Asynchronous Non-uniform Distributed Multi-target Tracking Method Based on Asymmetric Alpha Divergence

Abstract

The present invention discloses an asynchronous non-uniform distributed multi-target tracking method based on asymmetric alpha divergence, which is used for multi-target tracking in an asynchronous non-uniform distributed sensor network. By setting a time variable as the trigger condition for the time-triggered fusion structure, and obtaining the current system state based on a time judgment program, a time-triggered fusion TTF structure suitable for an asynchronous non-uniform sensor network is constructed in combination with a Bayesian estimation process. Secondly, based on the continuous-discrete multi-target dynamics CD model and the probability hypothesis density CPHD algorithm with potential estimation, in combination with the time-triggered fusion structure, a multi-target tracking TCD-CPHD structure with a multi-step birth process suitable for an asynchronous non-uniform sensor network is constructed. Furthermore, considering the sensitivity of the asymmetric alpha divergence AAD to noise data, a fusion rule based on AAD is constructed for the fusion process, which is called AAD consistency. Combining the TCD-CPHD structure and AAD consistency, a complete distributed multi-target tracking algorithm for an asynchronous non-uniform sensor network is constructed.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-sensor information fusion in information processing, and relates to an asynchronous non-uniform distributed multi-target tracking method based on asymmetric alpha divergence. Background Art

[0002] With the continuous increase of the demand for target tracking, distributed multi-target tracking based on wireless sensor networks has become one of the research hotspots in target tracking. Distributed multi-target tracking is more flexible than centralized multi-target tracking, can obtain more information than a single sensor, and has a wider application range and higher robustness. However, in practical applications, there are still many problems, such as target occlusion, severe clutter, and so on.

[0003] The multi-target tracking algorithm is one of the basic and important technologies in distributed target tracking. Early multi-target tracking research solved the uncertainty of the relationship between targets and measurements through the idea of data association. Such algorithms mainly use data association hypotheses to construct the relationship between measurements and targets, and combine the probability of each hypothesis (association probability) to obtain the final multi-target tracking result. The classic data association multi-target tracking algorithms mainly include global nearest neighbor, joint probabilistic data association, and multiple hypothesis tracking. However, since such algorithms rely on data association hypotheses, when the number of targets increases or severe clutter is encountered, the number of hypotheses of the multi-target tracking algorithm based on data association hypotheses will also increase exponentially, resulting in serious computational complexity. To reduce the computational complexity, ideas such as pruning, merging, and thresholding are applied to such algorithms. However, such ideas cannot enable the data association multi-target tracking algorithm to obtain both low computational complexity and high robustness at the same time. Therefore, to reduce the computational complexity of multi-target tracking, a multi-target tracking algorithm based on random finite set (RFS) is proposed. This type of multi-target tracking algorithm properly represents the concept of multi-target probability density by establishing the multi-target state and measurement as an RFS, so that terms such as state space model, Bayesian recursion, and Bayesian optimality in the single-target tracking field can be directly transformed and used in the multi-target tracking field. This type of algorithm can handle more complex multi-target tracking scenarios, such as newborn and dead targets, severe clutter, missed detections and false detections, etc. The classic random finite set-based multi-target tracking algorithms include probability hypothesis density filter, probability hypothesis density filter with cardinality estimation, multi-Bernoulli filter, and Poisson multi-Bernoulli filter, etc. Such algorithms do not consider data association hypotheses and are easy to implement. The fusion rule is another basic and important technology in distributed target tracking. Currently, the classic fusion algorithm is the consensus rule, such as arithmetic mean consensus, cardinality consensus, covariance intersection, and Kullback-Leibler (KL) divergence minimization.

[0004] The above-mentioned distributed multi-target tracking algorithm for random finite sets relies on the synchronization assumption of the sensor network. However, due to reasons such as communication delay and sampling period difference, the synchronization characteristics of the sensor network cannot be effectively guaranteed. Therefore, a multi-target tracking algorithm for asynchronous non-uniform multi-sensor networks should be considered. Summary of the Invention

[0005] In view of this, the present invention provides an asynchronous non-uniform distributed multi-target tracking method based on asymmetric alpha divergence, which can be used for multi-target tracking in asynchronous non-uniform distributed sensor networks.

[0006] To achieve the above object, an asynchronous non-uniform distributed multi-target tracking method based on asymmetric alpha divergence of the present invention includes the following steps:

[0007] Step 1: Set a time variable as the trigger condition for the time-triggered fusion structure, and obtain the current system state based on the time judgment program.

[0008] Step 2: Combine the Bayesian estimation process to construct a time-triggered fusion TTF structure suitable for asynchronous non-uniform sensor networks. The TTF structure uses time as the trigger condition.

[0009] Step 3: Based on the continuous-discrete multi-target dynamic CD model and the probability hypothesis density CPHD algorithm with potential estimation, combine the time-triggered fusion structure to construct an asynchronous non-uniform distributed multi-target tracking structure with a multi-step birth process, which is the TCD-CPHD structure.

[0010] Step 4: Construct an asymmetric alpha divergence AAD consensus fusion rule.

[0011] Step 5: Combine the TTF structure, the TCD-CPHD structure, and the AAD consensus fusion rule to construct a complete asynchronous non-uniform distributed multi-target tracking method based on asymmetric alpha divergence.

[0012] Further, in Step 2: Combine the Bayesian estimation process to construct a time-triggered fusion TTF structure suitable for asynchronous non-uniform sensor networks. The TTF structure uses time as the trigger condition, specifically: Set the time variable T as the trigger condition for the TTF structure, and call this variable the time trigger index; judge the current time t i,ki of sensor i and the relationship of integer multiples of the time trigger index T to obtain the system state; finally, based on the system state, combine the Bayesian recursive process and the corresponding fusion steps to achieve multi-target tracking of asynchronous non-uniform sensor networks.

[0013] Further, in Step 3, in the TCD-CPHD structure, the one-step birth process of a single sensor is split into a multi-step birth process.

[0014] Further, for the process of "prediction step: time t1 to the time LT of the L-th fusion - fusion step: the time LT of the L-th fusion - prediction step: time LT to time t2 - update step: time t2", the newborn process from time t1 to time t2 is divided into two-step newborn processes: the newborn process from time t1 to time LT and the newborn process from time LT to time t2; meanwhile, the newborn RFS obtained by the newborn process from time t1 to time LT is used as the target RFS at time LT after the fusion step at time LT.

[0015] Further, an Asymmetric Alpha Divergence (AAD) consistency fusion rule is constructed, specifically: using AAD to construct the difference in probability density functions of different sensors, and based on this, a new consistency fusion rule is constructed, which is the AAD consistency fusion rule.

[0016] Beneficial effects:

[0017] 1. For the asynchronous non-uniform sensor network, the present invention proposes a distributed multi-target tracking algorithm based on asymmetric alpha divergence. First, the present invention constructs a Time-Triggered Fusion (TTF) structure triggered by a time variable, avoiding the multi-sensor time registration process. Second, the CD model is used to compensate for the non-uniform sampling problem of sensors. Meanwhile, combining the TTF structure and the Cardinalized Probability Hypothesis Density (CPHD) filtering algorithm, a TCD-CPHD structure with a multi-step newborn process is constructed to realize the distributed multi-target tracking process under the asynchronous non-uniform sensor network. Furthermore, considering the sensitivity of the asymmetric alpha divergence to noise, the present invention derives a fusion rule based on the asymmetric alpha divergence. Finally, combining the TCD-CPHD structure with a multi-step newborn process and the fusion rule based on the asymmetric alpha divergence to construct a complete distributed multi-target tracking process for the asynchronous non-uniform sensor network.

[0018] 2. For the asynchronous non-uniform sensor network, the present invention uses the time variable as the trigger condition to construct a time-triggered fusion structure suitable for the asynchronous non-uniform sensor network, thereby compensating for the asynchronous characteristics between different sensors.

[0019] 3. The present invention combines the continuous-discrete multi-target motion model, the probability hypothesis density filtering with potential estimation, and the constructed time-triggered fusion structure to construct a distributed multi-target tracking algorithm with a multi-step newborn process suitable for the asynchronous non-uniform sensor network, overcoming the asynchronous and non-uniform characteristics of the asynchronous non-uniform sensor network.

[0020] 4. Considering the sensitivity of the asymmetric alpha divergence to noise, the present invention constructs a fusion rule based on the asymmetric alpha divergence, that is, the AAD consistency rule.

[0021] 5. The present invention constructs a complete distributed multi-target tracking algorithm applicable to asynchronous non-uniform sensor networks by combining a distributed multi-target tracking algorithm with a multi-step birth process and the AAD consistency rule. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flowchart of a method for asynchronous non-uniform distributed multi-target tracking based on asymmetric alpha divergence according to the present invention.

[0023] Figure 2 It is a time-triggered fusion structure diagram based on an asynchronous non-uniform sensor network according to the present invention.

[0024] Figure 3 It is a schematic diagram of the time-triggered fusion process based on an asynchronous non-uniform sensor network according to the present invention.

[0025] Figure 4 It is a structure diagram of an asynchronous non-uniform distributed sensor network during the experimental process of the present invention.

[0026] Figure 5 It is the sampling time intervals of 4 sensors during the experimental process of the present invention.

[0027] Figure 6 It is the movement trajectories and quantities of all targets during the experimental process of the present invention.

[0028] Figure 7 It is the comparative evaluation result based on GOPSA when the detection probability of the present invention is 0.95.

[0029] Figure 8 It is the comparative evaluation result based on GOPSA when the detection probability of the present invention is 0.95.

[0030] Figure 9 It is the target quantity estimation result when the detection probability of the present invention is 0.95.

[0031] Figure 10 It is the comparative evaluation results based on GOPSA when the detection probabilities of the present invention are 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, 0.99.

[0032] Figure 11 It is the comparative evaluation results based on OPSA when the detection probabilities of the present invention are 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, 0.99. DETAILED DESCRIPTION OF THE INVENTION

[0033] The present invention will be described in detail below with reference to the accompanying drawings and by way of examples.

[0034] The present invention is directed to an asynchronous non-uniform sensor network, and proposes a distributed multi-target tracking algorithm based on asymmetric alpha divergence. First, the present invention constructs a time-triggered fusion TTF structure triggered by a time variable, avoiding the multi-sensor time registration process. Second, the CD model is used to compensate for the non-uniform sampling problem of sensors. At the same time, combining the TTF structure and the CPHD filtering algorithm, a TCD-CPHD structure with a multi-step birth process is constructed to implement the distributed multi-target tracking process under an asynchronous non-uniform sensor network. Furthermore, considering the sensitivity of asymmetric alpha divergence to noise, the present invention derives a fusion rule based on asymmetric alpha divergence. Finally, combining the TCD-CPHD structure with a multi-step birth process and the fusion rule based on asymmetric alpha divergence to construct a complete distributed multi-target tracking process for an asynchronous non-uniform sensor network.

[0035] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0036] Step 1: Construct a time-triggered fusion structure

[0037] Assume that there are N nodes in an asynchronous non-uniform sensor network that share local information by communicating with their neighbors. An undirected graph is used to describe the topology of the network where represents the nodes of the network, represents the link relationship of all network nodes, For any nodes i and j (i≠j and (i,j)∈ ) of a sensor network, if node i can receive information from node j, then node j is a neighbor node of i, and For an asynchronous non-uniform sensor network, the sampling time of each sensor is asynchronous and non-uniform.

[0038] Based on the above sensor network, a TTF structure is constructed. This structure uses a time variable as the trigger condition and is mainly divided into four parts: a time judgment process, a prediction process, an update process, and a fusion process. The algorithm structure diagram is as shown in Figure 2 shown, and the algorithm flow schematic diagram is as shown in Figure 3 shown. The specific steps are as follows:

[0039] 1) Time judgment process

[0040] Set the time variable T as the time trigger index. For the time judgment process of sensor i, the specific operation is as follows

[0041]

[0042] where ι i = 1 represents the time judgment result of sensor i, L is the number of trigger times, and LT = L × T. t i,ki is the current sampling time of sensor i (continuous time index), and its value is equal to the discrete time index k of sensor i i . For the parameter η of sensor i i (or the discrete time index), the relationship between the previous fusion time (L - 1)T and the previous sampling time t of sensor i must be considered, that is i,ki-1 2) Prediction process

[0043]

[0044] 2) Prediction process

[0045] According to the time judgment result, there are also two cases in the prediction process:

[0046] · When ι i = 1, the time interval is

[0047] Δt i = LT - η i , (3)

[0048] Then the prediction process of sensor i can be calculated as

[0049]

[0050] where χ represents the target RFS. represents the multi-target prediction density of sensor i from the discrete time index η i to the fusion time index LT; represents the target motion model of sensor i from the discrete time index η i to the fusion time index LT; represents the multi-target prior density of sensor i at the discrete time index η i , and

[0051]

[0052] where represents the fusion density of sensor i at the fusion time index (L - 1)T.

[0053] · When ι i = 0, the time interval is

[0054] Δt i = t i,k - η i , (6)

[0055] Then the prediction process of sensor i can be calculated as

[0056]

[0057] in, and They represent the discrete time index η of sensor i. i to discrete time index k i Multi-target prediction density and sensor i in discrete time index η i The multi-objective prior density of ; Denotes the discrete time index η of sensor i i to discrete time index k i Target motion model.

[0058] 3) Update process

[0059] Although the prediction process has two cases, the update process only considers the case of obtaining new measurements (ι i =0).

[0060] At this time, the update process of sensor i is

[0061]

[0062] in, It means that sensor i goes from discrete time index 1 to discrete time index k i All measurements of represents the discrete time index k of sensor i i Measurement. represents the discrete time index k of sensor i i The multi-target measurement model at

[0063]

[0064] 4) Fusion process

[0065] The fusion process only considers the trigger condition (ι i =1). In this process, the predicted probability density based on sensor i and the probability density function of its neighbor nodes Combined with a suitable fusion algorithm to obtain the fused multi-target probability density function of sensor i At the same time, the TTF structure constructs a time-varying time trigger indicator by updating the trigger count L = L + 1 and returns to the time judgment step. Note that when the trigger condition is equal to the sampling time The fusion process uses the a posteriori information of sensor i Replacing sensor prediction information (The same situation is also considered for its neighbor nodes).

[0066] Based on the above four parts, the algorithm steps of the TTF structure are shown in Algorithm 1.

[0067]

[0068]

[0069]

[0070] Step 2: Construct an asynchronous non-uniform distributed multi-target tracking method with a multi-step birth process

[0071] For sensor i, consider a multi-target tracking process and model the multi-target state and measurement values as a random finite set (RFS)

[0072]

[0073] where and represent the target and measurement RFS of sensor i at discrete time index k i respectively. …, represent the first, second to the i th target of sensor i at discrete time index k respectively. ,…, represent the first, second to the i th measurement of sensor i at discrete time index k respectively. (unknown parameter) and represent the number of targets and measurements of sensor i respectively. and are the target space and measurement space respectively, and k i is the discrete time index. In the multi-target tracking process, the target RFS can be divided into two parts: the surviving target RFS and the newborn target RFS Therefore, the target RFS can be modeled as

[0074]

[0075] where ζ is from discrete time index k i -1 to discrete time index k iThe state of the surviving target, with a survival probability of p S (ζ). Denote the discrete-time index k i The RFS of the target state at -1. The symbol ∪ represents the union symbol, Denote the target Belonging to the target RFS

[0076] Meanwhile, due to the detection uncertainty of the sensor and the influence of the complex environment, the measurement RFS Can be divided into two parts: the target measurement RFS And the clutter RFS Therefore, the measurement RFS Can be modeled as

[0077]

[0078] Among them, the detection probability of each target is From discrete-time index 1 to discrete-time index k i All measurements can be described as Respectively denote the measurements at discrete-time index 1, discrete-time index 2 to discrete-time index k i Of, Denote all measurements from discrete-time index 1 to discrete-time index k i To -1. Denote that the target x belongs to the target RFS

[0079] For sensor i, the multi-target dynamic process is constructed using the CD model. The assumptions are as follows:

[0080] · The targets are independent of each other, and the motion model of each target is modeled as a linear time-invariant stochastic differential equation

[0081] dx (i) (t) = A (i) x (i) (t)dt + B (i) dβ (i) (t) (13)

[0082] Among them, dx (i) (t) represents the differential of the target ; Is the state of a single target of sensor i; Represents a Brownian motion with a diffusion matrix ; t is the continuous-time index. Denote the target x (i) (t) of the dimension, Denote B (i)Dimensions.

[0083] · The A2 newborn targets are independent of each other, and the time of their appearance follows a Poisson distribution with rate λ.

[0084] · For A3, the survival time τ of each target is independent of other targets and follows an exponential distribution p(τ) with rate μ. τ of.

[0085] At this time, the continuous motion model of the target can be discretized into

[0086]

[0087] where represents a Gaussian distribution with mean and variance , and

[0088]

[0089] where exp(AΔt k ) represents the matrix exponential of matrix , and ξ is a temporary variable. Note that the continuous-time index and the discrete-time index k i are different expressions of the same time. When the target survives (the surviving target) from the continuous-time index to , this means that the survival time τ of the target is greater than the time interval . Then, the survival probability of this target is

[0090]

[0091] Generally speaking, the processes of a target entering and leaving the sensor detection area are respectively called the birth and death processes of the target. However, the meanings of the processes of a target entering and leaving the detection area based on continuous time and discrete time are different. For continuous time, the time when the target enters the sensor detection area is t b , and For discrete time, the time when the target enters the sensor detection area is k i . When and only when t b and k i are equal (t b = t ki) When the target enters the detection area, the process is equal in continuous time and discrete time. When the target attributes are not considered (when the target re-enters the sensor detection area multiple times, it is not considered the same target), the process of the target leaving the detection area is approximately equal in continuous time and discrete time. Therefore, the present invention uses "appearance" and "disappearance", "newborn" and "death" to describe the process of the target entering and leaving the sensor detection area in continuous time and discrete time. When the appearance time of a new target is and the survival time of the appeared target exceeds the time interval this target is considered a newborn target at the discrete-time index k i . This means it is necessary to consider the movement process of the newborn target within the time interval κ. Model the newborn target as a Poisson point process. The number of newborn targets within the time interval follows a Poisson distribution:

[0092]

[0093] where, represents the single-target newborn density at the continuous-time index (or the discrete-time index k i ); is a truncated exponential distribution with rate μ within the time interval τ ; p k (x|κ) is the single-target newborn density based on the time interval κ. represents the potential distribution of the newborn target, represents the probability that the number of newborn targets is n B .

[0094] Combine the CD model, CPHD algorithm, and TTF structure to implement the multi-target tracking process of an asynchronous non-uniform sensor network, namely the TCD-CPHD structure. For sensor i, assumptions A4 - A8 are satisfied.

[0095] · A4 Each target is independent of each other;

[0096] · A5 Each target produces at most one measurement, and each measurement corresponds to at most one target

[0097]

[0098] where, represents the measurement matrix at the discrete-time index k i of sensor i;

[0099] · A6 Surviving targets and newborn targets are independent of each other, and the birth model is formula (17);

[0100] · The survival and detection probabilities of A7 ( and ) are independent of the target state, and the survival probability can be obtained through Equation (16);

[0101] · The clutter and target measurements of A8 are independent of each other.

[0102] The CD-CPHD filter for the multi-step birth process uses the intensity function v (i) (x) and the potential distribution p (i) (n) to replace the multi-target posterior probability density π (i) (x) and propagate it in the Bayesian recursion process. The multi-target posterior probability density at discrete time index k i is calculated as where

[0103] denotes the probability that the number of targets is n. Denoted as the multi-target intensity function at discrete time index k i . Assume that the intensity function is in the form of a Gaussian mixture, then

[0104]

[0105] where, denotes the number of Gaussian components of the Gaussian mixture intensity function at discrete time index k i . denotes the weight of the j-th Gaussian component of the Gaussian mixture intensity function at discrete time index k i ; denotes that the j-th Gaussian component of the Gaussian mixture intensity function at discrete time index k i follows a Gaussian distribution with mean and weight .

[0106] For sensor i, the multi-target tracking algorithm based on the CD model, CPHD algorithm, and TTF structure considering the multi-step birth process is as follows:

[0107] 1) Time judgment process

[0108] This process is the same as the TTF time judgment process in Step 1. Specifically, the parameters ι i and η i are obtained through Equations (1) and (2).

[0109] 2) Prediction process

[0110] · When ι i = 1, let t a be the parameter ιi The corresponding time index. Assume the prior intensity and the prior potential distribution are given. Then, the predicted intensity i from time index η a to time index t and the predicted potential distribution can be calculated as

[0111]

[0112] where

[0113]

[0114] and represents the potential distribution of the birth target, which can be obtained through formula (17); the symbol <a, b> represents the inner product of a and b. According to formula (16), is only related to the time interval and has nothing to do with the target state. represents the intensity of the surviving target from time index η i to time index t a ; represents the intensity of the newly born target from time index η i to time index t a .

[0115] For the surviving target, the intensity of the surviving target i from time index η a to time index t

[0116]

[0117] For the surviving target, using the prediction process of the Kalman filter, the predicted mean and covariance

[0118]

[0119] where and can be obtained through the time interval (3) and formula (15).

[0120] For the newly born target, assume that the newly born target at the appearance time t b is modeled as a Gaussian distribution

[0121]

[0122] or a Gaussian mixture distribution

[0123]

[0124] Among them, represents a Gaussian distribution with a mean of and a variance of . represents the number of Gaussian components of the Gaussian mixture distribution, and respectively represent the weight of the j-th Gaussian component and the component conforming to a Gaussian distribution with a mean of and a variance of . Then, the density of the target born at time t a is

[0125]

[0126] or

[0127]

[0128] Among them, and can be obtained by combining the time interval (3) and formula (15). Then, the intensity of the newborn target at time index t a is:

[0129]

[0130] At this time, the predicted intensity i from time index η a to time index t is

[0131]

[0132] Among them, represents the number of Gaussian components of the predicted Gaussian mixture intensity function at discrete time index t a . represents the weight of the j-th Gaussian component of the predicted Gaussian mixture intensity function at discrete time index t a ; represents the j-th Gaussian component of the predicted Gaussian mixture intensity function at discrete time index t a conforming to a Gaussian distribution with a mean of and a weight of .

[0133] · When ι i = 0, assume that the prior intensity and the prior potential distribution are given. Then, the predicted intensity i from time index η i to time index k and the predicted potential distribution can be calculated as

[0134]

[0135] where and can be obtained respectively by substituting time t a with time k i in formulas (17), (22) and (16), and the time interval (6). Therefore, the surviving target intensity i from time index η i to time index k can be obtained by substituting time t a with time k i in formulas (23)-(24), and the time interval (6). The newborn target intensity i from time index η i to time index k can be obtained by substituting time t a with time k i in formulas (25)-(29), and the time interval (6). In summary, the predicted intensity i from time index η i to time index k is

[0136]

[0137] where represents the number of Gaussian components of the predicted Gaussian mixture intensity function at discrete time index k i . represents the weight of the j-th Gaussian component of the predicted Gaussian mixture intensity function at discrete time index k i ; represents that the j-th Gaussian component of the predicted Gaussian mixture intensity function at discrete time index k i follows a Gaussian distribution with mean and variance .

[0138] 3) Update process

[0139] Assume that the predicted potential distribution and the predicted intensity are given by formulas (31)-(32). Then, the posterior potential distribution i and the posterior intensity at discrete time index k can be obtained based on Lemma 1.

[0140] Lemma 1: Assume that the predicted potential distribution and the predicted intensity is obtained, the updated potential distribution and the updated intensity can be calculated based on the measurement information where

[0141]

[0142] wherein

[0143]

[0144] and

[0145]

[0146] where m represents the number of measurements ; e j (·) represents the j-th elementary symmetric function of a finite set of real numbers; and represent the intensity of clutter and the potential distribution of clutter respectively. For a single target, the Kalman filter update process is adopted

[0147]

[0148] 4) Fusion process

[0149] This process is consistent with the TTF time judgment process in Step 1.

[0150] In summary, a distributed multi-target tracking algorithm (TCD-CPHD) with a multi-step prediction process is constructed based on the TTF structure, CD model, and CPHD filter.

[0151] Step 3: Construct the AAD consistency fusion rule

[0152] AAD provides a more robust solution for outliers and additive noise and is widely used in Bayesian neural networks, multi-class Gaussian process classification, and predictive density estimation processes. For two densities and the basic AAD can be defined as:

[0153]

[0154] where The basic AAD has the characteristics of strict positivity and convexity, which means that D α (p|q) ≥ 0, and D is equal to 0 if and only if α (p|q) = 0. When α → 1

[0155]

[0156] is also often referred to as the KL divergence. When α → 0

[0157]

[0158] is also often referred to as the inverse KL divergence. Theoretically, the unknown density can be composed of the known density and D α (p|q). However, the integral of the density power increases the difficulty of the actual solution process. According to the literature [Andrzej Cichocki and Shun-ichi Amari, "Families of Alpha-Beta-and Gamma-Divergences: Flexible and Robust Measures of Similarities", Entropy 12(2010), pp.1532-1568.], AAD can be expressed by the generalized KL divergence as follows

[0159]

[0160] Combining formulas (38)-(40), the AAD of the densities and can be written as

[0161]

[0162] Then, the objective function of multi-sensor fusion based on AAD is

[0163]

[0164] where ω i > 0. D α (π|π (i) ) represents the multi-target probability density function of sensor i and the multi-target probability density function after fusion of sensor i

[0165] Theorem 1: The multi-sensor multi-target tracking fusion rule based on AAD is

[0166]

[0167] Proof: Let Considering the fact that the density integral is equal to 1, D α (π|π (i) ) can be rewritten as

[0168]

[0169] When

[0170]

[0171] When α = 1,

[0172]

[0173] When α = 0,

[0174]

[0175] In summary, it is obvious that the solution of formula (42) is (43). The fusion rule of Theorem 1 is consistent with the fusion rules of the generalized CI and KL divergences and is not affected by α.

[0176] The construction process of the above fusion rule depends on formula (40). Therefore, the fusion rule based on the basic AAD needs to be further explored. According to (37), the basic AAD of sensor i can be rewritten as

[0177]

[0178] It is related to the Tsallis divergence and Tsallis entropy and is a generalization of the standard Boltzman - Gibbs entropy (or Shannon information). The objective function of multi - sensor fusion based on the basic AAD can be rewritten as

[0179]

[0180] Proof: When α ∈ (0, 1), let Then

[0181]

[0182] Let And According to the Hölder's inequality

[0183]

[0184] Therefore,

[0185]

[0186] Combining the strict positivity of the basic AAD and (52), This means that the fusion rule of Theorem 1 is the solution of (49).

[0187] Corollary 2: When the lower bound of (48) is 0.

[0188] Proof: Let Then

[0189]

[0190] Therefore, the function f i (α) determines the value. According to Lemma A of the literature [Chen-Huang Hong and Cheh-Chih Yeh, "ROGERS-HOLDER'S INEQUALITY ON TIME SCALES", International Journal of Pure and Applied Mathematics 29, 3 (2006), pp. 289-309.]

[0191]

[0192] Therefore,

[0193] f i (α) - 1 ≥ 0 (55)

[0194] So, when the lower bound of (49) is 0.

[0195] Unfortunately, when the upper bound of (49) is difficult to calculate. Therefore, rewrite as

[0196]

[0197] where is the ratio of probabilities. When tends to zero. According to the literature [Giorgio Battistelli, Luigi Chisci, Claudio Fantacci, Alfonso Farina, and Antonio Graziano, "Consensus CPHD Filter for Distributed Multi-target Tracking", IEEE Journal of Selected Topics in Signal Processing 7, 3 (2013), pp. 508-520.], the fusion rule of Theorem 1 is equal to the fusion rule of KL divergence, which means and the difference between them is very small, which means So when the fusion rule of Theorem 1 can be approximated as the solution of (49).

[0198] Step 4: Construct an Asynchronous Non-uniform Distributed Multi-target Tracking Method Based on Asymmetric Alpha Divergence

[0199] Combining the TTF structure, CD model, CPHD filtering, and AAD consistency fusion rule, construct a complete asynchronous non-uniform distributed multi-target tracking method based on asymmetric alpha divergence. For sensor node i, the multi-target fusion density can be obtained through the fusion rule of Theorem 1

[0200]

[0201] where

[0202]

[0203] How to ensure the Gaussian mixture structure of the TCD-CPHD intensity function is the research focus of this fusion rule. For the fusion process at the intensity There are two important techniques in the fusion process: the product of two Gaussian mixtures and the power of a Gaussian mixture. According to the literature [Jason L. Williams, "Gaussian Mixture Reduction for Tracking Multiple Maneuvering Targets in Clutter", in (2003).], the product of two Gaussian mixtures is still a Gaussian mixture

[0204] Assume Gaussian mixtures and The product of the two is

[0205] The power of a Gaussian mixture It is difficult to guarantee its Gaussian mixture form, but when the relationship between the components of the Gaussian mixture conforms to

[0206]

[0207] Or any two Gaussian components that do not conform to (60) are merged into one Gaussian component before calculating the power of the Gaussian mixture. Then, the sum of the powers of Gaussian components can be approximated as the weighted sum of the powers of Gaussian components

[0208] Establish a complete distributed multi-target tracking algorithm for asynchronous non-uniform sensor networks

[0209] Next, the effectiveness of the method of the present invention will be tested through simulation experiments

[0210] Hardware environment: computer

[0211] Software configuration: Windows 10; software in any language environment such as Matlab, C language, or C++.

[0212] In the experiment, the asynchronous non-uniform sensor network consists of 4 sensors. As Figure 4 shown, the sensor detection area is [-200, 400] × [0, 800] (m 2 ). The sampling interval of each sensor is as Figure 5 shown. The target state is represented as where (x p , y) and represent the position and velocity of the target respectively. The CD model parameters of the target are as follows:

[0213]

[0214] The appearance time rate and the lifespan rate are λ = 0.08 s -1 and μ τ = 0.01 s -1 . The clutter is modeled as a Poisson process with parameter λ c = 20. The true trajectory and the number of targets are as Figure 6 shown.

[0215] For the asynchronous non-uniform sensor network, to compensate for the problem of asynchronous sampling non-uniformity, the TTF structure and the TCD-CPHD structure based on the CD-CPHD algorithm and the TTF structure are constructed. Considering that AAD is more robust to outliers and additive noise, a fusion algorithm based on AAD consistency is constructed. Specifically, the MTT algorithm based on the ATCD-CPHD structure is ATCD-CPHD, the MTT algorithm based on the TCD-CPHD structure and AA consistency is AATCD-CPHD, and the MTT algorithm without the fusion process is NF. Further analyzing the performance of the TCD-CPHD structure, the TCD-CPHD1 structure that only considers the birth process (one-step birth process) in the prediction step before the update step is established. Therefore, the distributed multi-target tracking algorithms considering AAD consistency and AA consistency are called ATCD-CPHD1 and AATCD-CPHD1 respectively. At the same time, NF represents the tracking evaluation result without fusion, and Truth represents the true result. The experimental results are as Figures 7 - 11 shown.

[0216] Based on the experimental results with a detection probability of 0.95 Figure 7 and Figure 8 shown, the algorithm proposed by the present invention can effectively improve the accuracy of multi-target tracking. For Figure 7, sub - figure (a) shows the experimental results of the root - mean - square error of GOSPA with a detection probability of 0.95, sub - figure (b) shows the experimental results of the root - mean - square error of the localization error of GOSPA with a detection probability of 0.95, sub - figure (c) shows the experimental results of the root - mean - square error of the false target error of GOSPA with a detection probability of 0.95, and sub - figure (d) shows the root - mean - square error of the missed target error of GOSPA with a detection probability of 0.95. For Figure 8 , sub - figure (a) shows the experimental results of the root - mean - square error of OSPA with a detection probability of 0.95, sub - figure (b) shows the experimental results of the root - mean - square error of the localization error of OSPA with a detection probability of 0.95, and sub - figure (c) shows the experimental results of the root - mean - square error of the potential error of OSPA with a detection probability of 0.95. Figure 9 Shows the results of the number of multi - target tracking of each algorithm. According to Figure 7 and Figure 9 , it can be seen that the asymmetric alpha - divergence asynchronous non - uniform distributed multi - target tracking method constructed by the present invention can effectively improve the multi - target tracking accuracy.

[0217] In order to further analyze the effect of the proposed distributed multi - target tracking, different detection probability experiments [0.5, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, 0.99] were designed, and the experimental results are as shown in Figure 10 - Figure 11. For Figure 10 , sub - figure (a) shows the experimental results of the root - mean - square error of GOSPA with different detection probabilities, sub - figure (b) shows the experimental results of the root - mean - square error of the localization error of GOSPA with different detection probabilities, sub - figure (c) shows the experimental results of the root - mean - square error of the false target error of GOSPA with different detection probabilities, and sub - figure (d) shows the root - mean - square error of the missed target error of GOSPA. For Figure 11 , sub - figure (a) shows the experimental results of the root - mean - square error of OSPA with different detection probabilities, sub - figure (b) shows the experimental results of the root - mean - square error of the localization error of OSPA with different detection probabilities, and sub - figure (c) shows the experimental results of the root - mean - square error of the potential error of OSPA with different detection probabilities. Generally speaking, the root - mean - square error of GOSPA and the root - mean - square error of OSPA of ATCD - CPHD are better than those of other algorithms.

[0218] In summary, the above is only the preferred embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An asynchronous non-uniform distributed multi-object tracking method based on asymmetric alpha divergence, characterized in that It includes the following steps: Step 1: Set a time variable as the trigger condition for the time-triggered fusion structure, and obtain the current system state based on the time judgment program; Step 2: Combine the Bayesian estimation process to construct a time-triggered fusion TTF structure applicable to asynchronous non-uniform sensor networks, where the TTF structure uses time as the trigger condition; Step 3: Based on the continuous-discrete multi-target dynamic CD model and the probability hypothesis density CPHD algorithm with potential estimation, combine the time-triggered fusion structure to construct an asynchronous non-uniform distributed multi-target tracking structure with a multi-step birth process, which is the TCD-CPHD structure; Step 4: Construct an asymmetric alpha-divergence AAD consensus fusion rule; Step 5: Combine the TTF structure, the TCD-CPHD structure, and the AAD consensus fusion rule to construct a complete asynchronous non-uniform distributed multi-target tracking method based on asymmetric alpha-divergence.

2. The method according to claim 1, wherein Step 2: Construct a time-triggered fusion (TTF) structure applicable to asynchronous non-uniform sensor networks in combination with the Bayesian estimation process. The TTF structure uses time as the trigger condition, specifically: Set the time variable T as the trigger condition for the TTF structure, and this variable is called the time trigger index; Determine the relationship between the current time of sensor i and an integer multiple of the time trigger index T to obtain the system state. Finally, based on the system state, combine the Bayesian recursion process and the corresponding fusion steps to achieve multi-target tracking in asynchronous non-uniform sensor networks. And the relationship with an integer multiple of the time trigger index T to obtain the system state. Finally, based on the system state, combine the Bayesian recursion process and the corresponding fusion steps to achieve multi-target tracking in asynchronous non-uniform sensor networks.

3. The method according to claim 1 or 2, characterized in that, In Step 3, in the TCD-CPHD structure, the one-step birth process of a single sensor is split into a multi-step birth process.

4. The method according to claim 3, characterized in that For the process of "prediction step: time t1 to the time LT of the L-th fusion - fusion step: the time LT of the L-th fusion - prediction step: time LT to time t2 - update step: time t2", the birth process from time t1 to time t2 is divided into two-step birth processes: the birth process from time t1 to time LT and the birth process from time LT to time t2; meanwhile, the birth RFS obtained from the birth process from time t1 to time LT is used as the target RFS at time LT after the fusion step at time LT.

5. The method according to claim 1 or 2, characterized in that, The construction of the asymmetric alpha-divergence AAD consensus fusion rule is specifically as follows: Use AAD to construct the difference in the probability density functions of different sensors, and construct a new consensus fusion rule based on this, which is the AAD consensus fusion rule.

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