Multi-sensor multi-target active estimation method based on probability hypothesis density filtering

Abstract

The invention provides a multi-sensor multi-target active estimation method based on probability hypothesis density filtering. The method comprises the following steps: firstly, establishing kinematic models and observation models of sensors and targets; thirdly, locally estimating the states of multiple targets through a Gaussian mixture probability hypothesis density (GM-PHD) filtering algorithm with a limited sensor observation range; then, realizing fusion of multi-sensor information by utilizing generalized collaborative information (GCI) fusion; constructing a multi-target active state estimation optimization target function of multiple sensors; and finally, designing an optimal control framework of multi-sensor multi-target active estimation. According to the method, multi-sensor observation information is effectively fused, multi-target active tracking of variable target quantity is realized, and the precision of target state estimation is improved.

Description

Technical Field

[0001] The present invention relates to the field of intelligent control technology, and in particular to a multi-sensor multi-target active estimation method based on probability hypothesis density filtering. Background Art

[0002] In recent years, multi-agent systems have attracted much attention from the academic community. Relevant research directions cover a wide range, including collaborative control, distributed computing, and communication systems. Multi-agent systems have shown excellent practical value in the fields of sensor networks and multi-target tracking. Compared with a single agent, multi-agent collaborative tasks have higher autonomy, flexibility, robustness, reliability, and scalability.

[0003] Multi-target tracking refers to the joint estimation of the number of targets and their states from a series of noisy and cluttered observation sets (see Beard M, Vo BT, Vo B NA solution for large-scale multi-object tracking [J]. IEEE Transactions on Signal Processing, 2020, 68: 2754-2769). Related research in this field has far-reaching academic significance in the fields of military, autonomous driving, and medical image processing. In military applications, this technology provides decision support for real-time monitoring and tracking of threat targets; in autonomous driving, it can be used to perceive multiple moving targets in the surrounding environment, thereby achieving intelligent decision-making and avoiding collisions; in the medical field, by tracking the movement of tissues or cells, it helps to monitor lesions in real time, thereby improving the accuracy of medical diagnosis and treatment. These application scenarios highlight the importance of multi-target tracking in practical applications, and its research is crucial to promoting the development and innovation of related fields.

[0004] In the scenario of multi-target tracking, due to the dynamic changes of target states and the uncertainty of sensor observations, it is necessary to accurately associate each observation with the corresponding target. Among them, the observations may come from multiple targets and may also contain some false clutter observations. Therefore, the current multi-target tracking algorithms focus on solving the data association problem to cope with complex observation environments and target state changes. Commonly used joint probabilistic data association (see Fortmann TE, Bar-Shalom Y, Scheffe M. Multi-target tracking using joint probabilistic data association [C] / / 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes. IEEE, 1980: 807-812) and multiple hypothesis tracker methods (see Blackman SS. Multiple hypothesis tracking for multiple target tracking [J]. IEEE Aerospace and Electronic Systems Magazine, 2004, 19 (1): 5-18) usually transform the multi-target problem into a single target problem by allocating measurements. However, when the number of targets is large, this may lead to a combinatorial explosion problem, causing the amount of computation to grow exponentially. Unlike these methods, the probability hypothesis density (PHD) filtering algorithm recursively estimates the first-order moment of the target state distribution. On the one hand, this avoids the data association problem and can achieve joint detection and tracking of targets while removing clutter; on the other hand, it reduces the dimension of the multi-target state space, thereby greatly reducing the computational complexity. The literature (see Mahler RP S. Multitarget Bayes filtering via first-order multitarget moments [J]. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39 (4): 1152-1178) first introduced the probability hypothesis density filtering method based on the concept of random finite sets and provided rigorous theoretical derivation steps.The literature (see Vo BN, Ma W K. The Gaussian mixture probability hypothesis density filter [J]. IEEE Transactions on Signal Processing, 2006, 54 (11): 4091-4104) uses a Gaussian mixture model (GMM) to approximate the first-order moment of the target state distribution, and proposes a GM-PHD filter under the framework of the Kalman filter. This method avoids a large number of integral operations in the original PHD filter and successfully extends it to nonlinear systems, thereby further popularizing the application scenarios of the PHD filter.

[0005] However, the above methods only consider the multi-target tracking scenario in a single sensor environment. Combining the information of multiple sensors can significantly improve the reliability of observations. In the literature (see Liu S, Shen-tu H, Chen H, et al. Asynchronous multi-sensor fusion multi-target tracking method [C] / / 2018 IEEE 14th International Conference on Control and Automation (ICCA). IEEE, 2018: 459-463), the dependence on a single sensor is reduced by fusing data from different sensors, thereby improving the estimation accuracy of the overall system. However, the current information fusion is mostly based on the covariance crossover method. When the Gaussian mixture model has many components, there are problems such as high complexity and poor filtering convergence. In addition, existing research results usually only focus on passive multi-target tracking when the sensor position is fixed (see Mahler RP S. Multitarget Bayes filtering via first-order multitarget moments [J]. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39 (4): 1152-1178), which cannot give full play to the mobility of the intelligent body equipped with sensors. Summary of the invention

[0006] In order to solve the above problems in the prior art, such as limited estimation accuracy, high algorithm complexity, poor filtering convergence, etc., the present invention discloses a multi-sensor multi-target active estimation method based on probability hypothesis density filtering, which significantly improves the observation reliability and estimation accuracy of the system. At the same time, by introducing a mobile sensor network, the limitation of fixed sensor position is broken, so that the system has higher flexibility and adaptability in a dynamic environment, thereby realizing active tracking of multiple targets, effectively reducing target state estimation errors and enhancing multi-target tracking capabilities.

[0007] Technical solution: In order to achieve the above purpose, the present invention provides a multi-sensor multi-target active estimation method based on probability hypothesis density filtering, and the specific steps are as follows:

[0008] S1: Modeling of sensor and target kinematic models and observation models.

[0009] S2: Design a GM-PHD filtering algorithm with bounded sensor observation area for local multi-target state estimation.

[0010] S3: Multi-sensor information fusion based on generalized collaborative information (GCI) approach.

[0011] S4: Construction of optimization objective function for multi-sensor multi-objective active state estimation.

[0012] S5: Design of an optimal control framework for multi-sensor multi-target active estimation problems.

[0013] Furthermore, in step S1, the kinematic model and observation model of the sensor and target are modeled as follows: In PHD filtering, the probability hypothesis density (PHD) function, also known as the probability intensity function, is used to describe the distribution of multiple targets in the state space. It represents the target density of each state in the state space, and the result of integrating the function in any region is the expected number of targets in the region.

[0014] For each sensor, in the multi-target dynamic state estimation problem, it is assumed that the target state follows a Markov process in the state space, and its transfer function is f k|k-1 (·|·), that is, the state x at a given time k-1 k-1 , transfer to state x at time k k The probability intensity function is f k|k-1 (x k ∣x k-1 ). Let z k is the observed value of the target at time k. Assuming that the target can only be observed when it is in the sensor perception area, its observation model is composed of the likelihood function g k (·|·) means. That is, the state x at a given time k k , receiving the observation z kThe probability intensity is g k (z k |x k ). At the same time, the observation data of each sensor at time k will contain clutter, the amount of clutter n c Follows Poisson distribution Where V is the volume of the motion space C, λ c is the clutter density.

[0015] For each sensor s, its kinematic model can be expressed as:

[0016]

[0017] Among them, is the state of sensor s at time k, Represents the control input of the sensor at time k. In order to simplify the complexity of the problem, it is discretized, that is, the control is divided into static and eight-directional nine input modes.

[0018] Consider the target motion space A set of N sensors are deployed in the system to detect M at time k. k The location of the target (where M k is unknown and changing). Each sensor observes all possible targets in its own observation area. Our goal is to effectively fuse the predictions of multiple sensors through communication between sensors, and then design an optimal control framework for the multi-target active estimation problem, thereby improving the accuracy of each sensor's observation of the target.

[0019] In S2, a GM-PHD filtering algorithm with bounded sensor observation area is designed to perform local multi-target state estimation. Specifically:

[0020] (21) Determine the calculation form of PHD filtering: GM-PHD filtering uses a Gaussian mixture model to approximate the PHD function in the PHD filter, which means that v k (x) can be expressed as:

[0021]

[0022] Among them J k is the number of Gaussian components, are the weight, mean, and covariance of the jth component, respectively. Subsequently, the closed-form solution of the GM-PHD filter can be easily derived, which significantly reduces the computational burden. In addition, the number of targets can be directly calculated without integration as The state of each target can be extracted as the mean of the components in the Gaussian mixture model.

[0023] (22) Determine the updating method of the prior strength: Assume that the target survival probability P at time k is S,k is a constant, and the sensor’s observation area is bounded, so its detection probability at time k depends on its position m D,k , which can be modeled as:

[0024]

[0025] Now we can get the GM-PHD recursion with bounded sensor observation area. Assume that our intensity at time k-1 is:

[0026]

[0027] We can obtain the predicted survival intensity function v at time k S,k∣k-1 (x):

[0028]

[0029] And the related symbols are recorded as

[0030]

[0031] Therefore, the prediction strength function can be written as:

[0032]

[0033] The new strength function is:

[0034]

[0035] (23) Determine the updating method of the posterior strength under the state-dependent detection model: Combining the state-dependent detection probability, we can obtain the posterior strength:

[0036]

[0037] in

[0038]

[0039] And the related symbols are recorded as

[0040]

[0041] And the related symbols are recorded as

[0042]

[0043] in

[0044]

[0045] (24) Pruning and merging Gaussian components in the PHD function and extracting the target state: In the execution process of the GM-PHD filter, the core principle of pruning and merging is to remove components with smaller weights and merge multiple similar components into one. We can simply set a predetermined truncation threshold ε t to filter out the larger weights. During the merging process, we iteratively identify the components with the highest weights and associate them with the components whose Mahalanobis distance is below a specified threshold ε m Finally, if the number of components after pruning and merging is still greater than J max , we will continue to discard components with lower weights until the number of components reaches J max By adopting this strategy, the number of components is significantly reduced, thereby reducing the computational complexity. In addition, due to the existence of the negative sign in equation (8), the components with negative weights should be filtered out after the above merging, and then the remaining weights should be normalized to ensure the practical significance of the PHD function.

[0046] The multi-target state extraction method is to extract the function v k (x) is integrated, that is, the sum v k The weights of all Gaussian components in (x) can be used to estimate the number of targets, denoted by N t Then, the algorithm iteratively selects the mean of the components with the highest weight as the target state, repeating N times. t Once a component is selected, its weight will be reduced by 1.

[0047] Multi-sensor information fusion based on the generalized collaborative information (GCI) method in S3. Specifically:

[0048] (31) Multi-sensor target state estimation information fusion: This step aims to propose a consensus method by combining the local strength of each sensor To obtain higher target estimation accuracy. We introduce the notation represents the intensity function of sensor i. Assume that the initial posterior intensity of sensor i at time k is The formula for the vth iteration at time k is:

[0049]

[0050] in is the neighbor of sensor i, function It is called the opinion pool, which determines how to combine this set of strength functions. Based on this, the logarithmic opinion pool LogOP is defined as:

[0051]

[0052] where ∑ la l = 1. By using the logarithmic opinion pool, the prediction information of multiple sensors can be fused to improve the accuracy of state estimation.

[0053] (32) Information fusion approximation based on GCI method: The GCI algorithm establishes a framework for fusing data from different sensors while taking into account the uncertainty of each sensor's measurement. By considering the covariance of sensor measurements, GCI aims to obtain a better estimate of the true state. First, we use the GCI technique to implement LogOP, thereby combining the information of each sensor with its neighbors. For GMM, the following approximation is given:

[0054]

[0055] This approximation ignores the cross terms between different Gaussian components. But this is not a problem, because after the pruning and merging steps, the distance between each pair of components is far enough. So we have: GCI fusion of two GMMs with weights ω and 1-ω (LogOP) Still a GMM:

[0056]

[0057] in

[0058]

[0059] When the number of GMMs to be fused is N G When N is greater than 2, the above process can be performed G -1 times to obtain the fused GMM.

[0060] The multi-objective active state estimation optimization objective function of multiple sensors in S4 is constructed as follows: Plan the optimal control input of sensor i at the kth moment Therefore, consider the following goals:

[0061] The purpose of active sensing is to reduce the uncertainty of the target distribution, which is reflected in the size of the covariance matrix. Therefore, the following objective function can be used for sensor i to reduce the uncertainty of the target distribution:

[0062]

[0063] Among them, S i,k ={j|ω j >ε R ,ω j is The weights in}, ε R is the threshold for filtering out non-dominant components in GMM.

[0064] In addition, the mean vector center of the first K weighted components is selected as the target position to drive the sensor movement, and the relevant objective function is designed as follows:

[0065]

[0066] in, is in v k The index set of the first K components with the largest weight in (x), and dist is the distance function between calculated vectors.

[0067] Finally, we add a repulsive effect to sensors that are close to each other to prevent swarming. Using the hyperbolic tangent function as the target function of the repulsive force can help control the repulsive strength when the distance is too close. Assume that the distance between sensors i and j is d ij , its repulsive force objective function can be defined as:

[0068]

[0069] Among them, α r is the coefficient that controls the attenuation of the repulsive force, which can ensure that there is still a certain repulsive force when multiple sensors are far apart. Finally, the optimization function is obtained by weighted average.

[0070]

[0071] Design of the optimal control framework for multi-sensor multi-target active estimation problem in S5. Specifically:

[0072] (51) Design multi-sensor collision avoidance constraints: For sensor i, take action u at time k k , we can define a security vector N i,k (u i ), as follows:

[0073]

[0074] variable Non-negative, indicating that if sensor i takes action u k , may collide with sensor j. Therefore, the following constraints ensure the safe movement of sensor i:

[0075] ||N i,k (u k )||1=0.

[0076] (52) Multi-target active perception framework design: The optimal frame for sensor i can be written as:

[0077]

[0078] Among them, Φ(v k|k+1 (x)) = v k∣k (x)-v D,k∣k (x)+∑v D,k∣k (x; z) is the update of the GM-PHD filter with bounded sensor observation area. During the planning process, the pseudo observation data generated by the sensor observation model in step S1 is used to iterate the PHD filter. The last constraint is the boundary constraint of sensor i. Note that during the optimization problem solving process, a constant velocity model is used to predict the motion of neighbor sensors during the planning period, that is, each neighbor is assumed to move according to its control input at time k during the entire planning period.

[0079] The beneficial effects of the present invention are as follows:

[0080] 1. The present invention improves the accuracy of multi-target state estimation and reduces data association errors by establishing kinematic and observation models of sensors and targets and designing a Gaussian mixture probability hypothesis density (GM-PHD) filtering algorithm whose observation depends on sensor states.

[0081] 2. The multi-sensor information fusion based on the generalized collaborative information (GCI) fusion method of the present invention effectively reduces the dependence on a single sensor, enhances the robustness of observation, and improves the stability of the system and the accuracy of data fusion.

[0082] 3. The present invention constructs an optimization objective function for active multi-target tracking, combines the optimal control framework, and achieves more flexible dynamic environment adaptability through mobile sensor networks, effectively reducing target state estimation errors. Compared with other methods, the accuracy of state estimation is achieved.

[0083] 4. The method of the present invention has broad application prospects in multi-target tracking in dynamic environments and is suitable for complex scenarios that require the collaborative work of multiple agents.

[0084] In summary, compared with the prior art, the present invention achieves efficient and flexible multi-target tracking in a dynamic environment by establishing kinematic and observation models, designing a GM-PHD filtering algorithm that depends on sensor states, a multi-sensor information fusion method based on GCI, an active tracking strategy that optimizes the objective function, and an optimal control framework. The present invention effectively improves the accuracy of multi-target state estimation, reduces the complexity and dependence of data fusion, enhances the robustness and real-time adaptability of the system, and has broad application prospects and practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 Schematic diagram of the steps of the multi-sensor multi-target active estimation method based on probability hypothesis density filtering of the present invention;

[0086] Figure 2 It is a schematic diagram of simulation of state estimation results of multi-sensor active tracking of the present invention;

[0087] Figure 3 It is a schematic diagram of the path of multi-sensor active tracking of the present invention;

[0088] Figure 4 It is a schematic diagram of the OSPA index for measuring the estimation error of each sensor of the present invention;

[0089] Figure 5 is a graph showing the distance variation between each sensor and its nearest sensor at each time;

[0090] Figure 6 It is a comparison chart of the estimation results of the present invention and different active tracking methods. DETAILED DESCRIPTION

[0091] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to directions in the accompanying drawings, and the words "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0092] like Figure 1 As shown, the multi-sensor multi-target active estimation method based on probability hypothesis density filtering disclosed in an embodiment of the present invention first models the sensor and target kinematic models and observation models; then implements the GM-PHD filtering algorithm whose observation depends on the sensor state; then performs multi-sensor information fusion based on the GCI method; constructs a multi-sensor multi-target active tracking optimization objective function; then designs the optimal control framework for the multi-sensor multi-target tracking problem; and finally proves the superiority of the method of the present invention in estimation accuracy through relevant simulations.

[0093] Specifically, in an embodiment of the present invention, a method for designing a multi-point linearized model prediction trajectory tracking control framework based on a Gaussian process mainly includes the following steps:

[0094] Step 1. Model the sensor and target kinematic model and observation model. Specifically, in PHD filtering, the probability hypothesis density (PHD) function, also known as the probability intensity function, is used to describe the distribution of multiple targets in the state space. It represents the target density of each state in the state space, and the result of integrating the function in any region is the expected number of targets in the region.

[0095] For each sensor, in the multi-target dynamic state estimation problem, it is assumed that the target state follows a Markov process in the state space, and its transfer function is f k|k-1 (·|·), that is, the state x at a given time k-1 k-1 , transfer to state x at time k k The probability intensity function is f k|k-1 (x k ∣x k-1 ). Let z k is the observed value of the target at time k. Assuming that the target can only be observed when it is in the sensor perception area, its observation model is composed of the likelihood function g k (·|·) means. That is, the state x at a given time k k , receiving the observation z k The probability intensity is g k (z k |x k ). At the same time, the observation data of each sensor at time k will contain clutter, the amount of clutter n c Follows Poisson distribution Where V is the motion space The volume, λ c is the clutter density.

[0096] For each sensor s, its kinematic model can be expressed as:

[0097]

[0098] Among them, is the state of sensor s at time k, Represents the control input of the sensor at time k. In order to simplify the complexity of the problem, it is discretized, that is, the control is divided into static and eight-directional nine input modes.

[0099] Consider the target motion space A set of N sensors are deployed in the system to detect M at time k. k The location of the target (where M k is unknown and changing). Each sensor observes all possible targets in its own observation area. Our goal is to effectively fuse the predictions of multiple sensors through communication between sensors, and then design an optimal control framework for the multi-target active estimation problem, thereby improving the accuracy of each sensor's observation of the target.

[0100] Step 2. Design a GM-PHD filtering algorithm with bounded sensor observation area for local multi-target state estimation. Specifically:

[0101] Step 2-1. Determine the calculation form of PHD filtering: GM-PHD filtering uses a Gaussian mixture model to approximate the PHD function in the PHD filter, which means that v k (x) can be expressed as:

[0102]

[0103] Among them J k is the number of Gaussian components, are the weight, mean, and covariance of the jth component, respectively. Subsequently, the closed-form solution of the GM-PHD filter can be easily derived, which significantly reduces the computational burden. In addition, the number of targets can be directly calculated without integration as The state of each target can be extracted as the mean of the components in the Gaussian mixture model.

[0104] Step 2-2. Determine the update method of the prior strength: Assume that the target survival probability P at time k S,k is a constant, and the sensor’s observation area is bounded, so its detection probability at time k depends on its position m D,k , which can be modeled as:

[0105]

[0106] Now we can get the GM-PHD recursion with bounded sensor observation area. Assume that our intensity at time k-1 is:

[0107]

[0108] We can obtain the predicted survival intensity function v at time k S,k∣k-1 (x):

[0109]

[0110] The relevant symbols are recorded as

[0111]

[0112] Therefore, the prediction strength function can be written as:

[0113]

[0114] The new strength function is:

[0115]

[0116] Step 2-3. Determine the update method of the posterior strength under the state-dependent detection model: Combined with the state-dependent detection probability, we can obtain the posterior strength:

[0117]

[0118] in

[0119]

[0120] The relevant symbols are recorded as

[0121]

[0122] as well as

[0123]

[0124] The relevant symbols are recorded as

[0125]

[0126] Step 2-4. Prune and merge the Gaussian components in the PHD function and extract the target state: In the execution process of the GM-PHD filter, the core principle of pruning and merging is to remove components with smaller weights and merge multiple similar components into one. We can simply set a predetermined truncation threshold ε t to filter out the larger weights. During the merging process, we iteratively identify the components with the highest weights and associate them with the components whose Mahalanobis distance is below a specified threshold ε m Finally, if the number of components after pruning and merging is still greater than J max , we will continue to discard components with lower weights until the number of components reaches J max By adopting this strategy, the number of components is significantly reduced, thereby reducing the computational complexity. In addition, due to the existence of negative weights, the components with negative weights should be filtered out after the above merging, and then the remaining weights should be normalized to ensure the practical significance of the PHD function.

[0127] The multi-target state extraction method is to extract the function v k (x) is integrated, that is, the sum v k The weights of all Gaussian components in (x) can be used to estimate the number of targets, denoted by N t Then, the algorithm iteratively selects the mean of the components with the highest weight as the target state, repeating N times. t Once a component is selected, its weight will be reduced by 1.

[0128] In step 3, multi-sensor information fusion is based on the generalized collaborative information (GCI) method. Specifically:

[0129] Step 3-1. Multi-sensor target state estimation information fusion: This step aims to propose a consensus method by combining the local strength of each sensor To obtain higher target estimation accuracy. We introduce the notation represents the intensity function of sensor i. Assume that the initial posterior intensity of sensor i at time k is The formula for the vth iteration at time k is:

[0130]

[0131] in is the neighbor of sensor i, function It is called the opinion pool, which determines how to combine this set of strength functions. Based on this, the logarithmic opinion pool LogOP is defined as:

[0132]

[0133] where ∑ l a l = 1. By using the logarithmic opinion pool, the prediction information of multiple sensors can be fused to improve the accuracy of state estimation.

[0134] Step 3-2. Information fusion approximation based on GCI method: In the LogOP formula, the distribution The operation of raising the fractional power transforms the original Gaussian mixture model (GMM) into a non-standard distribution, which makes subsequent iterations in the GM-PHD filter difficult to perform. In addition, the integral in the denominator is also computationally difficult for hardware devices. Therefore, the GCI method can be used to solve this problem.

[0135] The GCI algorithm establishes a framework for fusing data from different sensors while taking into account the uncertainty of each sensor's measurement. By taking into account the covariance of sensor measurements, GCI aims to obtain a better estimate of the true state. First, we use the GCI technique to implement LogOP, thereby combining the information of each sensor with its neighbors. For GMM, Battistell gave the following approximation in the literature:

[0136]

[0137] This approximation ignores the cross terms between different Gaussian components. But this is not a problem because after the pruning and merging steps, the distance between each pair of components is far enough. Under the above approximation, the following results are used:

[0138] 1) The fractional power of a Gaussian component is still a Gaussian component:

[0139]

[0140] in

[0141] 2) Two Gaussian components and The product of is still a Gaussian component:

[0142]

[0143] in and Based on results 1) and 2), the GCI fusion of two GMMs (LogOP) With weights ω and 1-ω, it is still a GMM:

[0144]

[0145] in

[0146]

[0147] When the number of GMMs to be fused is N G When N is greater than 2, the above process can be performed G -1 times to obtain the fused GMM.

[0148] In step 4, the multi-objective active state estimation optimization objective function of multiple sensors is constructed. Specifically, the optimal control input of sensor i at the kth moment is planned. Therefore, consider the following goals:

[0149] The purpose of active sensing is to reduce the uncertainty of the target distribution, which is reflected in the size of the covariance matrix. Therefore, the following objective function can be used for sensor i to reduce the uncertainty of the target distribution:

[0150]

[0151] Among them, S i,k ={j|ω j >ε R ,ω j is The weights in}, ε R is the threshold for filtering out non-dominant components in GMM.

[0152] In addition, the mean vector center of the first K weighted components is selected as the target position to drive the sensor movement, and the relevant objective function is designed as follows:

[0153]

[0154] in, is in v k The index set of the first K components with the largest weight in (x), and dist is the distance function between calculated vectors.

[0155] Finally, we add a repulsive effect to sensors that are close to each other to prevent swarming. Using the hyperbolic tangent function as the target function of the repulsive force can help control the repulsive strength when the distance is too close. Assume that the distance between sensors i and j is d ij , its repulsive force objective function can be defined as:

[0156]

[0157] Among them, α r is the coefficient that controls the attenuation of the repulsive force, which can ensure that there is still a certain repulsive force when multiple sensors are far apart. Finally, the optimization function is obtained by weighted average.

[0158]

[0159] The optimal control framework design for the multi-sensor multi-target active estimation problem in step 5 is as follows:

[0160] Step 5-1. Design multi-sensor collision avoidance constraints: For sensor i at time k, take action u k , we can define a security vector N i,k (u i ), as follows:

[0161]

[0162] variable Non-negative, indicating that if sensor i takes action u k , may collide with sensor j. Therefore, the following constraints ensure the safe movement of sensor i:

[0163] ||N i,k (u k )||1=0.

[0164] Step 5-2. Multi-target active perception framework design: The optimal frame for sensor i can be written as:

[0165]

[0166] Among them, Φ(v k|k+1 (x)) = v k∣k (x)-v D,k∣k (x)+∑v D,k∣k(x; z) is the update of the GM-PHD filter with bounded sensor observation area. During the planning process, the sensor observation model (2) is used to generate pseudo observation data for the iteration of PHD filter. The last constraint is the boundary constraint of sensor i. Note that in the process of solving the optimization problem, a constant velocity model is used to predict the motion of neighbor sensors during the planning period, that is, it is assumed that each neighbor moves according to its control input at time k during the entire planning period.

[0167] The following is a simulation verification of the multi-sensor multi-target active state estimation framework based on PHD filtering designed by the present invention:

[0168] In this simulation, N = 4 sensors are deployed for target tracking, and the motion space range is [-1000, 1000] × [-1000, 1000] (unit: meter), ensuring that their detection area covers the entire motion space. The clutter is modeled as a Poisson random finite set K k , whose intensity is λ c Vu(·), where u(·) is uniformly distributed.

[0169] Target state Include position (x k ,y k ) and speed The target dynamics is denoted as x k =Fx k-1 +σ k ,in

[0170]

[0171] I2, O2 are the second-order identity matrix and the second-order zero matrix respectively. The measurement model is expressed as z k =Hx k +v k ,in

[0172] H=[I2 O2],R k =100I2.

[0173] The intensity function of the new target is set as:

[0174]

[0175] in P γ =diag([100,100,25,25]). Clutter density λ c =1.25×10 -5 m -2 , the volume of the motion space V = 4 × 10 6 m 2There are three targets in the simulation, and their initial states are Target 3 is generated at time step 10. The entire simulation runs N sim = 80 time steps. Table 1 shows the parameter values ​​used in the simulation.

[0176] Table 1. Parameter values ​​used in the simulations.

[0177]

[0178]

[0179] Multi-target tracking involves both the change in the number of targets and the estimation of the target states, which makes the mean square error unsuitable for evaluating its performance. In order to measure the error of the observation estimate, this paper introduces the optimal sub-pattern assignment (OSPA) metric as a common quantitative indicator for evaluating the effectiveness of multi-target tracking systems. For a finite set X = {x1,…,x m} and Y={y1,…,y n}(m≤n), the OSPA metric between X and Y is defined as:

[0180]

[0181] where d c (x,y)=min(c,d(x,y)) is the distance between x and y, truncated at c>0. k is a set of permutations on {1,2,…,k}, for any When m>n, OSPA X∣Y =OSPA Y∣X ; When m=n=0, OSPA X∣Y =0.

[0182] The simulation results are as follows Figure 2 , Figure 3 shown. Figure 2 It is shown that, using the designed multi-sensor multi-target active state estimation framework, each sensor can smoothly realize the state estimation of multiple targets, and can autonomously assign corresponding targets for tracking to ensure coverage of all targets. Figure 3 is the actual motion trajectory of each sensor. It can be seen that other sensors can be avoided and collision avoidance can be ensured during the motion. Figure 5 From the minimum distance between each autonomous subject and the nearest object at each moment, it can be seen that the designed active state estimation framework successfully ensures the collision avoidance constraint in the perception process. Figure 4 is the OSPA index of each sensor at each moment, which is constrained within a certain error range and can obtain a balance between the number of targets and the target state estimation. Figure 6Comparison of the average OSPA indicators of the following methods:

[0183] 1. The active state estimation method proposed in the present invention.

[0184] 2. 4 non-moving sensors,

[0185] Deployed at four fixed points: (500,500), (500,-500), (-500,500), and (-500,-500).

[0186] Selecting 3 sensors corresponding to the number of targets, and the motion trajectory of each sensor is consistent with the target motion trajectory, can be considered as the optimal allocation mode.

[0187] 3. The optimization objective only considers the active estimation method with the minimum covariance.

[0188] pass Figure 6 It can be seen that the average OSPA mean of the method proposed in the present invention is the smallest among the four methods, and the error is much smaller than the method using fixed sensor estimation. It is also better than the method that only considers covariance or optimal allocation and tracking.

[0189] It can be seen from the above simulation experimental results that the multi-sensor multi-target active state estimation framework based on PHD filtering designed in the present invention can effectively realize the state estimation of multiple targets when the number of targets is variable, and can ensure the coverage of all targets and the collision avoidance constraints in the perception process, which is suitable for actual sensor system intelligent control applications.

[0190] The present invention provides a multi-sensor multi-target active estimation method based on probability hypothesis density filtering, which has satisfactory results in multi-target state estimation applications with a variable number of targets. The above are only preferred implementations of the present invention. It should be pointed out that the above implementation does not constitute a limitation on the present invention. The various changes and modifications made by relevant staff without departing from the technical idea of ​​the present invention are all within the protection scope of the present invention.

Claims

1. A multi-sensor multi-target active estimation method based on probability hypothesis density filtering, characterized by: The following steps are involved: S1: Modeling of sensor and target kinematic models and observation models; S2: Design a GM-PHD filter algorithm with bounded sensor observation area for local multi-target state estimation; S3: Multi-sensor information fusion based on generalized collaborative information (GCI) method; S4: Construction of optimization objective function for multi-sensor multi-objective active state estimation; S5: Design of an optimal control framework for multi-sensor multi-target active estimation problems.

2. The multi-sensor multi-target active estimation method based on probability hypothesis density filtering according to claim 1 is characterized in that: In step S1, the sensor and target kinematic models and observation models are built, specifically: In PHD filtering, the probability hypothesis density PHD function, also known as the probability intensity function, is used to describe the multi-target distribution in the state space; it represents the target density of each state in the state space, and the result of integrating the function in any region is the expected number of targets in the region; For each sensor, in the multi-target dynamic state estimation problem, it is assumed that each target state follows a linear Gaussian dynamics model; Given the state x at time k-1 k-1 , transfer to state x at time k k The probability intensity function is f k|k-1 (x k ∣x k-1 ); Assume that the target can only be observed when it is in the sensor's sensing area and obeys the linear Gaussian observation model; let z k is the observed value of the target at time k, and its observation likelihood function g k (·|·) means that the state x at a given time k k , receiving the observation z k The probability intensity is g k (z k |x k ); At the same time, the observation data of each sensor at time k will contain clutter, the number of clutter n c Follows Poisson distribution Where V is the motion space The volume, λ c is the clutter density; For each sensor s, its kinematic model is expressed as: Among them, is the state of sensor s at time k, represents the control input of the sensor at time k. In order to simplify the complexity of the problem, it is discretized, that is, the control is divided into static and eight-way nine input modes; Consider the target motion space A set of N sensors are deployed in the system to detect M at time k. k The location of the target, where M k is unknown and changing; the predictions of multiple sensors are effectively fused through communication between sensors, and then the optimal control framework for the multi-objective active estimation problem is designed.

3. The multi-sensor multi-target active estimation method based on probability hypothesis density filtering according to claim 1 is characterized in that: Step S2 is specifically as follows: (21) Determine the calculation form of PHD filtering: GM-PHD filtering uses a Gaussian mixture model to approximate the PHD function v in the PHD filter. k (x), v k (x) is expressed as: Among them J k is the number of Gaussian components, are the weight, mean and covariance of the jth component respectively; then, the closed-form solution of the GM-PHD filter is derived; the number of targets is directly calculated without integration: The state of each target is extracted as the mean of the components in the Gaussian mixture model; (22) Determine the updating method of the prior strength: Assume that the target survival probability P at time k is S,k is a constant, and the sensor’s observation area is bounded, so its detection probability at time k depends on its position m D,k , modeled as: The GM-PHD recursion with bounded sensor observation area is obtained; Assume that our intensity at time k-1 is: Get the predicted survival strength function v at time k S,k∣k-1 (x): in Therefore, the predicted strength function is written as: The new strength function is: (23) Determine the updating method of the posterior strength under the state-dependent detection model: Combining the state-dependent detection probability, we can obtain the posterior strength in And the corresponding symbols are recorded as as well as And the corresponding symbols are recorded as (24) Prune and merge the Gaussian components in the PHD function and extract the target state: During the execution of the GM-PHD filter, a predetermined truncation threshold ε is set t To filter out t During the merging process, the components with the highest weights are iteratively identified and matched with the components whose Mahalanobis distance is lower than the specified threshold ε m Finally, if the number of components after pruning and merging is still greater than J max , will continue to discard weights less than the weight threshold ε ω until the number of components reaches J max Until; Due to the existence of negative signs in formula (8), the components with negative weights should be filtered out after the above merging, and then the remaining weights should be normalized to ensure the practical significance of the PHD function; The multi-target state extraction method is to extract the function v k (x) is integrated, that is, the sum v k The weights of all Gaussian components in (x) can be used to estimate the number of targets, denoted by N t ; Then, the algorithm iteratively selects the mean of the components with the highest weight as the target state, repeating N times t times; once a component is selected, its weight will be reduced by 1.

4. The multi-sensor multi-target active estimation method based on probability hypothesis density filtering according to claim 1 is characterized by: Step S3 is specifically as follows: (31) Multi-sensor target state estimation information fusion: A consensus method is proposed to combine the local strength of each sensor To obtain higher target estimation accuracy; introduce the symbol represents the intensity function of sensor i at time k; let the initial posterior intensity of sensor i at time k be The formula for the vth iteration at time k is: in is the neighbor of sensor i, function It is called the opinion pool, which determines how to combine this set of strength functions; accordingly, the logarithmic opinion pool LogOP is defined as: where a l is the weight, and there is ∑ l a l =1; adopt the logarithmic opinion pool, that is, fuse the prediction information of multiple sensors; (32) Information fusion approximation based on the generalized collaborative information (GCI) method: First, the GCI technique is used to implement LogOP, thereby combining the information of each sensor with its neighbors; for GMM, the following approximation is given: This approximation ignores the cross terms between different Gaussian components; however, this is not a problem because after the pruning and merging steps, the distance between each pair of components is far enough that the GCI fusion of two GMMs with weights ω and 1-ω (LogOP) Still a GMM: in When the number of GMMs to be fused is N G When N is greater than 2, the above process can be performed G -1 times to obtain the fused GMM.

5. The multi-sensor multi-target active estimation method based on probability hypothesis density filtering according to claim 1 is characterized by: Step S4 is specifically: planning the optimal control input of sensor i at the kth moment Sensor i uses the following objective function to reduce the uncertainty of the target distribution: in, ε R is the threshold for filtering out non-dominant components in GMM; In addition, the mean vector center of the first K weighted components is selected as the target position to drive the sensor movement, and the relevant objective function is designed as follows: in, is in v k The index set of the first K components with the largest weight in (x), dist is the distance function between calculated vectors; Finally, a repulsive effect is added to sensors that are close to each other to prevent swarming and tracking. The hyperbolic tangent function is used as the target function of the repulsive force to help control the repulsive strength when the distance is too close. Assume that the distance between sensors i and j is d ij , and its repulsive force objective function is defined as: Among them, α r is the coefficient that controls the attenuation of the repulsive force; finally, the optimization function is obtained by weighted averaging.

6. The multi-sensor multi-target active estimation method based on probability hypothesis density filtering according to claim 1 is characterized by: Step S5 is specifically as follows: (51) Design multi-sensor collision avoidance constraints: For sensor i, take action u at time k k , we can define a security vector N i,k (u i ), as follows: variable Non-negative, indicating that if sensor i takes action u k , which may collide with sensor j; Therefore, the following constraints ensure safe movement of sensor i: ||N i,k (u k )||1=0. (52) Multi-target active perception framework design: v k|k (x) = v k (x), the optimal frame of sensor i is written as: Among them, Φ(v k|k+1 (x)) = v k∣k (x)-v D,k∣k (x)+∑v D,k∣k (x; z) is the update of the GM-PHD filter with bounded sensor observation area. During the planning process, the sensor observation model of step S1 is used to generate pseudo observation data for iteration of PHD filtering; the last constraint is the boundary constraint of sensor i; note that in the process of solving the optimization problem, a constant velocity model is used to predict the motion of neighbor sensors during the planning time period, that is, it is assumed that each neighbor moves according to its control input at time k during the entire planning period.

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