A Robust Distributed State Estimation Method for Low, Slow, and Small Targets

Abstract

The present invention proposes a robust distributed state estimation method for low, slow and small targets, belonging to the technical field of signal processing. The method solves the problem of distributed state estimation of maneuvering small targets under the background of heavy-tailed noise for both process noise and measurement noise in practical engineering applications, and has the advantages of high parameter estimation accuracy, high state estimation accuracy, good adaptability and robustness to complex application backgrounds, high computational efficiency, and tolerance to node failures, etc., and can meet the requirements of engineering applications.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a robust distributed state estimation method for low, slow, and small targets. Background Art

[0002] Due to the convenience of acquisition, low requirements for take-off sites, and the need for no professional training, the number of "low, slow, and small" unmanned aerial vehicles has shown explosive growth. Therefore, low, slow, and small targets pose a serious threat to urban air defense on a daily basis. Low, slow, and small targets have target characteristics such as low altitude (10m - 500m), slow speed (0 - 100m / s), small radar cross-section (0.05 - 0.1m 2 ), and strong maneuverability. Common low, slow, and small targets include targets such as small unmanned aerial vehicles, model airplanes, balloons, paragliders, powered paragliders, and helicopters. These targets fly in complex backgrounds (such as tall buildings, ground moving objects, and tree vegetation), so they also pose high requirements for the detection capabilities of sensors.

[0003] Since radar can detect targets all day and all weather and provide target distance and angle information in real time, it has been widely used in the detection and tracking of low, slow, and small targets. Optoelectronic devices have played an increasingly important role in the tracking of low, slow, and small targets, threat assessment, and target recognition. Compared with radar, optoelectronic devices have the advantages of low price, flexible station layout, high detection accuracy, high data rate (less than 1 second / frame), and being less susceptible to electromagnetic interference. However, optoelectronic devices are easily affected by weather conditions. Therefore, optoelectronic devices are often used in combination with sensors such as radar and laser ranging devices. Laser ranging devices have a short ranging range, high cost, and a sampling frequency much lower than that of optoelectronic tracking. The role of laser ranging devices in actual installations is limited. Radar has a wide detection range and flexible target tracking. At the same time, ground slow small detection radars are generally two-dimensional (distance, azimuth). Therefore, by taking advantage of the complementary advantages of radar and optoelectronic devices, the effective detection of low, slow, and small targets can be achieved.

[0004] There have been many related studies on the effective detection and tracking of low, slow, and small targets by existing multi-sensors. However, most of their noise conditions are under Gaussian noise conditions. Since low, slow, and small devices are easily affected by strong ground clutter, sea clutter, etc. when flying near the ground or over the sea, the clutter model at this time is closer to a heavy-tailed distribution rather than the traditional Gaussian noise. If traditional methods such as Kalman filtering are still used to track targets, the filtering performance will drop sharply. Currently, there are still very few related studies on the problem of tracking maneuverable small targets under distributed state heavy-tailed noise conditions, and this problem has important engineering application value. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a robust distributed state estimation method for low, slow, and small targets, which solves the problem of target state estimation under the condition that both process noise and measurement noise follow heavy-tailed noise in the multi-sensor joint state estimation problem.

[0006] The present invention proposes a robust distributed state estimation method for low, slow, and small targets, and the method includes:

[0007] Step S1, initialize system parameters; including: initialize sensor network parameters; initialize the discrete-time state space transition model; and initialize the measurement space transition model;

[0008] Step S2, based on the initialized discrete-time state space transition model, perform model interaction on the motion states of each motion model included in the low, slow, and small target to obtain a motion state interaction result and a state covariance interaction result;

[0009] Step S3, according to the motion state interaction result and the state covariance interaction result, perform prediction calculation on the motion state values and motion state covariance matrices of each motion model included in the low, slow, and small target;

[0010] Step S4, use the initialized measurement space transition model, the motion state value, and the motion state covariance matrix to determine the target measurement innovation and the information covariance;

[0011] Step S5, based on the motion state covariance matrix and the information covariance, calculate the innovation gain;

[0012] Step S6, solve the state estimation value according to the motion state value, the target measurement innovation, and the innovation gain, and solve the state estimation covariance according to the motion state covariance matrix and the innovation gain;

[0013] Step S7, update the degrees of freedom, calculate the likelihood values of each motion model included in the low, slow, and small target, and calculate the model probability update value according to the likelihood values;

[0014] Step S8, based on the sensor network, perform multi-sensor consistency fusion processing on the state estimation value, the state estimation covariance, the updated degrees of freedom, and the model probability update value to obtain the fused model probability update value;

[0015] Step S9, use the fused model probability update value to calculate the multi-model interaction result of the state estimation value and the multi-model interaction result of the state estimation covariance, so as to obtain the state estimation of each sensor of the low, slow, and small target at the current moment.

[0016] According to the method of the present invention, in the step S1:

[0017] Initializing the sensor network parameters includes: defining the sensor network \(N = S\cup C, A\), where the sensor nodes \(S\) represent the nodes for receiving and processing data, the communication nodes \(C\) represent the nodes for completing data transmission, and the connection links represent the communication links between communicable nodes. Initialize the set of adjacent nodes of the \(s\)-th sensor as where \(p\) represents the adjacent node of sensor \(s\), and initialize the sensor consistency weighting coefficient as \(w\);

[0018] Initializing the discrete-time state space transition model includes: defining the set of target motion models at time \(k\) as where \(M\) represents the number of motion models included in the target motion process, and define the motion state of the \(s\)-th sensor at time \(k\) as Then there is:

[0019]

[0020] where represents that the model at time \(k\) is \(i\), and \(f i (·) represents the state transition function of the \(i\)-th motion model; the process noise obeys the tail distribution where \(p(·)\) represents the probability density function, and \(St(x|\mu,\sum,v)\) represents the Student’s-t distribution with mean \(\mu\), scale matrix \(\sum\), and degrees of freedom \(v\);

[0021] Initializing the measurement space transition model includes:

[0022]

[0023] where represents the measurement value, and \(h s,i (·) represents the measurement transfer function corresponding to the \(i\)-th motion model in the \(s\)-th sensor. The measurement noise obeys the tail distribution represents the measurement noise scale matrix of model \(i\) at time \(k\).

[0024] According to the method of the present invention, in the step S2,

[0025] Calculate the model prediction probability of the target model \(j\) of the \(s\)-th sensor and the model interaction probability

[0026]

[0027]

[0028] where Denote the probability update value of model \(i\) at time \(k - 1\), obtained from the previous time. Denote the Markov transition probability matrix \(TPM\) at time \(k\), where \(Pr(·)\) represents the probability value.

[0029] Calculate the motion state interaction result of the \(i\)-th model of the target. And the state covariance interaction result.

[0030]

[0031]

[0032] Among them, And Respectively denote the state estimate value and the state estimate covariance matrix of model \(j\) at time \(k - 1\), obtained from the previous time, and \(\sum·\) represents the summation operation.

[0033] According to the method of the present invention, in the step S3:

[0034] Calculate the one-step prediction value of the motion state of the \(i\)-th model of the \(s\)-th sensor of the target. And the one-step prediction covariance matrix.

[0035]

[0036]

[0037] Among them, \(F\) i (·) represents the Jacobian matrix of the state transition function \(f\) i (·). Denote the process noise scale matrix of model \(i\) at time \(k\), (·) T Represents the transpose operation.

[0038] According to the method of the present invention, in the step S4:

[0039] Calculate the target measurement innovation And the information covariance Perform the calculation.

[0040]

[0041]

[0042] Among them Denote the target measurement value obtained by the \(s\)-th sensor, \(H\) s,i Represents the Jacobian matrix of the measurement transfer function \(h\) s,i (·).

[0043] According to the method of the present invention, in the step S5:

[0044] Calculate the innovation gain

[0045]

[0046] According to the method of the present invention, in the step S6:

[0047] Calculate the state estimate value and the state estimate covariance:

[0048]

[0049]

[0050] where represents the degrees of freedom of the trailing distribution at time k-1,

[0051] According to the method of the present invention, in the step S7:

[0052] Perform the degrees of freedom update at time k:

[0053]

[0054] where represents the measurement dimension corresponding to the sensor s;

[0055] Calculate each model likelihood value ""

[0056]

[0057] Calculate the model probability update value:

[0058]

[0059] According to the method of the present invention, in the step S8:

[0060] Calculate the information vector and the information matrix

[0061]

[0062]

[0063]

[0064] Perform the first-step consistency fusion process:

[0065]

[0066]

[0067] where \(w\) represents the fusion weight coefficient and \(L\) represents the number of consistency fusion times;

[0068] Perform the second consistency fusion process:

[0069]

[0070] Perform the third consistency fusion process:

[0071]

[0072] According to the method of the present invention, in the step S9:

[0073] Calculate the state estimation value and the state estimation covariance matrix according to the consistency processing result:

[0074]

[0075]

[0076] where represents the information matrix after the \(L\)-th fusion, represents the information vector after the \(L\)-th fusion;

[0077] Calculate the multi-model interaction result of the state estimation value and the multi-model interaction result of the state estimation covariance

[0078]

[0079] where represents the model probability update value after the \(L\)-th fusion.

[0080] In summary, the technical solution proposed by the present invention assumes that both the process noise and measurement noise of the low, slow, and small target movement process are heavy-tailed noises. By modeling the heavy-tailed noise as a student's t-distribution estimation, the relevant distribution parameters of the process heavy-tailed noise and measurement heavy-tailed noise are corrected, and the state estimation accuracy is improved by performing consistency fusion processing on the state estimation value, estimation covariance, and relevant parameters. Next, the probabilities of each maneuver model are solved, thus solving the multi-model state estimation problem of maneuvering targets under the background of heavy-tailed noise. The method of the present invention solves the problem of distributed state estimation of maneuvering small targets under the background of heavy-tailed process noise and measurement noise in practical engineering applications, and has the advantages of high parameter estimation accuracy, high state estimation accuracy, good adaptability and robustness to complex application backgrounds, high computational efficiency, and tolerance to node failures, etc., and can meet the requirements of engineering applications. The present invention greatly improves the adaptability and robustness of the algorithm to complex scenarios, and improves the estimation accuracy of the distributed state of maneuvering small targets under the background of heavy-tailed noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0082] Figure 1 is the overall flowchart of the present invention;

[0083] Figure 2 is the sensor distribution diagram and target trajectory distribution diagram using the method of the present invention;

[0084] Figure 3 is the comparison diagram of the single-sensor target distance and speed estimation accuracies when using the optimal state estimation, without parameter estimation, and using the method of the present invention, where the number of Monte Carlo runs is 200;

[0085] Figure 4 is the partial enlarged view of the comparison diagram of the single-sensor target distance and speed estimation accuracies when using the optimal state estimation, without parameter estimation, and using the method of the present invention, where the number of Monte Carlo runs is 200;

[0086] Figure 5 is the comparison diagram of the distributed target distance and speed estimation accuracies when using the optimal state estimation, without parameter estimation, and using the method of the present invention, where the number of Monte Carlo runs is 200;

[0087] Figure 6It is a comparison chart of the distance and speed estimation accuracies of a single sensor and a distributed target when using the optimal state estimation, without parameter estimation, and when using the method of the present invention. The number of Monte Carlo runs is 200 times;

[0088] Figure 7 It is the model probability estimation value in the distributed state when using the optimal state estimation, without parameter estimation, and when using the method of the present invention. The number of Monte Carlo runs is 200 times. Detailed implementation manners

[0089] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part rather than all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0090] The first aspect of the present invention discloses a robust distributed state estimation method for low, slow, and small targets.

[0091] Step 1: Initialize system parameters

[0092] 1.1 Initialize sensor network parameters: Define the sensor network N = S ∪ C, A, where the sensor node S represents the node that receives and processes data, the communication node C represents the node that completes data transmission, and the connection link represents the communication link between communicable nodes. Initialize the set of adjacent nodes of the s-th sensor as where p represents the adjacent node of sensor s, and initialize the sensor consistency weighting coefficient as w;

[0093] In this example, but not limited to, the sensors are a search radar, a tracking radar, and optoelectronic devices respectively. The specific sensor distribution and communication relationship are as Figure 2 shown.

[0094] 1.2 Initialize the discrete-time state space transition model: Define the set of target motion models at time k as where M represents the number of motion models included in the target motion process. Define the motion state of the s-th sensor at time k as Then there is:

[0095]

[0096] where represents that the model at the k-th moment is i, and f i (·) represents the state transition function of the i-th motion model; the process noise obeys a heavy-tailed distribution where \(p(\cdot)\) represents the probability density function, and \(St(x|\mu,\sum,v)\) represents the Student's - t distribution with mean \(\mu\), scale matrix \(\sum\), and degrees of freedom \(v\).

[0097] In this example, the number of target motion models \(M = 3\) is selected, but not limited to, the uniform motion model, and the left - and right - turning models with known turning rates of \(\pm0.1\ rad / s\). Among them, model 1 represents the target in uniform motion, and its state transition matrix is expressed as:

[0098]

[0099] \(T\) represents the sampling time interval. In this example, \(T = 1s\) is selected, but not limited to. Models 2 and 3 represent the turning models with known turning rates, and their state transition matrices are expressed as:

[0100]

[0101] In this example, \(F_2 = F(w_1)\) with \(w_1 = 0.1\ rad / s\) and \(F_3 = F(w_2)\) with \(w_2=-0.1\ rad / s\) are selected, but not limited to.

[0102] In this example, the motion state vectors corresponding to the three motion models are selected, but not limited to where \(x\) and \(y\) respectively represent the distances of the target on the \(x\) - axis and \(y\) - axis, and respectively represent the velocities of the target on the \(x\) - axis and \(y\) - axis. The process noise variances in the three motion states are all \(1\ m / s\) 2 ;

[0103] 1.3 Initialize the measurement space transfer model:

[0104]

[0105] where represents the measurement value, and \(h\) s,i (·) represents the measurement transfer function corresponding to the \(i\) - th motion model in the \(s\) - th sensor. The measurement noise obeys the heavy - tailed distribution

[0106] In this example, the measurement vectors under the three motion models are selected, but not limited to \([R,\theta]\) T , where \(R\) represents the target distance and \(\theta\) represents the target azimuth angle. And the measurement noise of each sensor under the three models is initialized as \(\sigma\) R = 10m, \(\sigma\) θ = 0.2°.

[0107] Step 2: Perform model interaction on the motion states of each target model

[0108] 2.1 Calculate the model prediction probability of the s-th sensor target model j in combination with the following formula Interaction probability with the model

[0109]

[0110]

[0111] where represents the probability update value of model i at time k - 1 (obtained from the previous time), represents the Markov transition probability matrix (TPM) at time k, where Pr(·) represents the probability value.

[0112] In this example, the model probability at the initial time is initialized to The Markov transition probability matrix (TPM) is initialized to the following value:

[0113]

[0114] 2.2 Calculate the motion state interaction result of the i-th model of the target in combination with the following formula Interaction result with the state covariance

[0115]

[0116]

[0117] where, and respectively represent the state estimation value and the state estimation covariance matrix of model j at time k - 1 (obtained from the previous time), and ∑· represents the summation operation. In this example, the following initialization methods are selected but not limited to, where the state value is initialized according to the true state, and the state covariance at the initial time is initialized in the following way:

[0118]

[0119] where T = 1s represents the sensor data rate, and r takes the following form:

[0120]

[0121] Step 3: Perform a one-step prediction calculation on the motion state value and the motion state covariance matrix of each model of the target:

[0122] Calculate the one-step prediction value of the motion state of the i-th model of the s-th sensor of the target in combination with the following formula and the one-step prediction covariance matrix

[0123]

[0124]

[0125] where F i represents the Jacobian matrix of the state transition function f i (·), represents the process noise covariance matrix of model i at time k, (·) T represents the transpose operation.

[0126] Step 4. Calculate the target measurement innovation and the information covariance by combining the following formula:

[0127]

[0128]

[0129] where represents the target measurement value obtained by the s-th sensor, H s,i represents the Jacobian matrix of the measurement transition function h s,i (·).

[0130] Step 5. Calculate the innovation gain

[0131]

[0132] Step 6. Calculate the state estimate value and the state estimate covariance by combining the following formula:

[0133]

[0134]

[0135] where represents the degrees of freedom of the trailing distribution at time k - 1, this example selects but is not limited to the degrees of freedom at the initial time

[0136] Step 7. Complete the degrees of freedom update at time k and calculate the model probability update values corresponding to each model by combining the following formula:

[0137] 1. Complete the degrees of freedom update at time k by combining the following formula:

[0138]

[0139] where represents the measurement dimension corresponding to sensor s, this example selects but is not limited to the measurement dimension

[0140] 2. Calculate the likelihood values of each model by combining the following formula:

[0141]

[0142] 3. Calculate the model probability update value by combining the following formula:

[0143]

[0144] Step 8: Perform multi-sensor consistency fusion processing on the state update value and state update covariance in Step 6 and the degrees of freedom and model probability update value in Step 7 by combining the following formula:

[0145] 1. Calculate the corresponding information vector by combining the state update value and state update covariance obtained in Step 6 with the following formula and the information matrix

[0146]

[0147]

[0148]

[0149] 2. Perform consistency fusion processing on the information vector and information matrix obtained in Step 1 by combining the following formula:

[0150]

[0151]

[0152] where w represents the fusion weight coefficient, and L represents the number of consistency fusion times. In this example, L = 5 is selected but not limited to this value;

[0153] 3. Perform consistency fusion processing on the degrees of freedom update value obtained in Step 7 by combining the following formula:

[0154]

[0155] 4. Perform consistency fusion processing on the model probability update value obtained in Step 7 by combining the following formula:

[0156]

[0157] Step 9: Based on the target motion model probability update value and the state estimation covariance matrix

[0158] 1. Calculate the state estimation value and state estimation covariance matrix according to the consistency processing result:

[0159]

[0160]

[0161] wherein represents the information matrix after the L-th fusion, represents the information vector after the L-th fusion;

[0162] 2. Calculate the multi-model interaction result of the state estimate and the multi-model interaction result of the state estimate covariance

[0163]

[0164]

[0165] wherein represents the updated value of the model probability after the L-th fusion.

[0166] In summary, the state estimates of each sensor and the state estimate covariance matrix of the target at the current moment are obtained, and the state update is completed.

[0167] The practicability of the present invention is demonstrated by the following simulation example:

[0168] 1. Simulation conditions and parameters

[0169] The simulation scenario is a single-target tracking scenario. The distribution map of sensor positions is as shown in Figure 2 . The model numbers are respectively labeled as 1, 2, 3. The model transition process is: {1, 2, 3, 2, 1, 3, 1}. The duration of each model is 1→30s, 2→40s, 3→40s. The process noise variance q = 1, and the measurement noise variance is [σ R , σ θ = [10m, 0.2°]. The total simulation time length is 250s. The proportion of process noise outliers is 10%, and the corresponding process noise variance is 100; the proportion of measurement noise outliers is 10%, and the corresponding measurement noise variance is 40×[σ R , σ θ . The number of fusion times L = 5.

[0170] 2. Simulation content and result analysis

[0171] Figure 1 is the overall flowchart of the present invention;

[0172] Figure 2 is the sensor distribution map and the target trajectory distribution map using the method of the present invention;

[0173] Figure 3 It is a comparison chart of the target distance and speed estimation accuracies of a single sensor when using the optimal state estimation, without parameter estimation, and when using the method of the present invention. The number of Monte Carlo runs is 200 times. From Figure 3 it can be seen that under the condition of a single sensor, the student's t estimator is prone to error divergence;

[0174] Figure 4 It is a partially enlarged comparison chart of the target distance and speed estimation accuracies of a single sensor when using the optimal state estimation, without parameter estimation, and when using the method of the present invention. The number of Monte Carlo runs is 200 times. From Figure 4 it can be seen that when there is no divergence phenomenon, the estimation accuracy of the student's t estimator is significantly improved compared with the classical Kalman filter (the method without parameter estimation);

[0175] Figure 5 It is a comparison chart of the distributed target distance and speed estimation accuracies when using the optimal state estimation, without parameter estimation, and when using the method of the present invention. The number of Monte Carlo runs is 200 times. From Figure 5 it can be seen that after performing distributed state estimation, the method of the present invention has significantly improved robustness compared with the single-sensor condition, without error divergence, and the estimation accuracy of the method of the present invention is significantly improved compared with the classical Kalman filter method;

[0176] Figure 6 It is a comparison chart of the target distance and speed estimation accuracies of a single sensor and distributed sensors when using the optimal state estimation, without parameter estimation, and when using the method of the present invention. The number of Monte Carlo runs is 200 times. From Figure 6 it can be seen that the target state estimation accuracy in the distributed state is significantly higher than that in the single-sensor condition;

[0177] Figure 7 It is the model probability estimation value in the distributed state when using the optimal state estimation, without parameter estimation, and when using the method of the present invention. The number of Monte Carlo runs is 200 times. From Figure 7 it can be seen that the method of the present invention has a higher model probability estimation accuracy, thereby improving the final state estimation accuracy.

[0178] In summary, for the technical solution proposed by the present invention, the present invention assumes that both the process noise and the measurement noise of the low, slow, and small target motion process are heavy-tailed noises. By modeling the heavy-tailed noise as a student's t-distribution estimation, the relevant distribution parameters of the process heavy-tailed noise and the measurement heavy-tailed noise are corrected, and the state estimation accuracy is improved by performing consistency fusion processing on the state estimation value, the estimation covariance, and the relevant parameters. Next, the probabilities of each maneuver model are solved, thus solving the multi-model state estimation problem of maneuvering targets under heavy-tailed noise background. The method of the present invention solves the problem of distributed state estimation of maneuvering small targets under the background that both the process noise and the measurement noise are heavy-tailed noises in practical engineering applications, and has the advantages of high parameter estimation accuracy, high state estimation accuracy, good adaptability and robustness to complex application backgrounds, high calculation efficiency, and tolerance to node failures, etc., and can meet the requirements of engineering applications. The present invention greatly improves the adaptability and robustness of the algorithm to complex scenarios and improves the estimation accuracy of the distributed state of maneuvering small targets under heavy-tailed noise background.

[0179] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification. The above embodiments only represent several implementation manners of the present application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be pointed out that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.

Claims

1. A robust distributed state estimation method for low, slow, and small targets, characterized in that, The method includes: Step S1, initialize system parameters, including: initialize sensor network parameters; initialize the discrete-time state space transition model; and initialize the measurement space transition model; Step S2, based on the initialized discrete-time state space transition model, perform model interaction on the motion states of each motion model included in the low, slow, and small target to obtain a motion state interaction result and a state covariance interaction result; Step S3, according to the motion state interaction result and the state covariance interaction result, perform prediction calculations on the motion state values and motion state covariance matrices of each motion model included in the low, slow, and small target; Step S4, use the initialized measurement space transition model, the motion state value, and the motion state covariance matrix to determine the target measurement innovation and information covariance; Step S5, based on the motion state covariance matrix and the information covariance, calculate the innovation gain; Step S6, solve the state estimate value according to the motion state value, the target measurement innovation, and the innovation gain, and solve the state estimate covariance according to the motion state covariance matrix and the innovation gain; Step S7, update the degrees of freedom, calculate the likelihood values of each motion model included in the low, slow, and small target, and calculate the model probability update value according to the likelihood values; Step S8, based on the sensor network, perform multi-sensor consistency fusion processing on the state estimate value, the state estimate covariance, the updated degrees of freedom, and the model probability update value to obtain the fused model probability update value; Step S9, use the fused model probability update value to calculate the multi-model interaction result of the state estimate value and the multi-model interaction result of the state estimate covariance, so as to obtain the state estimates of each sensor of the low, slow, and small target at the current moment.

2. The robust distributed state estimation method for low, slow, and small targets according to claim 1, wherein In the step S1: Initializing the sensor network parameters includes: defining the sensor network N = S ∪ C, A, where the sensor nodes S represent the nodes for receiving and processing data, the communication nodes C represent the nodes for completing data transmission, and the connection links represent the communication links between communicable nodes, and initializing the set of adjacent nodes of the s-th sensor as where p represents the adjacent node of sensor s, and initializing the sensor consistency weighting coefficient as w; Initializing the discrete-time state space transition model includes: defining the set of target motion models at time k as where M represents the number of motion models included in the target motion process, and defining the motion state of the s-th sensor at time k as Then there is: Among them It means that at the k-th moment, the model is i, and f i (·) represents the state transition function of the i-th motion model; the process noise obeys a heavy-tailed distribution where p(·) represents the probability density function, and St(x|μ,∑,v) represents the Student’s-t distribution with mean μ, scale matrix ∑, and degrees of freedom v; Initializing the measurement space transition model includes: Wherein represents the measured value, h s,i (·) represents the measurement transfer function corresponding to the i-th motion model in the s-th sensor, and the measurement noise obeys a heavy-tailed distribution represents the measurement noise scale matrix of model i at time k.

3. A robust distributed state estimation method for low, slow, and small targets according to claim 2, characterized in that In the step S2, Calculate the model prediction probability of the s-th sensor target model j Interaction probability with the model Among them represents the probability update value of model i at time k-1, which is obtained from the previous time represents the Markov transition probability matrix TPM at time k, where Pr(·) represents the probability value; Calculate the motion state interaction result of the target's i-th model With the state covariance interaction result Among them, and respectively represent the state estimation value and the state estimation covariance matrix of model j at time k-1, which are obtained from the previous moment, and ∑· represents the summation operation.

4. A robust distributed state estimation method for low, slow, and small targets according to claim 3, characterized in that, In the step S3: Calculate the one-step predicted value of the motion state of the i-th model of the s-th sensor of the target And the one-step prediction covariance matrix where F i (·) represents the state transition function f i the Jacobian matrix of (·), represents the process noise scale matrix of model i at time k, (·) T represents the transpose operation.

5. A robust distributed state estimation method for low, slow, and small targets according to claim 4, characterized in that In the step S4: For the target measurement innovation and the information covariance perform calculations where represents the target measurement value obtained by the sth sensor, and H s,i represents the Jacobian matrix of the measurement transfer function h s,i (·).

6. A robust distributed state estimation method for low, slow and small targets according to claim 5, characterized in that In the step S5: Calculate the innovation gain 7. A robust distributed state estimation method for low, slow, and small targets according to claim 6, characterized in that In the step S6: Calculate the state estimate value and the state estimate covariance: wherein represents the degrees of freedom of the trailing distribution at time k-1, 8. A robust distributed state estimation method for low, slow and small targets according to claim 7, characterized in that, In the step S7: Perform the degrees of freedom update at time k: Among them represents the measurement dimension corresponding to the sensor s; Calculate the likelihood values of each model Calculate the model probability update value:

9. A robust distributed state estimation method for low, slow, and small targets according to claim 8, characterized in that In the step S8: Calculate the information vector and the information matrix Perform the first step of consistency fusion processing: where w represents the fusion weight coefficient and L represents the number of consistency fusion times; Perform the second step of consistency fusion processing: Perform the third step of consistency fusion processing:

10. A robust distributed state estimation method for low, slow, and small targets according to claim 9, characterized in that In the step S9: Calculate the state estimate value and the state estimate covariance matrix according to the consistency processing result: Among them represents the information matrix after the L-th fusion, represents the information vector after the L-th fusion; Calculate the multi-model interaction result of the state estimation value And the multi-model interaction result of the state estimation covariance Among them represents the updated value of the model probability after the L-th fusion.

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