A people flow and vehicle flow prediction method suitable for random sampling data loss

Abstract

This invention relates to the field of intelligent transportation and public safety management technology, and in particular to a method for predicting pedestrian and vehicle flow when random sampling data is lost. Starting from the moment of no lost sampling, this invention uses known real-time traffic data and regional dynamic event data, and employs a pre-built regression prediction model to predict real-time traffic data at each lost sampling moment, ensuring data integrity and monitoring reliability. Furthermore, this invention utilizes a gradient-based separable synchronous variable information iterative identification (GII-SS-VI) algorithm to solve for unknown parameters in the regression prediction model, resulting in higher estimation efficiency and accuracy. This effectively improves the accuracy of pedestrian and vehicle flow prediction results, providing a reliable basis for subsequent navigation systems, enabling them to identify potential risks and obstacles in advance, optimize real-time navigation paths, and improve traffic efficiency and safety.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation and public safety management technology, and in particular to a method for predicting pedestrian and vehicle flow that is suitable for cases of lost random sampling data. Background Technology

[0002] Real-time prediction of pedestrian and vehicle flow is crucial for urban traffic management, public safety early warning, intelligent navigation, and emergency command. Short-term predictions, such as those at the minute or hour level, are essential for congestion mitigation, early warning of crowd gathering risks, and dynamic route optimization. Existing methods for predicting pedestrian and vehicle flow can be mainly divided into process-driven models and data-driven models. Data-driven methods primarily establish the correlation between input features and output flow through mathematical means, with widely used methods including time series modeling and machine learning algorithms. Through system identification and parameter estimation techniques, mathematical models can be constructed to describe and predict the dynamic changes of pedestrian and vehicle flow in complex scenarios, considering various influencing factors such as regional events, weather conditions, and time-of-day characteristics. These models can not only be used to optimize traffic signal control and provide early warnings of congestion and gathering risks, but also provide decision support for navigation systems, security scheduling, and public space management.

[0003] However, in practical pedestrian and vehicle flow monitoring systems, random data loss often occurs due to sensor malfunctions or communication interruptions, severely impacting prediction performance and system reliability. For example, infrared or visual sensors may be affected by obstruction, changes in lighting, or equipment failure; data transmission may be affected by network fluctuations and signal interference; environmental factors such as severe weather and electromagnetic interference; and human and environmental factors such as improper equipment installation and untimely maintenance can all lead to random data loss, directly affecting the reliability of the monitoring system. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a method for predicting pedestrian and vehicle traffic flow that is suitable for random sampling data loss. Starting from the time when the sampling was never lost, based on known real-time traffic data and regional dynamic event data, a pre-built regression prediction model is used to predict the real-time traffic data at each time of lost sampling, so as to ensure data integrity and monitoring reliability. In addition, this invention uses the gradient-based separable synchronous variable information iterative identification (GII-SS-VI) algorithm to solve the unknown parameters in the regression prediction model, which has higher estimation efficiency and estimation accuracy.

[0005] This invention provides a method for predicting pedestrian and vehicle traffic flow suitable for cases of lost random sampling data, comprising the following steps: Acquire real-time traffic flow data of people and vehicles and regional dynamic event data in the monitored area during the monitoring period; The monitoring period is divided into two sets of time with lost sampling and time without lost sampling, based on whether there is any loss of real-time traffic data sampling. A set of prediction reference times is selected from the set of never-lost sampling times; for each prediction reference time in the set of prediction reference times, the n-1 times preceding that prediction reference time must belong to the set of never-lost sampling times. For each lost sampling moment in the set of lost sampling moments, the first moment in the prediction reference time set preceding that lost sampling moment is taken as the prediction starting moment. Based on the prediction starting moment itself, the real-time traffic data of the n-1 moments preceding it, and the pre-acquired regional dynamic event data of the m moments preceding the current lost sampling moment, the real-time traffic data of the lost sampling moment is predicted using a pre-constructed regression prediction model. Here, n and m represent the order of the traffic autoregression part and the regional dynamic event input part in the regression prediction model, respectively.

[0006] Optionally, real-time traffic flow data of pedestrians and vehicles in the monitoring area during the monitoring period is obtained through sensing sensors, including infrared thermal imaging sensors and / or visual sensors; the dynamic event data of the area is obtained by accessing the urban traffic management platform, the regional event monitoring system, or the environmental sensing network.

[0007] Optionally, the real-time traffic data at the time of the lost sampling can be predicted using a pre-built regression prediction model, including: Starting from the prediction start time, based on the prediction start time itself and the real-time traffic data of the previous n-1 times, the effective traffic data of each time after the prediction start time and before the lost sampling time is determined sequentially using a pre-built regression prediction model. Based on the real-time traffic data of the prediction start time itself and the n-1 times preceding it, the effective traffic data of each time after the prediction start time and before the lost sampling time, and the regional dynamic event data of the m times preceding the lost sampling time, the real-time traffic data of the lost sampling time is predicted using a pre-built regression prediction model.

[0008] Optionally, the effective flow data for each time point after the prediction start time and before the lost sampling time is determined sequentially using a pre-built regression prediction model, including: If the time point belongs to the set of time points without lost sampling, then the real-time traffic data sampled at that time point is determined as the valid traffic data at that time point; If the current moment belongs to the set of missing sampling moments, first determine the number of time intervals between this moment and the prediction starting moment. ; If the number of time intervals If it is less than n, then use the time before n. Effective traffic data at each moment, real-time traffic data at the predicted starting point moment itself, and traffic data going forward from the predicted starting point moment. The real-time traffic data at a given moment is combined with the regional dynamic event data from the previous m moments obtained in advance. The predicted traffic data at that moment is calculated using a pre-built regression prediction model, and the predicted traffic data is used to determine the effective traffic data at that moment. If the number of time intervals If the value is greater than n, then the effective flow data from n previous times is used, combined with the regional dynamic event data from m previous times obtained in advance, and the predicted flow data for that time is calculated using a pre-built regression prediction model. The predicted flow data is then used to determine the effective flow data for that time.

[0009] Optionally, the effective flow data for each time point after the prediction start time and before the lost sampling time is represented as: ; in, This represents the effective flow data at time t. This represents the set of sampling times that were not lost. Represents the set of missing sampling moments; This represents the real-time traffic data at time t; This represents the predicted flow data at time t; The predicted flow data is calculated using a regression prediction model. The expression for calculating the predicted flow data using the regression prediction model is as follows: ; ; ; in, Indicates the predicted start time. express Predicted traffic data at any given time; express Valid traffic data at any given moment; express Real-time traffic data at any given moment. Indicates To predict the starting time and the number of time intervals is The predicted information vector at that time; and They are respectively The linear and nonlinear parts; express The equivalent noise term at any given time; They represent time,…, Valid traffic data at any given moment; express The reference vector of the prediction information at that time, and They represent The linear and nonlinear parts; Represents nonlinear parameters; express Real-time regional dynamic event data, express Real-time regional dynamic event data, Represents a linear parameter vector; They represent time,…, Real-time traffic data at any given moment; They represent time,…, Real-time regional dynamic event data.

[0010] Optionally, linear parameter vector The expression is: ; in, The dimension is A set of vectors; and They represent linear parameter vectors respectively. The non-exponential part of the parameters and the exponential part of the parameters; These represent the 1st, 2nd, ..., 1st in the autoregressive part of the flow. One linear coefficient; These represent the 1st, 2nd, ..., 1st in the autoregressive part of the flow. One nonlinear coefficient; These respectively represent the 1st, 2nd, ..., 1st in the region dynamic event input section. One linear coefficient; These respectively represent the 1st, 2nd, ..., 1st in the region dynamic event input section. One nonlinear coefficient.

[0011] Optionally, the expression for the equivalent noise term is: ; in, express The original noise at any given moment express Time's up The sum of the original noise at each moment.

[0012] Optionally, linear parameter vector and nonlinear parameters The solution process includes: definition Linear augmented information vector at time step Linear augmented information vector The expression is: ; ; ; in, This represents the effective flow data at time t; This represents the real-time traffic data at time t; Represents a linear parameter information vector Transpose of; They represent time, time,……, Valid traffic data at any given moment; They represent time, time,……, Real-time regional dynamic event data; Define the criterion function Criterion function The expression is: ; in, ; Represents a set of unknown parameters; Indicates the length of the news feed; express Predicted traffic data at any given time; express The transpose of the linearly augmented information vector at time step; Based on the aforementioned criterion function, determine the first... The optimal innovation length in the next iteration ; Optimal news length The expression is: ; in, Indicates rounding operation. To adjust the parameters, ; Based on the criterion function and the appropriate innovation length, the linear parameter vector is... and nonlinear parameters Perform iterative solutions.

[0013] Optionally, linear parameter vector The solution process includes: Assuming nonlinear parameters Given a linear parameter vector Perform iterative estimation: Calculation criterion function For linear parameter vectors The first derivative; ; Using negative gradient optimization, a linear parameter vector is derived. linear parameter vector At any moment The The estimated value of the next iteration The expression is: ; ; ; ; in, Representing dimensions The identity matrix; For a moment For linear parameter vectors Conduct the first The step size for estimation in the next iteration. Indicates time forward A vector composed of augmented information vectors at each moment; Indicates time forward A vector consisting of effective traffic data at each moment; Represents a linear parameter vector At any moment The The estimated value of the next iteration; exist Time intervals for linear parameter vectors The iteration stops after the preset number of iterations is reached to obtain the linear parameter vector. The estimated value.

[0014] Optionally, nonlinear parameters The solution process includes: Assume a linear parameter vector It is known that for nonlinear parameters Perform iterative estimation: Define the stacking error vector Stacked error vectors Represented as: ; Calculate the criterion function with respect to the nonlinear parameter vector first derivative ; ; in, and They represent Time and Real-time effective traffic data express The transpose of the linearly augmented information vector at time step 1. express Predicted traffic data at any given time Represents the zero matrix of dimension n+m; express The linear parameter information vector at time step; Optimization using negative gradients, nonlinear parameters At any moment The The estimated value of the next iteration The expression is: ; ; in, Represents nonlinear parameters exist The first moment The estimated value of the next iteration. Nonlinear parameters exist The first moment The step size for estimation in the next iteration. Represents nonlinear parameters exist The first moment The estimated value of the next iteration; Represents the first nonlinear information vector The transpose of ; the expression for the first nonlinear information vector is: ; They represent time,…, The nonlinear augmented information vector at time step; The expression is: ; in, This represents the second nonlinear information vector; The expression is: ; in, They represent time, time,…, The third nonlinear information vector at time t; The expression is: ; This represents the fourth nonlinear information vector. The expression is: ; in, They represent time, time,…, The fifth nonlinear information vector at time t. The expression is: ; To ensure convergence, satisfy: ; At any moment For nonlinear parameters The iteration stops after the preset number of iterations is reached to obtain the nonlinear parameters. The estimated value.

[0015] Compared with the prior art, the present invention has the following advantages: This invention first acquires real-time traffic data and regional dynamic event data of the monitored area during the monitoring period; it then divides each moment within the monitoring period into a set of lost sampling moments and a set of non-lost sampling moments based on whether real-time traffic data sampling is lost; it then selects a prediction benchmark moment set from the set of non-lost sampling moments; for each moment in the prediction benchmark moment set, the moment m-1 moments prior to that moment must belong to the set of non-lost sampling moments; for each lost sampling moment in the set of lost sampling moments, the first moment prior to that lost sampling moment that belongs to the prediction benchmark moment set is taken as the prediction starting moment; based on the prediction starting moment itself, the real-time traffic data of the previous m-1 moments, and the pre-acquired regional dynamic event data of the previous n moments, a pre-constructed regression prediction model is used to predict the real-time traffic data of the lost sampling moment; where n and m represent the order of the traffic autoregression part and the regional dynamic event input part in the regression prediction model, respectively. Furthermore, this invention uses the gradient-based separable synchronous variable innovation iterative identification (GII-SS-VI) algorithm to solve for the unknown parameters in the regression prediction model, which has higher estimation efficiency and estimation accuracy. This invention establishes a regression prediction model based on the Exp-ARX model, which is suitable for traffic flow data with temporal correlation and random fluctuations in complex public places and urban streets. It can accurately map the relationship between the output real-time traffic flow data and the input regional dynamic event data. Based on the input regional dynamic event data and the output real-time traffic flow data of a given monitoring area within the monitoring period, a gradient-based separable synchronous variable information iterative identification algorithm is used to estimate and solve the unknown parameters of the regression prediction model. This fully utilizes effective information, significantly improves the accuracy of parameter estimation, and is suitable for dynamic modeling and prediction of pedestrian and vehicle traffic in complex urban environments. It helps to improve the accuracy of traffic flow prediction, thereby providing a reliable basis for intelligent navigation and risk warning. Attached Figure Description

[0016] Figure 1 A flowchart of a method for predicting pedestrian and vehicle traffic flow applicable to cases of lost random sampling data, provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the parameter estimation errors of the GII-MI, GII-SS-MI, and GII-SS-VI algorithms in the embodiments of the present invention; Figure 3 This is a schematic diagram illustrating the parameter estimation of the GII-MI, GII-SS-MI, and GII-SS-VI algorithms in embodiments of the present invention; Figure 4 This is a schematic diagram showing the comparison between the parameter estimates and the actual parameters of the GII-MI, GII-SS-MI, and GII-SS-VI algorithms in the embodiments of the present invention. Figure 5This is a schematic diagram of the parameter estimation errors of the GII-SS-MI (p=30, p=50) and GII-SS-VI algorithms in the embodiments of the present invention; Figure 6 This is a schematic diagram of the estimation error of the GII-SS-VI algorithm after 100 Monte Carlo runs in an embodiment of the present invention. Figure 7 This is a schematic diagram illustrating the estimation errors of the GII-MI and GII-SS-VI algorithms under different data loss percentages in embodiments of the present invention; Figure 8 This invention provides a partial time series result of pedestrian or vehicle flow obtained by using multi-source sensing devices such as infrared / vision to monitor changes in pedestrian / vehicle flow in a monitoring area. Figure 9 These are the fitting results of the GII-MI and GII-SS-VI algorithms in the embodiments of this invention; Figure 10 This is a schematic diagram illustrating the error between the actual output and the predicted output of the GII-MI and GII-SS-VI algorithms in the embodiments of the present invention. Detailed Implementation

[0017] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0018] Combination Figure 1 This embodiment provides a method for predicting pedestrian and vehicle traffic flow suitable for cases of lost random sampling data, including the following steps: Step S1: Obtain real-time traffic data and regional dynamic event data of the monitoring area during the monitoring period; divide each moment in the monitoring period into a set of lost sampling moments and a set of not lost sampling moments according to whether there is any loss of real-time traffic data sampling.

[0019] This embodiment is based on the actual operation of real-time traffic data detection by sensing sensors. Considering the possibility of lost random sampling output traffic data, a corresponding regression prediction model is established based on the Exp-ARX model (Exponential Autoregressive with Exogenous). Subsequently, a gradient-based Iterative Identification with Separable Synchronous Variable-innovation (GII-SS-VI) algorithm is used to identify the unknown parameters of the regression prediction model, thereby predicting the traffic data at the time when real-time traffic data sampling is lost. Specifically, real-time traffic data of the monitoring area during the monitoring period is acquired using sensing sensors, including infrared thermal imaging sensors and / or visual sensors. This embodiment uses sensing devices based on infrared, vision, or multi-source fusion to collect real-time traffic data, including dynamic information on pedestrian or vehicle flow, within the monitoring area in a non-contact manner. The cross-sectional traffic flow and cumulative traffic flow of the monitoring area are calculated in real time according to the built-in algorithm, and the real-time cross-sectional traffic flow is selected as the output data of the pedestrian or vehicle flow prediction system. Multi-source sensing devices can employ actual infrared thermal imaging sensors (such as FLIRA315), high-definition visual sensors (such as Hikvision MV-CE013-50GC), and fused data from both. This embodiment collects regional dynamic event data (such as the intensity of surrounding activities, traffic control information, and weather conditions) as input data for a regression prediction model by connecting to an urban traffic management platform, a regional event monitoring system, or an environmental sensing network.

[0020] The expression for the Exp-ARX model is: ; in, for Real traffic data for time points (t=0 to t=N). for The model consists of: 1) regional dynamic event input data at time t; 2) representing the order of the autoregressive component of the flow; 3) determining how many historical flow data points y(t-1), y(t-2), ..., y(tn) are needed to predict the current flow y(t); and 4) representing the order of the input component. 5) determining how many historical flow data points u(t-1), u(t-2), ..., u(tm) are needed to predict the current flow y(t). In this embodiment, it is assumed that the model order satisfies n ≥ m. These represent the 1st, 2nd, ..., 1st in the autoregressive part of the flow. One linear coefficient; These represent the 1st, 2nd, ..., 1st in the autoregressive part of the flow, respectively. One nonlinear coefficient; These respectively represent the 1st, 2nd, ..., 1st in the region dynamic event input section. One linear coefficient; These respectively represent the 1st, 2nd, ..., 1st in the region dynamic event input section. One nonlinear coefficient. (gamma) is a nonlinear parameter in the regression prediction model; it lies within the exponential term. Internally, it controls the decay rate of the nonlinear intensity. The size determines the square of the actual flow data at the previous moment. The degree of impact on the current moment.

[0021] In actual systems, real-time flow data measured by sensors There is an error The regression prediction model can be obtained, and its expression is: ; in, express The transpose of the regression prediction information vector at time step. The expression is: ; in, Represents a set of vectors.

[0022] Represents the predicted information vector. The expression is: It consists of information about output flow and dynamic event data in the input region; They represent time,…, Real-time traffic data at any given moment; They represent time,…, Real-time regional dynamic event data; Represents a linear parameter vector. The expression is: , It is composed of two parts: .

[0023] Linear parameter vector Parameters are divided into non-exponential parts. and exponential parameters .

[0024] Nonlinear parameters This is one of the unknown parameters to be identified. , (theta) represents the set of unknown parameters, which is the complete set of all unknown parameters of the model. It is a linear parameter vector. and nonlinear parameters Combined together, that is The ultimate goal of parameter estimation is to find the optimal... . The mean is zero and the variance is... A white noise sequence.

[0025] Considering that actual monitoring systems are often non-uniformly sampled data systems, and that the infrared and visual sensors used for data collection still suffer from data loss in practical applications, the causes include equipment obstruction, sudden changes in lighting, sensor malfunction, network transmission interruption, unstable power supply, environmental electromagnetic interference, improper installation location, and untimely maintenance. Furthermore, sudden strong interference (such as severe weather or signal blockage) may cause equipment to temporarily malfunction or enter a protection state, resulting in random data loss. This affects the system's prediction of pedestrian or vehicle traffic flow at the next moment, thus hindering the provision of accurate risk warnings and route optimization support for intelligent navigation systems.

[0026] This embodiment divides the monitoring period into sets of lost sampling times based on whether there is any loss of real-time traffic data sampling. and the set of time points without lost sampling .

[0027] For the time when no sampled data was lost Discussion: The regression prediction information vector of the regression equation at that moment. When there is no loss of sampled data, i.e. All data can be measured, and the regression prediction model is not affected by missing data, so it can directly predict the traffic data at the next moment.

[0028] When regression prediction information vector When there is sampling data loss, i.e. Measurable, but There is a problem with the loss of sampled output data. In order to reduce the impact of lost data on the system prediction results, this embodiment needs to improve the utilization rate of available output traffic data information and the performance of parameter estimation. The lost sampled output data is predicted from the most recent previously available output data, and the lost sampled output data is replaced with the predicted value.

[0029] This embodiment never loses the set of sampling times. Select the set of prediction reference times from the middle For each time point in the predicted baseline time set, the n-1 time points preceding that time point must belong to the set of time points without lost sampling; that is... Both can be measured.

[0030] Step S2: For each lost sampling moment in the set of lost sampling moments, take the first moment in the prediction reference time set preceding that lost sampling moment as the prediction starting moment; based on the prediction starting moment itself and the real-time traffic data of the previous n-1 moments and the pre-acquired regional dynamic event data of the previous m moments, use the pre-built regression prediction model to predict the real-time traffic data of that lost sampling moment; where n and m represent the order of the traffic autoregression part and the regional dynamic event input part, respectively.

[0031] Step S21: Starting from the prediction start time, based on the prediction start time itself and the real-time traffic data of the previous n-1 times, determine the effective traffic data of each time after the prediction start time and before the lost sampling time. If the current moment belongs to the set of moments without lost samples, then the real-time traffic data sampled at that moment is determined as the valid traffic data for that moment; if the current moment belongs to the set of moments with lost samples, first determine the number of time intervals between that moment and the prediction start time. If the number of time intervals If it is less than n, then use the time before n. Effective traffic data at each moment, real-time traffic data at the predicted starting point moment itself, and traffic data going forward from the predicted starting point moment. Real-time traffic data at a given time point is combined with pre-acquired regional dynamic event data from m time points prior to that time point to calculate the predicted traffic data for that time point. This predicted traffic data is then used to determine the valid traffic data for that time point. If the interval number of time points... If the value is greater than n, then the effective traffic data from n previous times is used, combined with the regional dynamic event data from m previous times that were obtained in advance, to calculate the predicted traffic data for that time, and the predicted traffic data is used to determine the effective traffic data for that time.

[0032] The expression for the effective flow data at each time point after the prediction start time and before the lost sampling time is: ; in, This represents the effective flow data at time t. This represents the set of sampling times that were not lost. Represents the set of missing sampling moments; This represents the real-time traffic data at time t; This represents the predicted flow data at time t; The predicted flow data is calculated using a regression prediction model. The expression for calculating the predicted flow data using the regression prediction model is as follows: ; ; ; ; in, Indicates the predicted start time. express Predicted traffic data at any given time; express Valid traffic data at any given moment; express Real-time traffic data at any given moment. Indicates To predict the starting time and the number of time intervals is The predicted information vector at that time; and They are respectively The linear and nonlinear parts; express The equivalent noise term at any given time; They represent time,…, Valid traffic data at any given moment; express The reference vector of the prediction information at that time, and They represent The linear and nonlinear parts; Represents nonlinear parameters; express Real-time regional dynamic event data, express Real-time regional dynamic event data, Represents a linear parameter vector; They represent time,…, Real-time traffic data at any given moment; They represent time,…, Real-time regional dynamic event data. express The original noise at any given moment express Time's up The sum of the original noise at each moment.

[0033] Once the effective flow data for each time point after the prediction start time and before the lost sampling time has been predicted, the real-time flow data for n time points before the lost sampling time (if missing, it will be filled with effective flow data) and the regional dynamic event data for m time points before the lost sampling time are known. Substituting these into the expression for the predicted flow data, the effective flow data for the lost sampling time can be calculated and used as the real-time flow data.

[0034] Step S3: Analyze the linear parameter vector in the regression prediction model. and nonlinear parameters The system parameters are identified by solving the problem and combining the hierarchical innovation theory with the gradient-based separable synchronous variable innovation iterative identification (GII-SS-VI) algorithm.

[0035] Step S31: Define the linear augmented information vector Linear augmented information vector The expression is: ; ; ; in, This represents the effective flow data at time t; This represents the real-time traffic data at time t; Represents a linear parameter information vector Transpose of; They represent time, time,……, Valid traffic data at any given moment; They represent time, time,……, Real-time regional dynamic event data; Define the criterion function Criterion function The expression is: ; in, ; Represents a set of unknown parameters; Indicates the length of the news feed; express Predicted traffic data at any given time; express The transpose of the linearly augmented information vector at time step; Based on the aforementioned criterion function, determine the first... The optimal innovation length in the next iteration The criterion function can be approximated as: ; in, , The parameter is used to adjust the weights of current and historical data during parameter estimation.

[0036] Optimal news length The expression is: ; in, Indicates rounding operation. To adjust the parameters, ; Step S32: Adjust the linear parameter vector according to the criterion function and the appropriate innovation length. and nonlinear parameters Perform iterative solutions.

[0037] Linear parameter vector The solution process includes: assuming nonlinear parameters Given a linear parameter vector Perform iterative estimation: Calculation criterion function For linear parameter vectors The first derivative; ; Using negative gradient optimization, a linear parameter vector is derived. linear parameter vector At any moment The The estimated value of the next iteration The expression is: ; ; ; ; in, Representing dimensions The identity matrix; For a moment For linear parameter vectors Conduct the first The step size for estimation in the next iteration. Indicates time forward A vector composed of augmented information vectors at each moment; Indicates time forward A vector consisting of effective traffic data at each moment; Represents a linear parameter vector At any moment The The estimated value of the next iteration; To ensure parameter estimation Convergence, The eigenvalues ​​must all be within the unit circle and cannot be repeated. The following conditions must be met: ; Furthermore, step size The conservative option is: ; in, This indicates the maximum coefficient that is preset.

[0038] Due to the complexity of eigenvalue calculation, the step size Alternatively, it can be simply taken as: ; exist Time intervals for linear parameter vectors The iteration stops after the preset number of iterations is reached to obtain the linear parameter vector. The estimated value.

[0039] Step S33: Assume a linear parameter vector It is known that for nonlinear parameters Perform iterative estimation: Define the stacking error vector Stacked error vectors For the time forward The vector formed by the noise terms at each time step; the stacked error vector The expression is: ; in, They represent time,…, The noise term at time step; for ease of solution, the error vector is stacked. Represented as: ; Calculate the criterion function with respect to the nonlinear parameter vector first derivative ; ; in, and They represent Time and Real-time effective traffic data express The transpose of the linearly augmented information vector at time step 1. express Predicted traffic data at any given time Represents the zero matrix of dimension n+m; express The linear parameter information vector at time step; Optimization using negative gradients, nonlinear parameters At any moment The The estimated value of the next iteration The expression is: ; ; in, Represents nonlinear parameters exist The first moment The estimated value of the next iteration. Nonlinear parameters exist The first moment The step size for estimation in the next iteration. Represents nonlinear parameters exist The first moment The estimated value of the next iteration; Represents the first nonlinear information vector The transpose of ; the expression for the first nonlinear information vector is: ; They represent time,…, The nonlinear augmented information vector at time step; The expression is: ; in, This represents the second nonlinear information vector; The expression is: ; in, They represent time, time,…, The third nonlinear information vector at time t; The expression is: ; This represents the fourth nonlinear information vector. The expression is: ; in, They represent time, time,…, The fifth nonlinear information vector at time t. The expression is: ; To ensure convergence, satisfy: ; Options include: ; in, This is the preset scaling factor.

[0040] At any moment For nonlinear parameters The iteration stops after the preset number of iterations is reached to obtain the nonlinear parameters. The estimated value.

[0041] To verify the effectiveness of this scheme, this embodiment compares the proposed GII-SS-VI algorithm with the GII-MI and GII-SS-MI algorithms. The results are as follows: Figures 2-10 As shown, where, Figure 2 The horizontal axis K represents the number of iterations, and the vertical axis represents... To account for the error, the results show that the GII-SS-VI algorithm has higher estimation accuracy and faster convergence speed than GII-MI (Gradient-based Iterative Identification with Multi-innovation) and GII-SS-MI (Gradient-based Separable Synchronous Multi-innovation Iterative Identification with Multi-innovation). In this simulation verification, we generated simulated data based on the physical characteristics and noise model of the real sensor. Figure 3 Based on the estimation results of all parameters, it can be seen that the GII-SS-VI algorithm has higher accuracy; Figure 4The horizontal axis K represents the number of iterations, and the vertical axis represents the system parameters. This indicates that the algorithm proposed in this scheme estimates parameter values ​​that are closer to the true parameter values, and the estimation accuracy is higher. Figure 5 The horizontal axis K represents the number of iterations, and the vertical axis represents... The error is shown to indicate that the proposed GII-SS-VI algorithm, which uses a time-varying innovation length, is superior to the GII-SS-MI algorithm with a fixed innovation length. Figure 6 The horizontal axis t represents the number of iterations, the vertical axis Run times represents the number of runs, and the vertical axis... The error is shown to be that the proposed GII-SS-VI algorithm is effective for identifying time-varying systems. Figure 7 The horizontal axis K represents the number of iterations, and the vertical axis represents... The error indicates that the proposed GII-SS-VI algorithm converges faster and is more accurate, but the prediction accuracy will decrease as the data loss rate increases. Figure 8 The horizontal axis represents time and the vertical axis represents system output. It can be seen that in the actual monitoring of pedestrian and vehicle flow, the obtained pedestrian and vehicle flow data are sometimes lost. This indicates that the iterative method for constructing output prediction proposed in this scheme based on the study of arbitrary data loss has practical application value. Figure 9 The horizontal axis represents time and the vertical axis represents system output. It can be seen that the model prediction output of this scheme can track the measured output very well. Figure 10 The horizontal axis represents time, and the vertical axis represents system output, indicating that the proposed GII-SS-VI algorithm has better accuracy; these response results fully verify the performance and design efficiency of this scheme.

[0042] In summary, this invention utilizes hierarchical identification technology and combines variable innovation identification theory with negative gradient search to propose a gradient-based separable synchronous variable innovation iterative identification (GII-SS-VI) algorithm, building upon the gradient-based variable innovation iterative identification (GII-VI) algorithm. By separating all parameters into linear and nonlinear parameter sets, two gradient-based variable innovation iterative sub-algorithms are derived based on these separated parameter sets. By combining the two different parameter sets and the two sub-algorithms, and employing interactive operations, the relevant parameter vectors that prevent the algorithm from executing are eliminated. This enables the system to efficiently, directly, and accurately identify multiple parameters. Compared to the gradient-based iterative identification with multi-innovation (GII-MI) algorithm and the gradient-based separable synchronous multi-innovation iterative identification (GII-SS-MI) algorithm, it exhibits higher estimation efficiency and accuracy.

[0043] This invention proposes a model building and parameter estimation method for pedestrian and vehicle flow prediction systems with lost random sampling data. Numerical examples show that the parameter estimation method converges to the true values, and the model estimation output curve matches the actual measured output curve. The proposed method for pedestrian and vehicle flow prediction system model building and parameter estimation, in handling cases of lost random sampling data, can also be combined with other estimation algorithms for parameter identification in linear and nonlinear stochastic systems with colored noise. Furthermore, this method can be further applied to related fields with data loss characteristics, such as intelligent traffic sensing, public safety monitoring, indoor navigation systems, and network transmission optimization.

Claims

1. A method for predicting pedestrian and vehicle traffic flow suitable for cases of lost random sampling data, characterized in that, Includes the following steps: Acquire real-time traffic flow data of people and vehicles and regional dynamic event data in the monitored area during the monitoring period; The monitoring period is divided into two sets of time with lost sampling and time without lost sampling, based on whether there is any loss of real-time traffic data sampling. A set of prediction reference times is selected from the set of never-lost sampling times; for each prediction reference time in the set of prediction reference times, the n-1 times preceding that prediction reference time must belong to the set of never-lost sampling times. For each lost sampling moment in the set of lost sampling moments, the first moment in the prediction reference time set preceding that lost sampling moment is taken as the prediction starting moment. Based on the prediction starting moment itself, the real-time traffic data of the n-1 moments preceding it, and the pre-acquired regional dynamic event data of the m moments preceding the current lost sampling moment, the real-time traffic data of the lost sampling moment is predicted using a pre-constructed regression prediction model. Here, n and m represent the order of the traffic autoregression part and the regional dynamic event input part in the regression prediction model, respectively.

2. The method for predicting pedestrian and vehicle flow with lost random sampling data as described in claim 1, characterized in that, Real-time pedestrian and vehicle traffic data for the monitored area during the monitoring period are obtained through sensing sensors, including infrared thermal imaging sensors and / or visual sensors; dynamic event data for the area are obtained by accessing the urban traffic management platform, regional event monitoring system, or environmental sensing network.

3. The method for predicting pedestrian and vehicle flow with lost random sampling data as described in claim 1, characterized in that, The real-time traffic data predicted at the time of the lost sampling using a pre-built regression prediction model includes: Starting from the prediction start time, based on the prediction start time itself and the real-time traffic data of the previous n-1 times, the effective traffic data of each time after the prediction start time and before the lost sampling time is determined sequentially using a pre-built regression prediction model. Based on the real-time traffic data of the prediction start time itself and the n-1 times preceding it, the effective traffic data of each time after the prediction start time and before the lost sampling time, and the regional dynamic event data of the m times preceding the lost sampling time, the real-time traffic data of the lost sampling time is predicted using a pre-built regression prediction model.

4. The method for predicting pedestrian and vehicle flow with lost random sampling data according to claim 3, characterized in that, The effective flow data for each time point after the prediction start time and before the lost sampling time is determined sequentially using a pre-built regression prediction model. If the time point belongs to the set of time points without lost sampling, then the real-time traffic data sampled at that time point is determined as the valid traffic data at that time point; If the current moment belongs to the set of missing sampling moments, first determine the number of time intervals between this moment and the prediction starting moment. ; If the number of time intervals If it is less than n, then use the time before n. Effective traffic data at each moment, real-time traffic data at the predicted starting point moment itself, and traffic data going forward from the predicted starting point moment. The real-time traffic data at a given moment is combined with the regional dynamic event data from the previous m moments obtained in advance. The predicted traffic data at that moment is calculated using a pre-built regression prediction model, and the predicted traffic data is used to determine the effective traffic data at that moment. If the number of time intervals If the value is greater than n, then the effective flow data from n previous times is used, combined with the regional dynamic event data from m previous times obtained in advance, and the predicted flow data for that time is calculated using a pre-built regression prediction model. The predicted flow data is then used to determine the effective flow data for that time.

5. The method for predicting pedestrian and vehicle flow with lost random sampling data according to claim 4, characterized in that, The effective flow data for each time point after the prediction start time and before the lost sampling time is represented as follows: ； in, This represents the effective flow data at time t. This represents the set of sampling times that were not lost. Represents the set of missing sampling moments; This represents the real-time traffic data at time t; This represents the predicted flow data at time t; The predicted flow data is calculated using a regression prediction model. The expression for calculating the predicted flow data using the regression prediction model is as follows: ； ； ； in, Indicates the predicted start time. express Predicted traffic data at any given time; express Valid traffic data at any given moment; express Real-time traffic data at any given moment. Indicates To predict the starting time and the number of time intervals is The predicted information vector at that time; and They are respectively The linear and nonlinear parts; express The equivalent noise term at any given time; They represent time,…, Valid traffic data at any given moment; express The reference vector of the prediction information at that time, and They represent The linear and nonlinear parts; Represents nonlinear parameters; express Real-time regional dynamic event data, express Real-time regional dynamic event data, Represents a linear parameter vector; They represent time,…, Real-time traffic data at any given moment; They represent time,…, Real-time regional dynamic event data.

6. The method for predicting pedestrian and vehicle flow with lost random sampling data as described in claim 5, characterized in that, Linear parameter vector The expression is: ； in, The dimension is A set of vectors; and They represent linear parameter vectors respectively. The non-exponential part of the parameters and the exponential part of the parameters; These represent the 1st, 2nd, ..., 1st in the autoregressive part of the flow. One linear coefficient; These represent the 1st, 2nd, ..., 1st in the autoregressive part of the flow. One nonlinear coefficient; These respectively represent the 1st, 2nd, ..., 1st in the region dynamic event input section. One linear coefficient; These respectively represent the 1st, 2nd, ..., 1st in the region dynamic event input section. One nonlinear coefficient.

7. The method for predicting pedestrian and vehicle flow with lost random sampling data according to claim 5, characterized in that, The expression for the equivalent noise term is: ； in, express The original noise at any given moment express Time's up The sum of the original noise at each moment.

8. The method for predicting pedestrian and vehicle flow with lost random sampling data according to claim 6, characterized in that, Linear parameter vector and nonlinear parameters The solution process includes: definition Linear augmented information vector at time step Linear augmented information vector The expression is: ； ； ； in, This represents the effective flow data at time t; This represents the real-time traffic data at time t; Represents a linear parameter information vector Transpose of; They represent time, time,……, Valid traffic data at any given moment; They represent time, time,……, Real-time regional dynamic event data; Define the criterion function Criterion function The expression is: ； in, ; Represents a set of unknown parameters; Indicates the length of the news feed; express Predicted traffic data at any given time; express The transpose of the linearly augmented information vector at time step; Based on the aforementioned criterion function, determine the first... The optimal innovation length in the next iteration ; Optimal news length The expression is: ； in, Indicates rounding operation. To adjust the parameters, ; Based on the criterion function and the appropriate innovation length, the linear parameter vector is... and nonlinear parameters Perform iterative solutions.

9. The method for predicting pedestrian and vehicle flow with lost random sampling data as described in claim 8, characterized in that, Linear parameter vector The solution process includes: Assuming nonlinear parameters Given a linear parameter vector Perform iterative estimation: Calculation criterion function For linear parameter vectors The first derivative; ； Using negative gradient optimization, a linear parameter vector is derived. linear parameter vector At any moment The The estimated value of the next iteration The expression is: ； ； ； ； in, Representing dimensions The identity matrix; For a moment For linear parameter vectors Conduct the first The step size for estimation in the next iteration. Indicates time forward A vector composed of augmented information vectors at each moment; Indicates time forward A vector consisting of effective traffic data at each moment; Represents a linear parameter vector At any moment The The estimated value of the next iteration; exist Time intervals for linear parameter vectors The iteration stops after the preset number of iterations is reached to obtain the linear parameter vector. The estimated value.

10. The method for predicting pedestrian and vehicle flow with lost random sampling data according to claim 9, characterized in that, Nonlinear parameters The solution process includes: Assume a linear parameter vector It is known that for nonlinear parameters Perform iterative estimation: Define the stacking error vector Stacked error vectors Represented as: ； in, This represents the second nonlinear information vector; The expression is: ； in, They represent time, time,…, The third nonlinear information vector at time t; The expression is: ； This represents the fourth nonlinear information vector. The expression is: ； in, They represent time, time,…, The fifth nonlinear information vector at time t. The expression is: ； Calculate the criterion function with respect to the nonlinear parameter vector first derivative ; ； in, and They represent Time and Real-time effective traffic data express The transpose of the linearly augmented information vector at time step 1. express Predicted traffic data at any given time Represents the zero matrix of dimension n+m; express The linear parameter information vector at time step; Optimization using negative gradients, nonlinear parameters At any moment The The estimated value of the next iteration The expression is: ； ； in, Represents nonlinear parameters exist The first moment The estimated value of the next iteration. Nonlinear parameters exist The first moment The step size for estimation in the next iteration. Represents nonlinear parameters exist The first moment The estimated value of the next iteration; Represents the first nonlinear information vector The transpose of ; the expression for the first nonlinear information vector is: ； They represent time,…, The nonlinear augmented information vector at time step; The expression is: ； To ensure convergence, satisfy: ； At any moment For nonlinear parameters The iteration stops after the preset number of iterations is reached to obtain the nonlinear parameters. The estimated value.

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