CN110031797B - Detection and tracking method for passive sensing system on target with discontinuous characteristic - Google Patents

Detection and tracking method for passive sensing system on target with discontinuous characteristic Download PDF

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CN110031797B
CN110031797B CN201910313100.2A CN201910313100A CN110031797B CN 110031797 B CN110031797 B CN 110031797B CN 201910313100 A CN201910313100 A CN 201910313100A CN 110031797 B CN110031797 B CN 110031797B
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CN110031797A (en
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杨晓波
付玲枝
库飞龙
蒋歆玥
易伟
李溯琪
孔令讲
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S11/00—Systems for determining distance or velocity not using reflection or reradiation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations

Abstract

The invention discloses a method for detecting and tracking a target with discontinuous characteristics by a passive sensing system, which is applied to the technical field of target detection and tracking of the passive sensing system and aims at solving the problems that the prior art is not suitable for tracking the discontinuous target and estimation of the discontinuous characteristics of signals is not considered; firstly, according to the latest discontinuous measurement received by a sensor, performing discontinuous cycle division on the sensor and adaptively estimating the discontinuous characteristic of a target by combining a signal cycle sliding window; then synchronously determining the updating time of the target state, and deducing a variable period filtering formula under a Bayes framework to obtain a posterior probability density function about the target state; and finally, estimating the target state by using the minimum mean square error criterion, wherein the method can realize the joint estimation of the discontinuous target state and the discontinuous characteristic thereof.

Description

Detection and tracking method for passive sensing system on target with discontinuous characteristic
Technical Field
The invention belongs to the field of target detection and tracking of a passive sensing system, and particularly relates to a detection and tracking technology for a target with a discontinuous characteristic.
Background
The passive sensing system does not emit signals outwards, only passively receives information carried by radiation, emission or refraction signals from a target, and then detects and tracks the target through signal processing and extraction. In future electronic countermeasure and modern intelligence systems, passive sensing mechanisms will play an increasingly important role.
In the application of an actual passive detection system, due to the blockage of a signal transmission channel, random missing detection of the system, the influence of uncertain factors such as an actual complex environment and the like, a system sensor can only obtain measurement related to noise clutter within certain random observation time, and measurement information of a target is lost. In this case, the sequence of measurements taken by the sensor with respect to the target is called intermittent measurements. For the traditional tracking algorithm, a series of serious problems of tracking precision attenuation, repeated starting, track segmentation, calculated amount burden and the like are caused by directly utilizing intermittent measurement to carry out filtering tracking. At present, scholars at home and abroad make a great deal of research on discontinuous measurement, and in a document of 'Kalman filtering with discontinuous measurement, IEEE Transactions on Automatic Control, vol.1, No.9, pp.1453-1464,2004', an author models discontinuous measurement caused by network transmission instability into a binary Bernoulli random process, proposes an IKF algorithm and deduces a boundary value of discontinuous measurement probability influencing system stability. Similarly, the document "Mean square stability for Kalman filtering with Markovian packet loss, automotive, vol.47, No.12, pp.2647-2657,2011" models the data packet loss rate of the sensor network by using the traversal markov process, and further analyzes the packet loss rate of the system. Currently, most of these research works are based on the assumption that the discontinuity of target measurement is modeled as a known stochastic process, so as to evaluate the stability of system operation.
In practical application, the passive detection system usually needs to detect and identify the target itself by using radiation such as radar of a stealth target, sonar, communication, electronic interference and the like or signals emitted by a specific target, analyze the motion property of the target, and provide a reliable decision instruction for the operation of a system in the next step. When these radiated or emitted signals are discontinuous and unknown, referred to as discontinuous characteristics of the target, the passive sensor will receive intermittent target measurements. Meanwhile, in actual detection systems such as passive radars and passive sonars, the analysis of the discontinuous characteristics of the signals is crucial to the identification of the behavior characteristics of the target. For the typical discontinuous target measurement, the discontinuous characteristic is often unknown and cannot be modeled by a known random process, so the discontinuous measurement model in the currently proposed algorithm cannot be directly applied to the tracking of the discontinuous target, and the estimation of the discontinuous characteristic of the signal is not considered.
Disclosure of Invention
In order to solve the above technical problem, the present invention provides a method for detecting and tracking a target with discontinuous characteristics by a passive sensing system, which performs discontinuous cycle division on received discontinuous measurements and adaptively estimates the discontinuous characteristics of the target in combination with a signal cycle sliding window.
The technical scheme adopted by the invention is as follows: a method for detecting and tracking a target with discontinuous characteristics by a passive sensing system comprises the following steps:
s1, the division of the discontinuous signal period is defined as: the target actively transmits signals, the duration of continuous transmission signals of the target actively transmits signals is called as signal pulse width, and the time interval between two adjacent continuous signals is called as a signal period; the pulse width is greater than or equal to one-time system sampling time;
s2, dividing the read measurement data into periods according to the definition of the step S1;
s3, updating the target state updating time interval sequence;
and S4, updating the time interval sequence according to the target state obtained in the step S3, and carrying out variable-period Bayesian filtering estimation.
Further, step S2 is preceded by: and step S20, initializing the period parameter and the pulse width parameter of the discontinuous signal.
Further, step S2 specifically includes the following sub-steps:
s21, reading the current moment measurement data from the passive sensor according to the system sampling interval;
s22, performing threshold detection on the measurement data read in the step S21;
s23, obtaining a measurement time sequence according to the recorded point measurement of the threshold crossing and the corresponding arrival time;
s24, dividing the measurement time sequence into periods according to the definition of step S1 to obtain the period parameter and pulse width parameter of the measurement.
Further, step S3 is specifically:
s31, estimating discontinuous characteristic parameters; if the data in the sliding window is not full at the moment, adopting the signal period and the pulse width of the previous signal period as the discontinuous characteristic parameters of the current signal period; otherwise, updating the discontinuous characteristic parameter of the current signal period by using the latest measured period parameter and pulse width parameter obtained in the step S24;
and S32, estimating discontinuous characteristic parameters according to the step S31, and calculating a target state updating time interval sequence.
Further, in step S31, the discontinuous characteristic parameter of the current signal period is updated by the latest measured period parameter and pulse width parameter obtained in step S24, and the calculation formula is as follows:
Figure BDA0002032170730000021
Figure BDA0002032170730000031
wherein the content of the first and second substances,
Figure BDA0002032170730000032
an estimated period parameter representing the current signal period, K representing the length of the sliding window, ps(m) represents the latest measured period parameter obtained in step S24, m represents the current signal period number,
Figure BDA0002032170730000033
an estimated pulse width parameter, w, representing the current signal periods(m) represents the latest measured pulse width parameter obtained in step S24, i ═ 1, 2.
Further, step S4 includes the following substeps:
s41, calculating the posterior probability density function of the current target state updating moment by adopting a Bayesian filtering criterion according to a plurality of measurements from the last target state updating moment to the current target state updating moment;
and S42, extracting the target state from the posterior probability density function at the current target state updating time by adopting a minimum mean square error estimation criterion.
Further, in step S41, the posterior probability density function at the current target state updating time is calculated as:
p(x(tk)|z1:k)∝p(zk|x(tk),z1:k-1)p(x(tk)|z1:k-1)
wherein, x (t)k) Indicating the current target state update time tkCorresponding state of target dynamics, z1:kRepresents tkAnd the set of all previous metrology data, z1:k-1Indicating the last target state update time tk-1And the set of all previous metrology data, p (z)k|x(tk),z1:k-1) A joint likelihood function, p (x (t), representing the current target state update timek)|z1:k-1) The prediction equation representing bayes, and oc represents a proportional sign.
Further, p (z)k|x(tk),z1:k-1) The calculation formula is as follows:
Figure BDA0002032170730000034
wherein N iskRepresents tk-1To tkInner measurement quantity, tauj,kRepresents tk-1～tkThe time, x (τ), corresponding to the jth measurementj,k) Corresponds to tauj,kTemporal movement patternState, x (t)k-1) Indicating the last target state update time tk-1Corresponding to the state of the target dynamics, z (τ)j,k) Denotes τj,kAnd measuring the time.
The invention has the beneficial effects that: aiming at the problem of detection and tracking of the target with the discontinuous characteristic, the discontinuous characteristic of the target is brought into a Bayes tracking process, so that the joint estimation of the discontinuous motion state and the signal discontinuous characteristic thereof can be realized; the solution framework provided by the invention is not limited by a measured discontinuous statistical model, and self-adaptive strain period Bayesian tracking is deduced by combining the discontinuous characteristic of the signal; the method can be widely applied to the application fields of passive radar detection, array sonar underwater target tracking, unmanned aerial vehicle positioning and tracking and the like.
Drawings
FIG. 1 is a scheme flow diagram of the present invention;
FIG. 2 is a diagram illustrating an mth signal period parameter provided by an embodiment of the present invention;
FIG. 3 is a timing diagram of an intermittent measurement provided by an embodiment of the present invention;
fig. 4 illustrates the true discontinuous characteristic of the target transmission signal provided by the embodiment of the present invention;
FIG. 5 is an azimuth history map of representative metrology data received by sensors provided by embodiments of the present invention;
FIG. 6 is a graph of the tracking effect of a single Monte experiment of the method of the present invention and other algorithms provided by embodiments of the present invention;
fig. 6(a) illustrates a conventional processing method, fig. 6(b) illustrates an existing algorithm IKF for measurement discontinuity processing, and fig. 6(c) illustrates a method proposed by the present invention;
FIG. 7 is a graph of the results of 100 Monte Carlo for target tracking accuracy in the method of the present invention provided by the embodiments of the present invention;
FIG. 8 is a graph of the results of a 100 Monte Carlo state update interval for different clutter rates according to the method of the present invention.
Detailed Description
In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to the accompanying drawings.
Fig. 1 is a flowchart of a scheme of the present invention, and a method for detecting and tracking an object with discontinuous characteristics by a passive sensing system of the present invention includes the following steps:
s1, the definition of the discontinuous signal period is as shown in fig. 2, which gives a schematic diagram of the mth signal period: the division of the discontinuous signal period is defined as: the target actively transmits signals, the duration of continuous transmission signals of the target actively transmits signals is called as signal pulse width w, and the time interval between two adjacent continuous signals is called as a signal period p; the pulse width is greater than or equal to one system sampling time T.
In this embodiment, initializing system parameters includes: the system sampling interval T is 1s, the total tracking time L is 200s, and the target initial state updating time interval sequenceL＝{T0,T0,…,T0With an initial update time interval set to T0The initialization time variable t is 1s for 3 s. In consideration of the non-continuity of the target transmitting signal, introducing a binary variable f (t),
Figure BDA0002032170730000041
definition of tkAt the k-th target state update time, the initialization variable k is 0, and the target state x is initialized (t)0) The initial discontinuous signal period parameter p (0) ═ 3 and the pulse width parameter w (0) ═ 1, and the initialization variable m ═ 0.
S2, dividing the read measurement data into periods according to the definition of the step S1;
s21, reading the current moment measurement data from the passive sensor according to the system sampling interval;
in the embodiment, a moving target with a discontinuous characteristic is designed, and a pure orientation target tracking method commonly used in a passive detection system is considered. The passive sensor receives discontinuous signals transmitted by a moving target and acquires measurement information about the azimuth angle of the target, the azimuth angle state of the target is modeled into uniform linear motion, and the measurement equation is as follows:
Figure BDA0002032170730000051
wherein HtRepresenting the measurement function, and n (t) representing the measurement noise.
In the present embodiment, the estimated target state is
Figure BDA0002032170730000052
In which the sum of the values of theta (t),
Figure BDA0002032170730000053
representing the azimuth angle of the target and its azimuthal velocity, respectively. As shown in FIG. 4, considering a case of a discontinuous characteristic time variation, the interval is 4s in 1-69 s, 5s in 70-149 s, 3s in 150-200 s, and the duration time in a single period is 1 s. Accordingly, the azimuth history as shown in FIG. 5 characterizes the measurement data received by the sensors at a plurality of time instants, and the discontinuity is also time-varying.
S22, performing threshold detection on the measurement data read in the step S21;
reading measurement data at the current moment t from a passive sensor according to a system sampling interval, carrying out threshold detection on the received measurement, and recording the detected point measurement falling in a relevant wave gate as z (t) when the threshold is measured, wherein z (t) represents a target state value represented by the point measurement; otherwise, z (t) is null;
s23, obtaining a measurement time sequence according to the recorded point measurement of the threshold crossing and the corresponding arrival time;
s24, dividing the measurement time sequence into periods according to the definition of step S1 to obtain the period parameter and pulse width parameter of the measurement.
And carrying out periodic division on the obtained measurement time sequence to obtain a pseudo-periodic parameter related to measurement discontinuity. If there is no relevant over-threshold point measurement data, i.e., z (t) is null, signal period iteration m-m + 1. To divide the m-th pseudo signal period parameter ps(m) and ws(m) is an exampleThe method comprises the following specific steps: the measured time sequence obtained after threshold detection is periodically divided according to the definition of signal period, and the period p related to measurement can be obtainedwAnd pulse width wsSince the division is obtained by dividing the received measurement sequence, it does not completely represent the real period of the signal, which is also called pseudo signal period.
S3, updating the target state updating time interval sequence; the method comprises the following steps:
s31: non-continuous characteristic parameter estimation
If m < K, at which time the data in the sliding window is not yet full, follow the system initial settings
Figure BDA0002032170730000061
Figure BDA0002032170730000062
If m is greater than or equal to K, the newly measured pseudo signal period parameter p is useds(m) and ws(m) updating the signal period parameters, i.e. recursively estimating the parameters in the mth signal period
Figure BDA0002032170730000063
Figure BDA0002032170730000064
S32: calculating a target state update time interval sequence according to the estimated discontinuous characteristic parameters
Figure BDA0002032170730000065
Further, the next target state update time can be determined: t is tk+1＝tk+Tk+1。
And S4, updating the time interval sequence according to the target state obtained in the step S3, and carrying out variable-period Bayesian filtering estimation.
S41: from the result of step S3, it is determined whether the value of t is equal to the (k + 1) th state update time tk+1If yes, go to step S42; otherwise, step S5 is executed.
S42: number of iterative target state updates: k is k +1, for tk-1～tkN within timekThe measurements are sorted and recorded
Figure BDA0002032170730000067
Wherein t iskIndicates the time of the kth target state update, τj,k,j＝1,2,…,NkRepresents tk-1～tkThe discontinuity distribution of the jth measurement at the time corresponding to the jth measurement in time is schematically shown in fig. 3. The following uses these measurements to achieve the pair tkBayes estimation of time, firstly, according to Markov property and Bayes criterion, calculating the joint likelihood function of current update time
Figure BDA0002032170730000066
Wherein, p (x (τ))j,k)|x(tk-1),x(tk) Denotes x (. tau.)j,k) Distribution of functions obeyed, p (z (τ)j,k)|x(τj,k) Is a measurement z (τ)j,k) Likelihood function of x (t)k) Represents tkThe state of the target dynamics at time, x (τ)j,k) Corresponds to tauj,kMotion state at time, z1:k-1＝{z(i),1≤i≤tk-1Represents tk-1And all previous metrology data sets.
In this embodiment, the specific bayesian implementation algorithm adopted is a Kalman algorithm, and the specific implementation manner is as follows: under the assumption of linear gauss, using j, j ═ 1,2, …, NkSeparately performing Kalman filtering on the individual measurements to obtain one-step prediction of state
Figure BDA0002032170730000071
Covariance one-step prediction
Figure BDA0002032170730000072
Measurement covariance Sj,kGain Kj,k. To obtain NkAfter the measured kalman sub-estimation result, step S43 is executed.
S43: calculating t according to Bayes filtering criterionkPosterior probability density function of time target state
p(x(tk)|z1:k)∝p(zk|x(tk),z1:k-1)p(x(tk)|z1:k-1) (5)
Wherein, p (x (t)k)|z1:k-1) The prediction equation representing Bayes can be obtained from a state equation and a Chapman-Kolmogorov equation, and oc represents a proportional sign.
Then, extracting the target state from the posterior probability density function of the target state by using a minimum mean square error estimation criterion:
Figure BDA0002032170730000073
under the assumption of linear gauss, the state posterior probability density function and the prediction density function at the previous state updating time are respectively as follows:
Figure BDA0002032170730000074
Figure BDA0002032170730000075
wherein the content of the first and second substances,
Figure BDA0002032170730000076
representing a Gaussian distribution function obeying a mean value x and a variance p, i.e. muk|k-1、Pk|k-1A gaussian parameter representing the state posterior density function at the time of the previous state update. Mu.sk|k-1、Pk|k-1Representing the gaussian parameter of the predicted density function.
Further, a posterior probability density function of the target state at the current update time is calculated according to the formula (5)
Figure BDA0002032170730000077
Wherein the content of the first and second substances,
Figure BDA0002032170730000078
Figure BDA0002032170730000079
and then the minimum mean square error of the target state is estimated as
Figure BDA0002032170730000081
S5, iterating T ═ T + T; if t > L, the algorithm ends; otherwise, the execution returns to step S2.
Through the steps, the combined estimation of the dynamic state of the discontinuous target and the discontinuous characteristic of the signal can be realized.
Fig. 4 shows the intermittent measurements received by the sensor with respect to the target in this embodiment, and it is apparent that the corresponding target measurements are lost at the moment when the target does not transmit a signal.
Fig. 6 provides a tracking effect diagram of a single monte experiment of a conventional tracking algorithm, an existing measurement discontinuity processing-oriented algorithm IKF, and the method of the present invention, respectively, and it can be known that the existing method causes problems of multiple initiations, track segmentation, discontinuity characteristic loss, and the like, and the method of the present invention can effectively avoid these problems.
FIG. 7 shows the target state estimation error accuracy result of the algorithm of the present invention counted for 100 Monte Carlo experiments. As the algorithm iterates, the estimation error RMSE (root mean square error) tends to converge, indicating that the estimation algorithm is functioning. The unit "°" in fig. 7 is a unit of the azimuth of the target state in the present embodiment.
Fig. 8 is a statistical result of 100 monte carlo experiments on a target state update time interval in the tracking process in the embodiment of the present invention, and the result shows that the method of the present invention can accurately estimate the discontinuous characteristic of the target. In addition, in order to embody the robustness of the algorithm, the method also provides results under different clutter ratios, and the method can still perform estimation well under the background of existence of complex clutter. Due to the existence of the data sliding window, under the condition that the discontinuous characteristic is time-varying, a section of estimated time delay exists. In practical application, under the condition that the discontinuous characteristic is slowly time-varying, the time delays can be ignored, and finally, the real transmission characteristic can be correctly fitted and estimated all the time. Clutter ratios are characterized in fig. 8 by the poisson distribution parameter β per unit area.
In conclusion, the method and the device can well realize stable detection and continuous tracking of the target with the discontinuous characteristic, can accurately estimate the discontinuous characteristic of the target signal while realizing correct tracking of the target track, and have great significance for target tracking and identification decision of an actual detection system.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (7)

1. A method for detecting and tracking a target with discontinuous characteristics by a passive sensing system is characterized by comprising the following steps:
s1, the division of the discontinuous signal period is defined as: the target actively transmits signals, the duration of continuous transmission signals of the target actively transmits signals is called as signal pulse width, and the time interval between two adjacent continuous signals is called as a signal period; the pulse width is greater than or equal to one-time system sampling time;
s2, dividing the read measurement data into periods according to the definition of the step S1;
s3, updating the target state updating time interval sequence; step S3 specifically includes:
s31, estimating discontinuous characteristic parameters; if m is less than K, the data in the sliding window is not full, and the signal period and the pulse width of the previous signal period are used as the discontinuous characteristic parameters of the current signal period; if m is larger than or equal to K, updating the discontinuous characteristic parameter of the current signal period by the latest measured period parameter and the pulse width parameter obtained in the step S24; m represents the sequence number of the current signal period, and K represents the length of the sliding window;
s32, estimating discontinuous characteristic parameters according to the step S31, and calculating a target state updating time interval sequence;
and S4, updating the time interval sequence according to the target state obtained in the step S3, and carrying out variable-period Bayesian filtering estimation.
2. The method for detecting and tracking the target with the discontinuous characteristic by the passive sensing system according to claim 1, wherein the step S2 is preceded by: and step S20, initializing the period parameter and the pulse width parameter of the discontinuous signal.
3. The method for detecting and tracking the target with the discontinuous characteristic by the passive sensing system according to claim 2, wherein the step S2 specifically comprises the following sub-steps:
s21, reading the current moment measurement data from the passive sensor according to the system sampling interval;
s22, performing threshold detection on the measurement data read in the step S21;
s23, obtaining a measurement time sequence according to the recorded point measurement of the threshold crossing and the corresponding arrival time;
s24, dividing the measurement time sequence into periods according to the definition of step S1 to obtain the period parameter and pulse width parameter of the measurement.
4. The method as claimed in claim 3, wherein the step S31 updates the discontinuous characteristic parameter of the current signal period by the latest measured period parameter and pulse width parameter obtained in the step S24, and the calculation formula is as follows:
Figure FDA0002607760410000011
Figure FDA0002607760410000012
wherein the content of the first and second substances,
Figure FDA0002607760410000021
an estimated period parameter representing the current signal period, K representing the length of the sliding window, ps(m) represents the latest measured period parameter obtained in step S24, m represents the current signal period number,
Figure FDA0002607760410000022
an estimated pulse width parameter, w, representing the current signal periods(m) represents the latest measured pulse width parameter obtained in step S24, i ═ 1, 2.
5. The method for detecting and tracking the target with the discontinuous characteristic by the passive sensing system according to claim 3, wherein the step S4 comprises the following sub-steps:
s41, calculating the posterior probability density function of the current target state updating moment by adopting a Bayesian filtering criterion according to a plurality of measurements from the last target state updating moment to the current target state updating moment;
and S42, extracting the target state from the posterior probability density function at the current target state updating time by adopting a minimum mean square error estimation criterion.
6. The method according to claim 5, wherein the posterior probability density function at the current target state updating time in step S41 is calculated as:
p(x(tk)|z1:k)∝p(zk|x(tk),z1:k-1)p(x(tk)|z1:k-1)
wherein, x (t)k) Indicating the current target state update time tkCorresponding state of target dynamics, z1:kRepresents tkAnd the set of all previous metrology data, z1:k-1Indicating the last target state update time tk-1And the set of all previous metrology data, p (z)k|x(tk),z1:k-1) A joint likelihood function, p (x (t), representing the current target state update timek)|z1:k-1) The prediction equation representing bayes, and oc represents a proportional sign.
7. The method for detecting and tracking the target with the discontinuous characteristic by the passive sensing system according to claim 6, wherein p (z)k|x(tk),z1:k-1) The calculation formula is as follows:
Figure FDA0002607760410000023
wherein N iskRepresents tk-1To tkInner measurement quantity, tauj,kRepresents tk-1～tkThe time, x (τ), corresponding to the jth measurementj,k) Corresponds to tauj,kMotion state at time, x (t)k-1) Indicating the last target state update time tk-1Corresponding to the state of the target dynamics, z (τ)j,k) Denotes τj,kAnd measuring the time.
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