A Multi-Source Out-of-Order Track Fusion Method Based on Equivalent Augmented Measurement One-Step Update

Abstract

The present invention discloses a multi-source out-of-order track fusion method based on equivalent augmented measurement one-step update. Based on the idea of equivalent measurement and state augmentation, the method obtains equivalent augmented measurements by performing decorrelation operations on local track predictions and local track estimations, extracts the position information in the equivalent augmented measurements, and efficiently fuses the equivalent augmented measurements containing only position information with the central track updated at the current moment in the augmented space, solving the problem of efficient fusion of multi-source out-of-order tracks at any transmission rate. This method can not only obtain the posterior estimation of the target at the current moment, but also obtain the smoothed estimation of the target at past moments. Compared with the discard method, the time-averaged position root mean square error of the posterior estimation of this method is reduced by 24.39%, and the time-averaged position root mean square error of the smoothed estimation of this method is reduced by 57.75%, effectively improving the tracking accuracy of the central track.

Description

Technical Field

[0001] The present invention belongs to the field of multi-sensor information fusion, and relates to a one-step update fusion method for multi-source disordered tracks at any transmission rate. Specifically, it relates to a multi-source disordered track fusion method based on one-step update of equivalent augmented measurement (OU-EAM: One-step Updating based on Equivalent Augmented Measurement). Background Art

[0002] In a distributed multi-sensor information fusion system, each sensor performs local tracking and transmits the obtained local estimates to the fusion center for subsequent fusion. However, in practical applications, each sensor may not be able to maintain the same transmission rate to send information to the fusion center. When communication resources are sufficient, the sensor transmits at full rate, and its communication cycle is equal to the scanning cycle of the sensor; when communication resources are limited, the sensor transmits at a reduced rate, and information at multiple moments is packed and then transmitted to the fusion center at one time. How to efficiently fuse information at multiple moments at one time becomes extremely challenging. At the same time, due to the different communication distances from each sensor to the fusion center, different degrees of communication delays will occur, and the delay time will increase with the increase of the transmission distance. The communication delay causes the data arriving at the fusion center to be out of order, and since the fusion center processes data in real time, it cannot directly fuse the disordered information.

[0003] Regarding the problem of the fusion center receiving disordered tracks, the commonly used processing method is the discard method, that is, after the fusion center receives a disordered track, it directly discards it. Its main idea is: in the current fusion cycle, compare the timestamp of the local track with the timestamp of the central track to determine whether the local track is a disordered track. If it is a disordered track, it is directly discarded and not used; if it is not a disordered track, the sequential track fusion method is used for sequential update. In summary, it is very urgent and necessary to efficiently fuse multi-source disordered tracks at any transmission rate to improve target tracking performance. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention proposes a multi-source disordered track fusion method based on one-step update of equivalent augmented measurement. This method is based on the idea of equivalent measurement and state dimension expansion. By performing decorrelation operations on the local track prediction and local track estimation, equivalent augmented measurement is obtained, and the position information in the equivalent augmented measurement is extracted. The equivalent augmented measurement containing only position information is efficiently fused with the central track updated at the current moment in the augmented space, solving the problem of efficient fusion of multi-source disordered tracks at any transmission rate, while reducing the computational complexity and improving the track tracking accuracy.

[0005] For two sensors in a distributed multi-sensor system, assume that there is no time delay in the communication between sensor 2 and the fusion center. At the current time k+1, the fusion center receives the posterior probability density function of the local augmented track updated by sensor 1 at time h and the prior probability density function of the local augmented track The latest update time node of the central track is time k. Among them, h < k, so the local augmented track estimate received by the fusion center is an out-of-order augmented track.

[0006] The local augmented track estimate is where the mean of the augmented track estimate p(·) represents the probability density function; indicates that the target augmented state contains the standard state of d 1 time instants, and its value is determined by the transmission rate of the sensor; the start and end times of this augmented state are and h respectively; Z h (1) represents all the measurements of sensor 1 up to time h; N(·) represents the Gaussian function; represents the posterior augmented estimate mean of sensor 1 at time h; represents the posterior augmented estimate covariance of sensor 1 at time h; represents the state estimate mean of the target at time h in the standard space.

[0007] A multi-source out-of-order track fusion method based on one-step update of equivalent augmented measurements uses the local augmented track estimate and the local augmented track prediction to update the central track from the current target dynamics state to the fused E k (2) represents all the equivalent augmented measurements of sensor 2 up to time k. d f represents the augmented dimension of the central track, and its size is determined by the transmission rates and delay durations of all sensors. d f = n×d 1 , where n is a positive integer and satisfies the inequality:

[0008] (n - 1)d 1 < d 2 + T 2 ≤ nd 1 + 1

[0009] Among them, d 1 represents the dimension of the local equivalent augmented measurement of sensor 1, and d 2 represents the dimension of the local equivalent augmented measurement of sensor 1, and T 2 represents the number of steps of the communication delay of the sensor.

[0010] A multi-source out-of-order track fusion method based on equivalent augmented measurement one-step update is solved through the following steps Complete out-of-order augmented track fusion.

[0011] Step 1: Calculate the equivalent augmented measurement using the local augmented track estimate and the local augmented track prediction

[0012] Given the probability density function of the local augmented track estimate of sensor 1 received by the fusion center at the current moment and the probability density function of the local augmented track prediction Then the covariance and mean of the equivalent augmented measurement of sensor 1 at time h are:[[]]

[0013]

[0014]

[0015] Step 2: Extract the position information from the equivalent augmented measurement

[0016] Eliminate the velocity information in the mean of the equivalent augmented measurement obtained in Step 1 as well as the velocity information and position cross-covariance in the equivalent augmented measurement error covariance to obtain the position information at time h in the out-of-order equivalent augmented measurement:[[]]

[0017]

[0018]

[0019] Among them, That is, the submatrix of the i-th row and i-th column in M i is not a zero matrix.

[0020] Step 3: Out-of-order track fusion

[0021] Use the mean of the equivalent augmented measurement containing only position information obtained in Step 2 Covariance and the posterior estimate probability density function of the central track to perform out-of-order track fusion.

[0022] s3.1. Augmented state prediction

[0023] At the current time k + 1, the posterior estimate probability density function of the central track follows a Gaussian distribution, and its mean and covariance are respectively and Then the mean and covariance of the augmented state prediction are respectively:[[]]

[0024]

[0025]

[0026] s3.2, Augmented Measurement Prediction

[0027] Convert the augmented state prediction from the augmented state domain to the augmented measurement domain, and the obtained augmented measurement prediction mean and covariance are respectively:

[0028]

[0029]

[0030] s3.3, Augmented State Update

[0031] Utilize the shuffled equivalent augmented measurement mean and covariance to update the central track. After obtaining the fused shuffled track, the posterior estimation probability density function of the central track at time k whose mean and error covariance are respectively:

[0032]

[0033]

[0034] where the augmented Kalman gain

[0035] The present invention has the following beneficial effects:

[0036] Fully utilize the target information implicit in the shuffled tracks. Based on the ideas of dimension expansion and equivalent measurement, solve the problem of efficient fusion of multi-source shuffled tracks at any transmission rate, while reducing the computational amount and significantly improving the target tracking accuracy. Description of the Drawings

[0037] Figure 1 Schematic diagram of multi-source shuffled tracks reaching the fusion center at any transmission rate;

[0038] Figure 2 Simulation scenario diagram in the embodiment;

[0039] Figure 3 Comparison diagram of position RMSE between the discard method and the embodiment. Detailed Embodiment

[0040] The following further explains the present invention in conjunction with the drawings:

[0041] As Figure 1 shown, Sensor 1 transmits data every three frames, and transmits the local track estimation at time h and local track prediction to the fusion center. Sensor 2 transmits data every two frames and transmits the local track estimate and local track prediction to the fusion center. Since there is no communication delay in Sensor 2 while there is communication delay in Sensor 1, the fusion center first receives the data of Sensor 2, updates the central track to the k-th moment, and obtains the posterior state estimate at the k-th moment At the (k + 1)-th moment, the fusion center receives the data of Sensor 1. This method uses out-of-order track estimation and out-of-order track prediction to update the central track at the k-th moment from the current target dynamic state estimate to the fused

[0042] Set up the simulation scenario as Figure 2 shown, where the monitoring ranges of the two sensors are the same, the target moves in a straight line at a constant speed within the monitoring area, and this method and the discard method are used for simulation, and the results of 100 Monte Carlo experiments are statistically analyzed. The RMSE calculated using the non-smoothed data of the posterior estimate mean of this method is denoted as OU-EAM; the RMSE calculated using the smoothed data of the posterior estimate mean of this method is denoted as SOU-EAM;

[0043] The root mean square error of the position of the discard method and this method is as Figure 3 shown. This method can effectively improve the tracking accuracy of the target compared with the discard method. As shown in Table 1, the time-averaged position RMSE of OU-EAM is reduced by 24.39% compared with the discard method, and the time-averaged position RMSE of SOU-EAM is reduced by 57.75% compared with the discard method.

[0044]

[0045] Table 1.

Claims

1. A multi-source out-of-order track fusion method based on equivalent augmented measurement one-step update, Characterized in that: For two sensors with different transmission rates in a distributed multi-sensor system, the fusion center solves the posterior probability density function of the central track at time k through the following steps Complete out-of-order augmented track fusion, where d f represents the augmented dimension of the central track; E k (2) represents all the equivalent augmented measurements of sensor 2 up to time k; Step 1, obtain equivalent augmented measurement by using local augmented track estimation and local augmented track prediction The local augmented track estimation probability density function of sensor 1 received by the known fusion center at the current moment and the local augmented track prediction probability density function Then the equivalent augmented measurement covariance and mean of sensor 1 at time h are as follows: Among them, indicates that the target augmented state includes the standard states at d 1 moments; the start and end times of this augmented state are and h respectively; Z h (1) represents all the measurements of sensor 1 up to time h; N(·) represents the Gaussian function; represents the posterior augmented estimation mean of sensor 1 at time h, represents the posterior augmented estimation covariance of sensor 1 at time h; Step 2, extract position information in the equivalent augmented measurement Eliminate the equivalent augmented measurement mean obtained in step 1 The velocity information in , and the equivalent augmented measurement error covariance The velocity information and position covariance in the random equivalent augmented measurement are obtained as follows: Among them, that is, M i the sub-matrix of the i-th row and i-th column in i = 1, 2,..., d 1 ; Step 3, out-of-order track fusion Using the equivalent augmented measurement mean containing only position information obtained in Step 2 Covariance and the posterior estimation probability density function of the central track perform scrambled track fusion; s3.1, augmented state prediction At time k+1, the posterior estimated probability density function of the central track obeys a Gaussian distribution, and its mean and covariance are respectively and Then the mean and covariance of the augmented state prediction are respectively: s3.2, augmented measurement prediction Convert the augmented state prediction from the augmented state domain to the augmented measurement domain to obtain the augmented measurement prediction mean and covariance: s3.3, augmented state update Using the shuffled equivalent augmented measurement mean and covariance to update the central track, after obtaining the fused shuffled track, the posterior estimated probability density function of the central track at time k whose mean and error covariance are respectively:[[]] Among them, the augmented Kalman gain

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