A multi-unmanned aerial vehicle cooperative sensing method of directional information loss compensation and event triggered echo fusion

Abstract

The application discloses a kind of directionality information lack compensation and event trigger echo fusion's multi-unmanned aerial vehicle cooperative sensing method, comprising: current target state prediction is carried out, and further constructs directionality information lack;Candidate anchor point generation and distribution are carried out;Unmanned aerial vehicle safety position is updated, and the distribution of communication power and sensing power is carried out;With noisy measurement and the result of current prediction state calculation innovation, local information contribution and correlation contribution;Get adjusted local information contribution matrix;Get the state posteriori of current time and final position covariance, as the input of next time state prediction.The application is weighted to candidate virtual anchor point by directionality information lack matrix, using double time scale safety control to realize executable spatial reconfiguration, and with relative to low code rate abstract conditional fusion information gain trigger original complex echo upload, so as to reduce invalid return under the premise of guaranteeing communication rate and flight safety.

Description

Technical Field

[0001] This invention belongs to the technical field of UAV cooperative control and multi-sensor information fusion, specifically involving a multi-UAV cooperative sensing method for directional information deficiency compensation and event-triggered echo fusion. Background Technology

[0002] Existing UAV integrated sensing solutions typically use trajectory, beam, power, or time slot as joint optimization variables to improve communication rate and sensing accuracy. However, fixed circling, distance-priority, or spatial configurations that only target total information volume can easily lead to multiple UAVs observing the target from similar perspectives, resulting in a long-term information deficit in a certain main direction. When the target turns rapidly, the error ellipse of the filter will lengthen rapidly along the weak direction.

[0003] On the other hand, uploading complete complex echoes frame by frame from multiple UAVs consumes a significant amount of uplink bandwidth. Furthermore, observations from different UAVs often share transmitted waveforms, prediction priors, and target trajectory history. Directly superimposing the local information matrix may underestimate relevant errors, resulting in an overconfident fusion covariance. Event triggering using only a single innovation threshold also fails to distinguish between echoes with "large innovation but no help in the weak direction" and echoes with "high information gain per bit."

[0004] Therefore, a technical solution is needed that can integrate the directionality of posterior uncertainty, the spatial configuration of UAVs, the communication sensing power budget of each UAV, the two-stage transmission of the summary and the original echo, and the bounded correlation into the same causal closed loop. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, the present invention aims to provide a multi-UAV cooperative sensing method that combines directional information deficiency compensation with event-triggered echo fusion. This method weights candidate virtual anchor points using a directional information deficiency matrix, implements executable spatial reconfiguration using dual-timescale security control, and triggers the uploading of the original complex echo with conditional fusion information gain relative to the low-bitrate digest, thereby reducing invalid backhauls while ensuring communication speed and flight safety.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] The present invention provides a multi-UAV cooperative sensing method for compensating for directional information deficiency and fusing event-triggered echoes, comprising the following steps:

[0008] 1) Predict the current target state and further construct directional information deficiencies;

[0009] 2) Generate and assign candidate anchor points;

[0010] 3) Perform safe location updates for the UAV and allocate communication and sensing power;

[0011] 4) Calculate the innovation, local information contribution, and correlation contribution by combining the noisy measurement and the current prediction state results;

[0012] 5) Based on the directional information deficit, local information contribution, and new information as the basis for the current event judgment, determine the form of information uploaded by each UAV, and update the threshold for the next moment and the current data efficiency in combination with the communication interruption status; thus obtaining the adjusted local information contribution matrix.

[0013] 6) Calculate the correlation fusion weight by combining the correlation contribution and the adjusted local information contribution matrix; use the correlation fusion weight and data efficiency to correct the effective perception quality, and sequentially complete the central extended Kalman filter update to obtain the state posterior and final position covariance at the current time, which are used as the input for the state prediction at the next time.

[0014] Further, step 1) specifically includes:

[0015] Current moment target state Defined as:

[0016] ;

[0017] In the formula, For the current moment The target planar position; For the current moment Target plane velocity; superscript Indicates transpose;

[0018] At the present moment The target state is predicted based on the posterior state estimate of the target at the previous time step, as follows:

[0019] ;

[0020] In the formula, Predict the state column vector for the current time step; The state transition matrix is ​​constructed from time intervals; This is the posterior column vector of the state at the previous time step;

[0021] Update the prediction covariance matrix corresponding to the target state at the current time step. as follows:

[0022] ;

[0023] In the formula, The posterior covariance matrix of the previous time step; The process noise covariance matrix;

[0024] Extract the prediction location covariance matrix from the prediction covariance matrix. And perform feature decomposition as follows:

[0025] ;

[0026] In the formula, For direction The variance of the predicted location; It is an orthogonal matrix formed by the corresponding unit eigenvectors; This indicates the construction of a diagonal matrix;

[0027] Based on the predicted location variance, the directional information deficiency is obtained as follows:

[0028] ;

[0029] In the formula, For direction The lack of non-negative information in the data; The threshold for loss of target information; Non-negative truncation;

[0030] Constructing a direction deficiency matrix based on direction information deficiency as follows:

[0031] ;

[0032] In the formula, This is the set of main directions of position.

[0033] Further, step 2) specifically includes:

[0034] Candidate anchor points are generated around the predicted target location. ,as follows:

[0035] ;

[0036] In the formula, Candidate anchor points; For the positional components of the predicted state; The radius of the anchor point ring; The anchor point height; The circumferential azimuth angles of the candidate anchor points are as follows:

[0037] ;

[0038] In the formula, This represents the total number of candidate anchor points. Pi; For the set of candidate anchor points;

[0039] Information matrix of corresponding candidate anchor points for:

[0040] ;

[0041] In the formula, To predict the target location and candidate anchor points, calculate and extract the Jacobian matrix obtained by the partial derivatives of distance and azimuth with respect to position; For the perceived signal-to-noise ratio parameter The obtained positive definite covariance matrices of the same order; superscript This indicates a generalized form of pseudo-rebellion;

[0042] Calculate candidate anchor point scores ,as follows:

[0043] ;

[0044] In the formula, Let be the identity matrix of the same order as the positional subspace; Directional Deficiency Matrix The positive semidefinite square root; Represents the natural logarithm of the determinant of a matrix; For the cost of flight; For the cost of communication; and These are the flight cost weight and the communication cost weight, respectively.

[0045] Flight Cost The formula for calculation is:

[0046] ;

[0047] In the formula, Number of drones; These are distance normalization parameters; and The drones at the previous moment The position and the position of the current candidate anchor point; For drones; Represents the Euclidean norm;

[0048] Communication cost The formula for calculation is:

[0049] ;

[0050] In the formula, To cooperate with drones The corresponding fixed communication user location;

[0051] From the candidate anchor set A greedy selection algorithm is performed to obtain the set of selected anchor points. ,as follows:

[0052] ;

[0053] In the formula, The minimum azimuth angle separation threshold; The selection operation involves selecting the candidate with the highest score from the current set of options in each round, and then deleting the candidate with an azimuth difference less than that of the selected option. The candidate options are selected until all are selected or the current selection set is empty; if the number is insufficient after angle separation filtering, the remaining unselected candidates are supplemented according to their scores from highest to lowest to obtain the final selection. Then, construct the allocation cost matrix from the UAV to the selected anchor point;

[0054] For any drone and any selected anchor point Calculate the cost of anchor point allocation ,as follows:

[0055] ;

[0056] An anchor point allocation cost matrix is ​​constructed based on the anchor point allocation costs between all drones and all selected anchor points. ,as follows:

[0057] ;

[0058] Using the anchor point allocation cost matrix as input to the Hungarian algorithm, a one-to-one matching process is performed with the objective of minimizing the sum of the anchor point allocation costs for all UAVs, resulting in a UAV set. To the selected anchor set Anchor point assignment mapping .

[0059] Furthermore, step 3) specifically includes:

[0060] Based on the anchor point allocation results, the current moving targets of each UAV are determined, and the UAV positions are updated under the constraints of flight distance, altitude range, and safe distance between UAVs. Then, communication power and sensing power are divided according to the communication link status, and the current communication rate and interruption status are calculated. Specifically:

[0061] Mapping based on anchor points To be allocated to drones Selected anchor points As a moving target, for drones Previous position Perform a safe position projection to obtain the current position. The safe position projection should simultaneously satisfy the maximum displacement constraint, height constraint, and inter-machine safe distance constraint; wherein, the maximum displacement constraint at adjacent moments is:

[0062] ;

[0063] In the formula, and The drones at the current moment and the previous moment are respectively. Location; and These represent the drone's maximum speed and time interval, respectively.

[0064] The distance between unmanned aerial vehicles (UAVs) should meet the following requirements:

[0065] ;

[0066] ;

[0067] In the formula, The altitude of the drone; Minimum drone altitude This represents the maximum altitude of the drone. Index for another drone; Minimum safe distance;

[0068] Communication distance between drones and communication users for:

[0069] ;

[0070] No communication channel gain for:

[0071] ;

[0072] In the formula, The spatial distance from the drone to the corresponding communication user; For reference communication gain; This is a measure of communication distance attenuation.

[0073] The drone transmit power required to meet the minimum communication rate of communication users for:

[0074] ;

[0075] In the formula, is the base of the logarithm of the rate function; Minimum communication rate; For communication bandwidth;

[0076] Actual communication power of communication users for:

[0077] ;

[0078] In the formula, and These are the lower bound of communication power and the upper bound of single-unit power, respectively. Perform interval truncation;

[0079] Sensing power of the target for:

[0080] ;

[0081] Communication rate of communication users for:

[0082] ;

[0083] The communication interruption flag for a communication user is obtained by comparing the current rate:

[0084] ;

[0085] In the formula, It is a Boolean variable; This is a conditional function. When the condition within the parentheses is true, its output is 1; otherwise, its output is 0.

[0086] Further, step 4) specifically includes:

[0087] Ideal measurement of the perceived target for:

[0088] ;

[0089] In the formula, It is a nonlinear measurement function; This is the target truth state column vector; Let m be the column vector of the current position of the drone.

[0090] Distance between drone and perceived target for:

[0091] ;

[0092] In the formula, This represents the distance from the drone to the target. The column vector of positions representing the target truth values; Let m be the position of the drone;

[0093] The sensing path gain and signal-to-noise ratio between the UAV and the target are:

[0094] ;

[0095] ;

[0096] In the formula, To sense path gain; For reference sensing gain; The attenuation scale for perceived distance; To perceive the signal-to-noise ratio; Based on the signal-to-noise ratio; For sensing power gain coefficient; To sense power;

[0097] The standard deviation of noise in the perceived target measurement is uniformly written as:

[0098] ;

[0099] In the formula, A set of labels for distance, azimuth, and radial velocity measurement components; For measuring component labels; For components The noise standard deviation; This is the lower limit of the noise level for the component. For noise scale parameters; The current perceived signal-to-noise ratio;

[0100] Perceived target measurement noise covariance:

[0101] ;

[0102] In the formula, The positive definite diagonal noise covariance matrix is ​​constructed according to the order of measurement components;

[0103] The calculated noisy measurement is as follows:

[0104] ;

[0105] In the formula, For noisy measurements; for The Kolesky factor satisfies ; Standard Gaussian noise;

[0106] New information on drone-based target measurement for:

[0107] ;

[0108] The covariance of the measurement information of the perceived target by the UAV is:

[0109] ;

[0110] In the formula, For the new information covariance; To measure the Jacobian matrix; To predict covariance;

[0111] A single UAV contributes a matrix of local information to the perceived user. for:

[0112] ;

[0113] In the formula, To fully measure the submatrix of distance and square in the Jacobian; This represents the second-order positive definite submatrices of range and azimuth, truncated from the measurement noise covariance; superscript This indicates a generalized form of pseudo-rebellion;

[0114] True line-of-sight azimuth of the UAV for the perceived target for:

[0115] ;

[0116] In the formula, To perceive the true location of the target; This indicates the current horizontal position of the drone. It is the arctangent function;

[0117] The correlation contribution of drones to the perceived target for:

[0118] ;

[0119] In the formula, Basic related items; The weights are related to location.

[0120] Furthermore, step 5) specifically includes:

[0121] The directional event gain for drone echo upload event determination is:

[0122] ;

[0123] In the formula, Contributes to information gain for non-negative events; It is the second-order identity matrix of the position subspace; The contribution matrix for second-order local information; The positive semidefinite square root is obtained by the code through eigenvalue decomposition; It is the natural logarithm of the determinant of a positive definite matrix;

[0124] The normalized information statistic of the perceived target is:

[0125] ;

[0126] In the formula, The square of the non-negative normalized new information; This is the current column vector for measuring new information from unmanned aerial vehicles (UAVs). The new information covariance matrix is ​​of the same positive definite order;

[0127] The trigger variable for drones to upload summary information is:

[0128] ;

[0129] In the formula, It is a boolean trigger variable; The total number of complete data bits; This is the information threshold scaling factor; For dynamic information thresholds; This is the scaling factor for the new information threshold; Basic information threshold; Indicates logical OR;

[0130] Update the dynamic information threshold for the next timeframe drone upload summary information as follows:

[0131] ;

[0132] In the formula, , These are the information thresholds for the next time step and the current time step, respectively. , These are the basic coefficient and the communication interruption correction coefficient in the threshold recursive formula, respectively. These are the lower threshold and the upper threshold, respectively; The average interruption rate at the current moment is expressed as follows:

[0133] ;

[0134] The data efficiency corresponding to the echo upload method used by the drone is:

[0135] ;

[0136] In the formula, For data efficiency; , The efficiencies are those of the complete echo and the summary echo, respectively. For event judgment Boolean;

[0137] Local information contribution matrix after data efficiency weighting adjustment corresponding to echo upload format as follows:

[0138] .

[0139] Furthermore, step 6) specifically includes:

[0140] The correlation fusion weight is calculated by combining the correlation contribution and the adjusted local information contribution matrix, as follows:

[0141] ;

[0142] In the formula, For drones Correlation fusion with log weights; For drones Relevance contribution; These are the lower and upper bounds of the correlation contribution, respectively; The trace of the matrix;

[0143] The normalized drone index correlation fusion weights are as follows:

[0144] ;

[0145] In the formula, The current drone index normalized fusion weights; It is a natural exponential function; The maximum weighted logarithm is expressed as follows:

[0146] ;

[0147] In the formula, This indicates another drone index, taken from... ;

[0148] The drone correlation fusion information matrix is ​​as follows:

[0149] ;

[0150] In the formula, Contribute an information matrix to the fused location; To predict location covariance;

[0151] The effective sensing signal-to-noise ratio of the central extended Kalman filter is calculated as follows:

[0152] ;

[0153] In the formula, The effective signal-to-noise ratio used for extended Kalman filtering; The original perceived signal-to-noise ratio; This is the lower limit of the fusion weight; For data efficiency;

[0154] Calculate the standard deviation of measurement noise for the central extended Kalman filter update. ,as follows:

[0155] ;

[0156] In the formula, , These are the measurement component labels and their sets; , The noise constant;

[0157] Calculate the effective measurement noise covariance matrix ,as follows:

[0158] ;

[0159] Perform a sequential extended Kalman filter update for each UAV, as follows:

[0160] ;

[0161] In the formula, It is a sequential information column vector; For current noisy measurements; The state before updating to the current order; Location of the drone; Derived from the measurement function;

[0162] ;

[0163] In the formula, The sequential information covariance matrix; Let be the Jacobian matrix of the current nonlinear measurement function with respect to the state of the sensed target; To update the covariance before; To effectively measure noise covariance; superscript Indicates transpose;

[0164] Perform sequential extended Kalman filtering on the gain matrix for each UAV. for:

[0165] ;

[0166] In the formula, To deal with the previous drones A symmetric positive semidefinite covariance matrix;

[0167] Update the state estimate of the perceived target as follows:

[0168] ;

[0169] In the formula, and These are the state column vectors after sequential update and before update, respectively;

[0170] The state covariance matrix of the perceived target before and after the update for:

[0171] ;

[0172] In the formula, It is the state-space identity matrix;

[0173] Calculate the position covariance matrix obtained from the fused information matrix. ,as follows:

[0174] ;

[0175] The position covariance matrix obtained by fusing the information matrix is ​​weighted and fused with the position covariance matrix output by the central extended Kalman filter, and then subjected to positive semi-definite projection to obtain the final target position covariance matrix. ,as follows:

[0176] ;

[0177] In the formula, The position covariance submatrix of the output of the central extended Kalman filter; and Both have fixed weights and their sum is a unit value; It represents symmetry and positive semi-definite projection; after obtaining the state estimate and final position covariance matrix of the perceived target at the current time, it is used as the input for the state prediction at the next time.

[0178] The beneficial effects of this invention are:

[0179] 1. This invention uses a directional information deficiency matrix to weight the information contribution of candidate anchor points and adopts a greedy selection with azimuth separation to prioritize compensation for the weak direction of the predicted position covariance, thereby reducing the risk of excessive concentration of observation directions by multiple UAVs.

[0180] 2. This invention separates anchor planning and position control by generating and allocating candidate anchor points at the anchor point update time and projecting the safe position of the UAV at each time step, and satisfies the constraints of maximum displacement, height boundary and minimum inter-UAV spacing, thereby reducing frequent anchor point replanning.

[0181] 3. Based on the communication link status of each UAV corresponding to the user, the present invention allocates actual communication power and sensing power within the power budget of a single UAV, prioritizes meeting the minimum communication rate requirement, and forms a communication interruption flag when the power budget is insufficient, thereby keeping the power constraints of each UAV independent.

[0182] 4. This invention makes event decisions based on the ratio of directional event information gain to the number of complete data bits and the normalized square of the innovation, selects the upload format between the complete echo and the digest echo, and uses the data efficiency coefficient to adjust the local information contribution, thereby reducing the transmission of low-value echoes.

[0183] 5. This invention constructs a line-of-sight azimuth weight based on the target line-of-sight azimuth angle, and calculates an exponentially normalized fusion weight by combining it with the adjusted local information contribution. When the line-of-sight azimuth weighting factor is large, the fusion weight of the corresponding local information contribution is reduced, thereby suppressing excessive contraction of the fusion position covariance. Attached Figure Description

[0184] Figure 1 This is a schematic diagram of the method of the present invention;

[0185] Figure 2 This is a schematic diagram of the multi-UAV collaborative sensing system architecture of the present invention;

[0186] Figure 3 The method of this invention includes the target's true trajectory, the fused estimated trajectory, the trajectories of each UAV, and the location map of ground users;

[0187] Figure 4 This is a graph showing the variation of the positional error between the method of the present invention and various comparative methods over frames;

[0188] Figure 5 for Figure 4 Enlarged view of the middle and last 30 frames;

[0189] Figure 6 This is a graph showing the variation of the posterior position covariance trace between frames for the method of this invention and various comparative methods. Detailed Implementation

[0190] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0191] Reference Figure 1 As shown, the multi-UAV cooperative sensing method of the present invention, which combines directional information deficiency compensation and event-triggered echo fusion, comprises the following steps:

[0192] 1) Predict the current target state based on the posterior target state and its covariance formed in the previous moment, and further construct directional information deficiency; specifically as follows:

[0193] Current moment target state Defined as:

[0194] ;

[0195] In the formula, For the current moment The target planar position; For the current moment Target plane velocity; superscript Indicates transpose;

[0196] At the present moment The target state is predicted based on the posterior state estimate of the target at the previous time step, as follows:

[0197] ;

[0198] In the formula, Predict the state column vector for the current time step; The state transition matrix is ​​constructed from time intervals; This is the posterior column vector of the state at the previous time step;

[0199] Update the prediction covariance matrix corresponding to the target state at the current time step. as follows:

[0200] ;

[0201] In the formula, The posterior covariance matrix of the previous time step; The process noise covariance matrix;

[0202] Extract the prediction location covariance matrix from the prediction covariance matrix. And perform feature decomposition as follows:

[0203] ;

[0204] In the formula, For direction The variance of the predicted location; It is an orthogonal matrix formed by the corresponding unit eigenvectors; This indicates the construction of a diagonal matrix;

[0205] Based on the predicted location variance, the directional information deficiency is obtained as follows:

[0206] ;

[0207] In the formula, For direction The lack of non-negative information in the data; The threshold for loss of target information; Non-negative truncation;

[0208] Constructing a direction deficiency matrix based on direction information deficiency as follows:

[0209] ;

[0210] In the formula, This is the set of main directions of position.

[0211] 2) Generate and assign candidate anchor points; details are as follows:

[0212] At any moment To guide the UAV to observe the target from different directions, compensate for directions with large positioning errors, and take into account communication and flight costs, candidate anchor points are generated around the predicted target location. ,as follows:

[0213] ;

[0214] In the formula, Candidate anchor points; For the positional components of the predicted state; The radius of the anchor point ring; Set the anchor point height to maintain the same target height. The circumferential azimuth angles of the candidate anchor points are as follows:

[0215] ;

[0216] In the formula, This represents the total number of candidate anchor points. Pi; For the set of candidate anchor points;

[0217] Information matrix of corresponding candidate anchor points for:

[0218] ;

[0219] In the formula, To predict the target location and candidate anchor points, calculate and extract the Jacobian matrix obtained by the partial derivatives of distance and azimuth with respect to position; For the perceived signal-to-noise ratio parameter The obtained positive definite covariance matrices of the same order; superscript This indicates a generalized form of pseudo-rebellion;

[0220] Calculate candidate anchor point scores ,as follows:

[0221] ;

[0222] In the formula, Let be the identity matrix of the same order as the positional subspace; Directional Deficiency Matrix The positive semidefinite square root; Represents the natural logarithm of the determinant of a matrix; For the cost of flight; For the cost of communication; and These are the flight cost weight and the communication cost weight, respectively.

[0223] Flight Cost The formula for calculation is:

[0224] ;

[0225] In the formula, Number of drones; These are distance normalization parameters; and The drones at the previous moment The position and the position of the current candidate anchor point; For drones; Represents the Euclidean norm;

[0226] Communication cost The formula for calculation is:

[0227] ;

[0228] In the formula, To cooperate with drones The corresponding fixed communication user location;

[0229] From the candidate anchor set A greedy selection algorithm is performed to obtain the set of selected anchor points. ,as follows:

[0230] ;

[0231] In the formula, The minimum azimuth angle separation threshold; The selection operation involves selecting the candidate with the highest score from the current set of options in each round, and then deleting the candidate with an azimuth difference less than that of the selected option. The candidate options are selected until all are selected or the current selection set is empty; if the number is insufficient after angle separation filtering, the remaining unselected candidates are supplemented according to their scores from highest to lowest to obtain the final selection. Then, construct the allocation cost matrix from the UAV to the selected anchor point;

[0232] For any drone and any selected anchor point Calculate the cost of anchor point allocation ,as follows:

[0233] ;

[0234] An anchor point allocation cost matrix is ​​constructed based on the anchor point allocation costs between all drones and all selected anchor points. ,as follows:

[0235] ;

[0236] Using the anchor point allocation cost matrix as input to the Hungarian algorithm, a one-to-one matching process is performed with the objective of minimizing the sum of the anchor point allocation costs for all UAVs, resulting in a UAV set. To the selected anchor set Anchor point assignment mapping .

[0237] 3) Perform safe location updates for the UAV and allocate communication and sensing power accordingly; details are as follows:

[0238] Based on the anchor point allocation results, the current moving targets of each UAV are determined, and the UAV positions are updated under the constraints of flight distance, altitude range, and safe distance between UAVs. Then, communication power and sensing power are divided according to the communication link status, and the current communication rate and interruption status are calculated. Specifically:

[0239] Mapping based on anchor points To be allocated to drones Selected anchor points As a moving target, for drones Previous position Perform a safe position projection to obtain the current position. The safe position projection should simultaneously satisfy the maximum displacement constraint, height constraint, and inter-machine safe distance constraint; wherein, the maximum displacement constraint at adjacent moments is:

[0240] ;

[0241] In the formula, and The drones at the current moment and the previous moment are respectively. Location; and These represent the drone's maximum speed and time interval, respectively.

[0242] To ensure the safe flight of drones, the distance between drones should meet the following requirements:

[0243] ;

[0244] ;

[0245] In the formula, The altitude of the drone; Minimum drone altitude This represents the maximum altitude of the drone. Index for another drone; Minimum safe distance;

[0246] Communication distance between drones and communication users for:

[0247] ;

[0248] No communication channel gain for:

[0249] ;

[0250] In the formula, The spatial distance from the drone to the corresponding communication user; For reference communication gain; This is a measure of communication distance attenuation.

[0251] The drone transmit power required to meet the minimum communication rate of communication users for:

[0252] ;

[0253] In the formula, is the base of the logarithm of the rate function; Minimum communication rate; For communication bandwidth;

[0254] Actual communication power of communication users for:

[0255] ;

[0256] In the formula, and These are the lower bound of communication power and the upper bound of single-unit power, respectively. Perform interval truncation;

[0257] Sensing power of the target for:

[0258] ;

[0259] Communication rate of communication users for:

[0260] ;

[0261] The communication interruption flag for a communication user is obtained by comparing the current rate:

[0262] ;

[0263] In the formula, It is a Boolean variable; This is a conditional function. When the condition within the parentheses is true, its output is 1; otherwise, its output is 0.

[0264] 4) Calculate the innovation, local information contribution, and correlation contribution by combining the noisy measurement and the predicted state column vector at the current time; the details are as follows:

[0265] Ideal measurement of the perceived target for:

[0266] ;

[0267] In the formula, It is a nonlinear measurement function; This is the target truth state column vector; Let m be the column vector of the current position of the drone.

[0268] Distance between drone and perceived target for:

[0269] ;

[0270] In the formula, This represents the distance from the drone to the target. The column vector of positions representing the target truth values; Let m be the position of the drone;

[0271] The sensing path gain and signal-to-noise ratio between the UAV and the target are:

[0272] ;

[0273] ;

[0274] In the formula, To sense path gain; For reference sensing gain; The attenuation scale for perceived distance; To perceive the signal-to-noise ratio; Based on the signal-to-noise ratio; For sensing power gain coefficient; To sense power;

[0275] The standard deviation of noise in the perceived target measurement is uniformly written as:

[0276] ;

[0277] In the formula, A set of labels for distance, azimuth, and radial velocity measurement components; For measuring component labels; For components The noise standard deviation; This is the lower limit of the noise level for the component. For noise scale parameters; The current perceived signal-to-noise ratio;

[0278] Perceived target measurement noise covariance:

[0279] ;

[0280] In the formula, The positive definite diagonal noise covariance matrix is ​​constructed according to the order of measurement components;

[0281] The calculated noisy measurement is as follows:

[0282] ;

[0283] In the formula, For noisy measurements; for The Kolesky factor satisfies ; Standard Gaussian noise;

[0284] New information on drone-based target measurement for:

[0285] ;

[0286] The covariance of the measurement information of the perceived target by the UAV is:

[0287] ;

[0288] In the formula, For the new information covariance; To measure the Jacobian matrix; To predict covariance;

[0289] A single UAV contributes a matrix of local information to the perceived user. for:

[0290] ;

[0291] In the formula, To fully measure the submatrix of distance and square in the Jacobian; This represents the second-order positive definite submatrices of range and azimuth, truncated from the measurement noise covariance; superscript This indicates a generalized form of pseudo-rebellion;

[0292] True line-of-sight azimuth of the UAV for the perceived target for:

[0293] ;

[0294] In the formula, To perceive the true location of the target; This indicates the current horizontal position of the drone. It is the arctangent function;

[0295] The correlation contribution of drones to the perceived target for:

[0296] ;

[0297] In the formula, Basic related items; The weights are related to location.

[0298] 5) Based on the directional information deficit, local information contribution, and new information constituting the basis for current event judgment, the form of information uploaded by each UAV is determined, and the threshold for the next time step is updated in conjunction with the communication interruption status and the current data efficiency; the adjusted local information contribution matrix is ​​obtained; as follows:

[0299] The directional event gain for drone echo upload event determination is:

[0300] ;

[0301] In the formula, Contributes to information gain for non-negative events; It is the second-order identity matrix of the position subspace; The contribution matrix for second-order local information; The positive semidefinite square root is obtained by the code through eigenvalue decomposition; It is the natural logarithm of the determinant of a positive definite matrix;

[0302] The normalized information statistic of the perceived target is:

[0303] ;

[0304] In the formula, The square of the non-negative normalized new information; This is the current column vector for measuring new information from unmanned aerial vehicles (UAVs). The new information covariance matrix is ​​of the same positive definite order;

[0305] The trigger variable for drones to upload summary information is:

[0306] ;

[0307] In the formula, It is a boolean trigger variable; The total number of complete data bits; This is the information threshold scaling factor; For dynamic information thresholds; This is the scaling factor for the new information threshold; Basic information threshold; Indicates logical OR;

[0308] Update the dynamic information threshold for the next timeframe drone upload summary information as follows:

[0309] ;

[0310] In the formula, , These are the information thresholds for the next time step and the current time step, respectively. , These are the basic coefficient and the communication interruption correction coefficient in the threshold recursive formula, respectively. These are the lower threshold and the upper threshold, respectively; The average interruption rate at the current moment is expressed as follows:

[0311] ;

[0312] The data efficiency corresponding to the echo upload method used by the drone is:

[0313] ;

[0314] In the formula, For data efficiency; , The efficiencies are those of the complete echo and the summary echo, respectively. For event judgment Boolean;

[0315] Local information contribution matrix after data efficiency weighting adjustment corresponding to echo upload format as follows:

[0316] .

[0317] 6) Calculate the correlation fusion weight by combining the correlation contribution and the adjusted local information contribution matrix; use the correlation fusion weight and data efficiency to correct the effective perception quality, and sequentially complete the central extended Kalman filter update to obtain the current state posterior and the final position covariance, which serve as the input for the state prediction at the next time step; specifically as follows:

[0318] The correlation fusion weight is calculated by combining the correlation contribution and the adjusted local information contribution matrix, as follows:

[0319] ;

[0320] In the formula, For drones Correlation fusion with log weights; For drones Relevance contribution; These are the lower and upper bounds of the correlation contribution, respectively; The trace of the matrix;

[0321] The normalized drone index correlation fusion weights are as follows:

[0322] ;

[0323] In the formula, The current drone index normalized fusion weights; It is a natural exponential function; The maximum weighted logarithm is expressed as follows:

[0324] ;

[0325] In the formula, This indicates another drone index, taken from... ;

[0326] The drone correlation fusion information matrix is ​​as follows:

[0327] ;

[0328] In the formula, Contribute an information matrix to the fused location; To predict location covariance;

[0329] The effective sensing signal-to-noise ratio of the central extended Kalman filter is calculated as follows:

[0330] ;

[0331] In the formula, The effective signal-to-noise ratio used for extended Kalman filtering; The original perceived signal-to-noise ratio; This is the lower limit of the fusion weight; For data efficiency;

[0332] Calculate the standard deviation of measurement noise for the central extended Kalman filter update. ,as follows:

[0333] ;

[0334] In the formula, , These are the measurement component labels and their sets; , The noise constant;

[0335] Calculate the effective measurement noise covariance matrix ,as follows:

[0336] ;

[0337] Perform a sequential extended Kalman filter update for each UAV, as follows:

[0338] ;

[0339] In the formula, It is a sequential information column vector; For current noisy measurements; The state before updating to the current order; Location of the drone; Derived from the measurement function;

[0340] ;

[0341] In the formula, The sequential information covariance matrix; Let be the Jacobian matrix of the current nonlinear measurement function with respect to the state of the sensed target; To update the covariance before; To effectively measure noise covariance; superscript Indicates transpose;

[0342] Perform sequential extended Kalman filtering on the gain matrix for each UAV. for:

[0343] ;

[0344] In the formula, To deal with the previous drones A symmetric positive semidefinite covariance matrix;

[0345] Update the state estimate of the perceived target as follows:

[0346] ;

[0347] In the formula, and These are the state column vectors after sequential update and before update, respectively;

[0348] The state covariance matrix of the perceived target before and after the update for:

[0349] ;

[0350] In the formula, It is the state-space identity matrix;

[0351] Calculate the position covariance matrix obtained from the fused information matrix. ,as follows:

[0352] ;

[0353] The position covariance matrix obtained by fusing the information matrix is ​​weighted and fused with the position covariance matrix output by the central extended Kalman filter, and then subjected to positive semi-definite projection to obtain the final target position covariance matrix. ,as follows:

[0354] ;

[0355] In the formula, The position covariance submatrix of the output of the central extended Kalman filter; and Both have fixed weights and their sum is a unit value; It represents symmetry and positive semi-definite projection; after obtaining the state estimate and final position covariance matrix of the perceived target at the current time, it is used as the input for the state prediction at the next time.

[0356] The method of the present invention was verified by simulation, as follows:

[0357] Three UAVs, three ground users, and one two-dimensional maneuvering target are set up in a 1000m×1000m low-altitude area; the initial altitude of the UAVs is 90m, the maximum speed is 12m / s, the altitude range is 60m to 120m, and the minimum distance between UAVs is 45m; the anchor point loop radius is 110m, updated every 10 frames, and the number of candidate points is 36.

[0358] The simulation time interval is 1 second, the target position process noise variance is 36 m², and the velocity process noise variance is 16 m / s². The minimum communication spectral efficiency is 1.0 bit / s / Hz, and the total power of a single UAV is normalized to 1. Each frame summary is 160 bits, the original complex echo adds 9600 bits of transmission, and the summary equivalent information efficiency is 0.58.

[0359] Using a fixed random seed and 30 Monte Carlo repeats, the communication-first, distance-first, and fixed loop methods were compared. All three methods uploaded complete echoes at each time step and used the same target motion, filtering model, and safety constraints to ensure that the comparison only reflected differences in anchor points, power, triggering, and fusion mechanisms.

[0360] The position RMSE is calculated as the square root of the mean of the squared position errors for all repeated trials and all time points; the normalized uplink load is calculated as the sum of the summary bits and the newly added bits of the trigger original echo relative to the frame-by-frame complete echo reference.

[0361] In example scenarios, such as Figure 2 As shown in the figure, the collaborative relationship between three sensing drones, three ground users, one mobile target, and one fusion node is illustrated. The blue bidirectional links carry local information summaries, on-demand raw echoes, fusion results, and control commands. The orange links represent the sensing illumination and echoes formed by each drone from different perspectives of the target. The green links represent communication services for ground users.

[0362] right Figure 3 Analysis shows that the representative experiment shown in the figure comprises 120 frames. The target's actual trajectory moved from approximately (450, 450) meters to (945, 781.10) meters, and the fused estimated trajectory closely approximates the actual trajectory. The RMSE of the position in this experiment is 14.08 meters, the mean absolute position error is 11.05 meters, and the minimum pairwise distance between the three representative UAV trajectories is 110 meters. The three UAV trajectories are distributed in different directions from the target and have not degenerated into following in the same direction.

[0363] right Figure 4 , Figure 5 Analysis shows that the figure indicates an increase in error for all methods after the target's motion state changes around frame 47. Based on the unsmoothed original error sequence, the peak error of the method in this invention is approximately 30.52 meters, lower than the 43.76 meters for communication-first, 33.52 meters for range-first, and 34.54 meters for fixed-circle navigation; the average errors for the last 30 frames are 17.01 meters, 30.92 meters, 23.97 meters, and 24.65 meters, respectively. The advantage of the algorithm in this invention lies in the fact that after the target maneuvers around frame 47, directional deficit compensation reconstructs the multi-aircraft observation geometry, and the aircraft-by-aircraft power allocation and event-triggered original echo concentrate resources on the high-information period, making the peak error of 30.52 meters and the average error of 17.01 meters for the last 30 frames both lower than the three baselines. Among them, the average error of the range-first method, which is the closest, decreases by approximately 29.0% in the final segment. The method of this invention recovers to a lower level after the error rises, which is consistent with the mechanism that the posterior covariance forms a directional deficiency and drives the UAV to adjust the observation geometry, sensing power and echo upload. It supports the technical effect of reducing the accumulation of errors during the maneuver phase from a temporal perspective.

[0364] right Figure 6 Analysis reveals that the posterior position covariance traces of all four methods rapidly decrease from an initial value of approximately 6.2 × 10³ square meters. However, the mean value for the last 30 frames of the method described in this invention is 4.15 square meters, with a final value of 4.31 square meters. The corresponding values ​​for communication priority are 21.94 square meters and 22.42 square meters, distance priority is 53.65 square meters and 60.47 square meters, and fixed loop is 26.89 square meters and 28.74 square meters. The advantage of this algorithm lies in using directional information deficiency to first reinforce the weak direction of the posterior covariance, and using correlation conservative fusion constraints to share priors and repeat counts of echoes from the same source. Therefore, the mean value of the covariance trace in the last 30 frames is only 4.15 square meters, a reduction of approximately 81.1% compared to the closest value of 21.94 square meters for the communication priority method, achieving lower steady-state uncertainty under correlation conservative fusion constraints. Furthermore, the covariance trace itself does not constitute a separate consistency statistical test.

[0365] The method of this invention can still reduce the posterior uncertainty to a low level after experiencing maneuvering disturbances, indicating that the directional information compensation increases the information that is effective for the current weak direction, while the correlation contribution suppresses the repeated inclusion of shared priors and echoes from the same source. From the perspective of covariance evolution, this supports the technical effect of improving estimation stability and avoiding overconfidence.

[0366] This invention uses the fused target posterior covariance as the closed-loop feedback quantity, which sequentially couples the directional information deficiency construction, virtual anchor point selection, per-machine perceptual power allocation, original complex echo triggering, and correlation conservative fusion. Each link corresponds to a measurable link state, flight state, or filtering state.

[0367] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A multi-UAV cooperative sensing method for directional information deficiency compensation and event-triggered echo fusion, characterized in that, The steps are as follows: 1) Predict the current target state and further construct directional information deficiencies; 2) Generate and assign candidate anchor points; 3) Perform safe location updates for the UAV and allocate communication and sensing power; 4) Calculate the contributions of new information, local information, and correlation; 5) The basis for the current event judgment is to determine the form of information uploaded by each UAV, and to obtain the adjusted local information contribution matrix by combining the communication interruption status to update the threshold for the next moment and the current data efficiency. 6) The effective perception quality is corrected by using correlation fusion weights and data efficiency, and the central extended Kalman filter is updated in sequence to obtain the state posterior and final position covariance at the current time, which are used as inputs for the state prediction at the next time.

2. The multi-UAV cooperative sensing method for directional information deficiency compensation and event-triggered echo fusion according to claim 1, characterized in that, Step 1) specifically includes: Current moment target state Defined as: ； In the formula, For the current moment The target planar position; For the current moment Target plane velocity; superscript Indicates transpose; At the present moment The target state is predicted based on the posterior state estimate of the target at the previous time step, as follows: ； In the formula, Predict the state column vector for the current time step; The state transition matrix is ​​constructed from time intervals; This is the posterior column vector of the state at the previous time step; Update the prediction covariance matrix corresponding to the target state at the current time step. as follows: ； In the formula, The posterior covariance matrix of the previous time step; The process noise covariance matrix; Extract the prediction location covariance matrix from the prediction covariance matrix. And perform feature decomposition as follows: ； In the formula, For direction The variance of the predicted location; It is an orthogonal matrix formed by the corresponding unit eigenvectors; This indicates the construction of a diagonal matrix; Based on the predicted location variance, the directional information deficiency is obtained as follows: ； In the formula, For direction The lack of non-negative information in the data; The threshold for loss of target information; Non-negative truncation; Constructing a direction deficiency matrix based on direction information deficiency as follows: ； In the formula, This is the set of main directions of position.

3. The multi-UAV cooperative sensing method for directional information deficiency compensation and event-triggered echo fusion according to claim 2, characterized in that, Step 2) specifically includes: Candidate anchor points are generated around the predicted target location. ,as follows: ； In the formula, Candidate anchor points; For the positional components of the predicted state; The radius of the anchor point ring; The anchor point height; The circumferential azimuth angles of the candidate anchor points are as follows: ； In the formula, This represents the total number of candidate anchor points. Pi; For the set of candidate anchor points; Information matrix of corresponding candidate anchor points for: ； In the formula, To predict the target location and candidate anchor points, calculate and extract the Jacobian matrix obtained by the partial derivatives of distance and azimuth with respect to position; For the perceived signal-to-noise ratio parameter The obtained positive definite covariance matrices of the same order; superscript This indicates a generalized form of pseudo-rebellion; Calculate candidate anchor point scores ,as follows: ； In the formula, Let be the identity matrix of the same order as the positional subspace; Directional Deficiency Matrix The positive semidefinite square root; Represents the natural logarithm of the determinant of a matrix; For the cost of flight; For the cost of communication; and These are the flight cost weight and the communication cost weight, respectively. Flight Cost The formula for calculation is: ； In the formula, Number of drones; These are distance normalization parameters; and The drones at the previous moment The position and the position of the current candidate anchor point; For drones; Represents the Euclidean norm; Communication cost The formula for calculation is: ； In the formula, To cooperate with drones The corresponding fixed communication user location; From the candidate anchor set A greedy selection algorithm is performed to obtain the set of selected anchor points. ,as follows: ； In the formula, The minimum azimuth angle separation threshold; The selection operation involves selecting the candidate with the highest score from the current set of options in each round, and then deleting the candidate with an azimuth difference less than that of the selected option. The candidate options are selected until all are selected or the current selection set is empty; if the number is insufficient after angle separation filtering, the remaining unselected candidates are supplemented according to their scores from highest to lowest to obtain the final selection. Then, construct the allocation cost matrix from the UAV to the selected anchor point; For any drone and any selected anchor point Calculate the cost of anchor point allocation ,as follows: ； An anchor point allocation cost matrix is ​​constructed based on the anchor point allocation costs between all drones and all selected anchor points. ,as follows: ； Using the anchor point allocation cost matrix as input to the Hungarian algorithm, a one-to-one matching process is performed with the objective of minimizing the sum of the anchor point allocation costs for all UAVs, resulting in a UAV set. To the selected anchor set Anchor point assignment mapping .

4. The multi-UAV cooperative sensing method for directional information deficiency compensation and event-triggered echo fusion according to claim 3, characterized in that, Step 3) specifically includes: Based on the anchor point allocation results, the current moving targets of each UAV are determined, and the UAV positions are updated under the constraints of flight distance, altitude range, and safe distance between UAVs. Then, communication power and sensing power are divided according to the communication link status, and the current communication rate and interruption status are calculated. Specifically: Mapping based on anchor points To be allocated to drones Selected anchor points As a moving target, for drones Previous position Perform a safe position projection to obtain the current position. The safe position projection should simultaneously satisfy the maximum displacement constraint, height constraint, and inter-machine safe distance constraint; wherein, the maximum displacement constraint at adjacent moments is: ； In the formula, and The drones at the current moment and the previous moment are respectively. Location; and These represent the drone's maximum speed and time interval, respectively. The distance between unmanned aerial vehicles (UAVs) should meet the following requirements: ； ； In the formula, The altitude of the drone; Minimum drone altitude This represents the maximum altitude of the drone. Index for another drone; Minimum safe distance; Communication distance between drones and communication users for: ； No communication channel gain for: ； In the formula, The spatial distance from the drone to the corresponding communication user; For reference communication gain; This is a measure of communication distance attenuation. The drone transmit power required to meet the minimum communication rate of communication users for: ； In the formula, is the base of the logarithm of the rate function; Minimum communication rate; For communication bandwidth; Actual communication power of communication users for: ； In the formula, and These are the lower bound of communication power and the upper bound of single-unit power, respectively. Perform interval truncation; Sensing power of the target for: ； Communication rate of communication users for: ； The communication interruption flag for a communication user is obtained by comparing the current rate: ； In the formula, It is a Boolean variable; This is a conditional function. When the condition within the parentheses is true, its output is 1; otherwise, its output is 0.

5. The multi-UAV cooperative sensing method for directional information deficiency compensation and event-triggered echo fusion according to claim 4, characterized in that, Step 4) specifically includes: Ideal measurement of the perceived target for: ； In the formula, It is a nonlinear measurement function; This is the target truth state column vector; Let m be the column vector of the current position of the drone. Distance between drone and perceived target for: ； In the formula, This represents the distance from the drone to the target. The column vector of positions representing the target truth values; Let m be the position of the drone; The sensing path gain and signal-to-noise ratio between the UAV and the target are: ； ； In the formula, To sense path gain; For reference sensing gain; The attenuation scale for perceived distance; To perceive the signal-to-noise ratio; Based on the signal-to-noise ratio; For sensing power gain coefficient; To sense power; The standard deviation of noise in the perceived target measurement is uniformly written as: ； In the formula, A set of labels for distance, azimuth, and radial velocity measurement components; For measuring component labels; For components The noise standard deviation; This is the lower limit of the noise level for the component. For noise scale parameters; The current perceived signal-to-noise ratio; Perceived target measurement noise covariance: ； In the formula, The positive definite diagonal noise covariance matrix is ​​constructed according to the order of measurement components; The calculated noisy measurement is as follows: ； In the formula, For noisy measurements; for The Kolesky factor satisfies ; Standard Gaussian noise; New information on drone-based target measurement for: ； The covariance of the measurement information of the perceived target by the UAV is: ； In the formula, For the new information covariance; To measure the Jacobian matrix; To predict covariance; A single UAV contributes a matrix of local information to the perceived user. for: ； In the formula, To fully measure the submatrix of distance and square in the Jacobian; This represents the second-order positive definite submatrices of range and azimuth, truncated from the measurement noise covariance; superscript This indicates a generalized form of pseudo-rebellion; True line-of-sight azimuth of the UAV for the perceived target for: ； In the formula, To perceive the true location of the target; This indicates the current horizontal position of the drone; It is the arctangent function; The correlation contribution of drones to the perceived target for: ； In the formula, Basic related items; The weights are related to location.

6. The multi-UAV cooperative sensing method for directional information deficiency compensation and event-triggered echo fusion according to claim 5, characterized in that, Step 5) specifically includes: The directional event gain for drone echo upload event determination is: ； In the formula, Contributes to information gain for non-negative events; It is the second-order identity matrix of the position subspace; The contribution matrix for second-order local information; The positive semidefinite square root is obtained by the code through eigenvalue decomposition; It is the natural logarithm of the determinant of a positive definite matrix; The normalized information statistic of the perceived target is: ； In the formula, The square of the non-negative normalized new information; This is the current column vector for measuring new information from unmanned aerial vehicles (UAVs). The new information covariance matrix is ​​of the same positive definite order; The trigger variable for drones to upload summary information is: ； In the formula, It is a boolean trigger variable; The total number of complete data bits; This is the information threshold scaling factor; For dynamic information thresholds; This is the scaling factor for the new information threshold; Basic information threshold; Indicates logical OR; Update the dynamic information threshold for the next timeframe drone upload summary information as follows: ； In the formula, , These are the information thresholds for the next time step and the current time step, respectively. , These are the basic coefficient and the communication interruption correction coefficient in the threshold recursive formula, respectively. These are the lower threshold and the upper threshold, respectively; The average interruption rate at the current moment is expressed as follows: ； The data efficiency corresponding to the echo upload method used by the drone is: ； In the formula, For data efficiency; , The efficiencies are those of the complete echo and the summary echo, respectively. For event judgment Boolean; Local information contribution matrix after data efficiency weighting adjustment corresponding to echo upload format as follows: 。 7. The multi-UAV cooperative sensing method for directional information deficiency compensation and event-triggered echo fusion according to claim 6, characterized in that, Step 6) specifically includes: The correlation fusion weight is calculated by combining the correlation contribution and the adjusted local information contribution matrix, as follows: ； In the formula, For drones Correlation fusion with log weights; For drones Relevance contribution; These are the lower and upper bounds of the correlation contribution, respectively; The trace of the matrix; The normalized drone index correlation fusion weights are as follows: ； In the formula, The current drone index normalized fusion weights; It is a natural exponential function; The maximum weighted logarithm is expressed as follows: ； In the formula, This indicates another drone index, taken from... ; The drone correlation fusion information matrix is ​​as follows: ； In the formula, Contribute an information matrix to the fused location; To predict location covariance; The effective sensing signal-to-noise ratio of the central extended Kalman filter is calculated as follows: ； In the formula, The effective signal-to-noise ratio used for extended Kalman filtering; The original perceived signal-to-noise ratio; This is the lower limit of the fusion weight; For data efficiency; Calculate the standard deviation of measurement noise for the central extended Kalman filter update. ,as follows: ； In the formula, , These are the measurement component labels and their sets; , The noise constant; Calculate the effective measurement noise covariance matrix ,as follows: ； Perform a sequential extended Kalman filter update for each UAV, as follows: ； In the formula, It is a sequential information column vector; For current noisy measurements; The state before updating to the current order; Location of the drone; Derived from the measurement function; ； In the formula, The sequential information covariance matrix; Let be the Jacobian matrix of the current nonlinear measurement function with respect to the state of the sensed target; To update the covariance before; To effectively measure noise covariance; superscript Indicates transpose; Perform sequential extended Kalman filtering on the gain matrix for each UAV. for: ； In the formula, To deal with the previous drones A symmetric positive semidefinite covariance matrix; Update the state estimate of the perceived target as follows: ； In the formula, and These are the state column vectors after sequential update and before update, respectively; The state covariance matrix of the perceived target before and after the update for: ； In the formula, It is the state-space identity matrix; Calculate the position covariance matrix obtained from the fused information matrix. ,as follows: ； The position covariance matrix obtained by fusing the information matrix is ​​weighted and fused with the position covariance matrix output by the central extended Kalman filter, and then subjected to positive semi-definite projection to obtain the final target position covariance matrix. ,as follows: ； In the formula, The position covariance submatrix of the output of the central extended Kalman filter; and Both have fixed weights and their sum is a unit value; It represents symmetry and positive semi-definite projection; after obtaining the state estimate and final position covariance matrix of the perceived target at the current time, it is used as the input for the state prediction at the next time.

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