, and extract the vehicle ID, time, location, speed, and acceleration, and arrange the driving records of each vehicle in chronological order; Step S2: Based on the driving records of each vehicle, searching for the inflection point of the speed change of the intelligent connected vehicle and calculating the shock wave velocity; Step S3: Calculate the speed of the manually driven vehicle at any point on the target road section under the influence of congested flow disturbance and free flow disturbance respectively, and the speed of the manually driven vehicle at any point on the target road section under the combined influence of congested flow disturbance and free flow disturbance; To infer the velocity values ​​of all space-time coordinate points; Step S4: Based on the trajectory data of the manually driven vehicle observed by the intelligent connected vehicle, the position intervals of the previously unobserved vehicles are divided to generate candidate positions of the unobserved vehicles; Step S5: Establish a full-time and space vehicle trajectory reconstruction model. Based on the candidate positions of the unobserved vehicles and the speed of the vehicles at any point on the target road section, infer the optimal position of the unobserved vehicles at each time section, and obtain the complete trajectory sequence of the unobserved vehicles through iterative reconstruction. The specific steps of step S5 are as follows: Step S5.1: For unobserved vehicles V u,J Different candidate positions x′ u,J , calculate the unobserved vehicle V u,J With the observable vehicle V f,1 The distance difference Δs; based on Unobserved Vehicle V u,J Speed ​​v u,J , calculate the unobserved vehicle V u,J With the observable vehicle V f,1 The speed difference Δv; Step S5.2: Calculate different candidate positions x′ u,J Generate an observable vehicle V f,1 The acceleration value is expressed as: Among them, v f,1 (t) is the observable vehicle V f,1 The speed, v max is the free stream velocity, γ is the acceleration factor, is the observable vehicle V f,1 The expected spacing is calculated as follows: Where S min is the safety distance, H is the safe headway, b is the comfortable deceleration, a max is the maximum acceleration; Calculate the observable vehicle V f,1 The position at the next time step is: Step S5.3: Establish a trajectory reconstruction model to solve the unobserved vehicle V at each moment u,J The optimal position of is as follows: Step S5.4: Iterate steps S3-S5 to reconstruct the unobserved vehicle V u,J The front car V u,J-1 Until the reconstructed trajectory is consistent with the intelligent connected vehicle CAV h The detected trajectories intersect to reconstruct the trajectory of the unobserved vehicle in all time and space.

2. The method for inferring and reconstructing the velocity of an unobserved vehicle in a connected environment according to claim 1, characterized in that: The specific method of step S1 is as follows: For intelligent connected vehicles, the complete trajectory data of the vehicle is obtained from the data packets received by the vehicle communication module of the intelligent connected vehicle, and the vehicle ID, time, location, speed, and acceleration are extracted; For manually driven vehicles, all recorded trajectory data fragments of manually driven vehicles are retrieved from the data packet, and the license plate number is used as the vehicle ID; for the same vehicle ID, all driving information related to the vehicle in the data packet, including timestamp, position, speed and acceleration, is extracted and sorted by timestamp.

3. The method for inferring and reconstructing the velocity of an unobserved vehicle in a connected environment according to claim 1, wherein: The specific steps of step S2 are as follows: Step S2.1: For a pair of adjacent CAVs in the same lane h and CAV f , from the first timestamp to the last timestamp, set the sliding time window m to 5s, and gradually calculate the speed standard deviation σ in each time window m m : Among them, v i is the velocity of the trajectory point of the intelligent connected vehicle, μ m is the vehicle speed v in the time window i The average value of If σ m >2.5, then it is considered that v i is the inflection point of the speed change of the intelligent connected vehicle; Step S2.2: Assume that the intelligent connected vehicle CAV h and CAV f The positions of the inflection points are x hi and x fi , and the corresponding times are t hi and t fi , the shock wave velocity is calculated as follows: Where c cong is the shock wave velocity.

4. The method for inferring and reconstructing the velocity of an unobserved vehicle in a connected environment according to claim 1, wherein: The specific steps of step S3 are as follows: Step S3.1: For any spatial point coordinate (x, t) on the target road section, the speed of the manually driven vehicle spatial coordinate point observed by the intelligent connected vehicle is known to be v d (x i ,t i ), then the kernel density function under free flow state Expressed as: Among them, φ is the kernel function; x i is the spatial coordinate point of the manually driven vehicle observed by the intelligent connected vehicle, t i is the speed of the spatial coordinate point of the manually driven vehicle observed by the intelligent connected vehicle, c free is the disturbance velocity in the free stream state; The speed v of the manually driven vehicle at point (x, t) under the influence of free flow disturbance is free (x, t) is calculated as follows: Step S3.2: For any spatial point coordinate (x, t) on the target road section, the speed of the manually driven vehicle spatial coordinate point observed by the intelligent connected vehicle is known to be v d (x i ,t i ), then the kernel density function under congestion flow state Expressed as: Among them, c cong is the shock wave velocity; Under the influence of congestion flow disturbance, the speed v of the manually driven vehicle at point (x, t) is cong (x, t) is calculated as follows: Step S3.3: For any spatial point coordinate (x, t) on the target road segment, considering the superposition of congestion flow disturbance and free flow disturbance, the speed v(x, t) of the manually driven vehicle is calculated as follows: v(x,t)=ω(x,t)·v free (x,t)+(1-ω(x,t))·v cong (x,t) Among them, ω(x,t) is the adaptive weight function, which is as follows: in, is the speed threshold between the free flow state and the congested flow state; Δv is the transition width between the free flow and congested flow states.

5. The method for inferring and reconstructing the velocity of an unobserved vehicle in a connected environment according to claim 4, characterized in that: The kernel functions in step S3.1 and step S3.2 are specifically as follows: Where σ is the spatial smoothing width and τ is the temporal smoothing width.

6. The method for inferring and reconstructing the velocity of an unobserved vehicle in a connected environment according to claim 1, characterized in that: The specific steps of step S4 are as follows: Step S4.1: For a pair of adjacent CAVs in the same lane h and CAV f , defining intelligent connected vehicles (CAVs) h The last observable human-driven vehicle within the detection range is V h,I , Intelligent Connected Vehicle (CAV) f The first observable human-driven vehicle within the detection range is V f,1 , the vehicle body length is l, and the static safety distance between vehicles is s0; since the time from T0 to T e Moment, V h,I and V f,1 The vehicles between them cannot be observed. Assuming that there are at most N unobserved vehicles, N is calculated as follows: Where x h,I 、x f,1 They are respectively manually driven vehicles V h,I 、V f,1 location; Step S4.2: For each time segment, the unobserved vehicles V u,J The candidate position interval is calculated by the following formula: x f,1 +s0+l≤x u,J ≤x h,I -N·(s0+l)。

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