CN111025281B - Threshold acquisition method for dynamically planning track-before-detection based on approximate algorithm - Google Patents

Threshold acquisition method for dynamically planning track-before-detection based on approximate algorithm Download PDF

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CN111025281B
CN111025281B CN201911236903.9A CN201911236903A CN111025281B CN 111025281 B CN111025281 B CN 111025281B CN 201911236903 A CN201911236903 A CN 201911236903A CN 111025281 B CN111025281 B CN 111025281B
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CN111025281A (en
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龙腾
胡程
蔡炯
王锐
周超
曾涛
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Beijing Institute of Technology BIT
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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
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    • G01S13/66—Radar-tracking systems; Analogous systems
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    • 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
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Abstract

The invention discloses a threshold acquisition method for dynamically planning tracking before detection by an approximate algorithm, which relates to the technical field of radar detection.

Description

Threshold acquisition method for dynamically planning track-before-detection based on approximate algorithm
Technical Field
The invention relates to the technical field of radar detection, in particular to a threshold acquisition method for dynamically planning track-before-detection based on an approximate algorithm.
Background
In the traditional radar detection and tracking, each frame is detected, and then the detected target is associated and tracked through Kalman filtering, probability data association and the like. Due to the fact that a detection threshold is applied to each frame to screen measurement, partial measurement information is lost, and the traditional method easily causes detection omission in a low signal-to-noise ratio (SNR) environment. Therefore, pre-detection Tracking (TBD) is proposed for detection tracking under low SNR conditions. The TBD algorithm does not use a threshold to detect objects in each frame data processing. Instead, it performs threshold detection after jointly processing many frames of data and returns the estimated target trajectory.
Dynamic programming pre-detection tracking (DP-TBD) is one of the TBD methods. Currently, many papers on DP-TBD have been reported. The papers mainly improve the aspects of calculation flow, tracking performance and the like, but the analysis of the value function and the detection threshold thereof in the DP-TBD is unclear, because the probability distribution function of the value function usually has no closed solution, and the detection threshold thereof is difficult to determine. The general method is to simply use a large number of monte carlo simulation experiments to obtain the threshold of the DP-TBD value function at a certain false alarm rate, which is extremely time-consuming.
Of course, there are some papers that have detailed analyses of the DP-TBD detection threshold and proposed some faster algorithms. In environments where the noise follows a gaussian distribution, Tonissen uses a gaussian approximation method to analyze the value function and its detection threshold. However, it assumes that the value functions of the stages in the DP algorithm are statistically independent and have gaussian distributions, which are clearly unrealistic.
Johnson then uses extreme value theory to analyze the value function in a gaussian noise environment. Although the method does not need to evaluate the functions independently and in Gaussian distribution, the method also needs to perform Monte Carlo simulation for a certain number of times to estimate the distribution parameters and finally sets the threshold, so that the method is time-consuming.
In a radar environment, the real-time performance is high and the noise power is generally assumed to be exponential distribution rather than gaussian distribution, so the above-mentioned gaussian approximation method is not suitable for DP-TBD detection threshold acquisition in a radar environment.
Although the method for analyzing the value function in the gaussian noise environment by using the extreme value theory can be suitable for acquiring the DP-TBD detection threshold in the radar environment, the distribution parameters need to be estimated by performing monte carlo simulation for a certain number of times, and finally the threshold is set, so that time is consumed.
In a radar environment, a Monte Carlo counting method can be adopted for obtaining the DP-TBD detection threshold, and the method can obtain a more accurate detection threshold result under a large amount of simulation statistics, but is more time-consuming compared with an extreme value theory method.
Therefore, a method which considers both the accuracy of the detection threshold result and the time-consuming degree of calculation is urgently needed for obtaining the DP-TBD detection threshold in the radar environment at present.
Disclosure of Invention
In view of this, the present invention provides a threshold obtaining method for dynamically planning tracking before detection based on an approximate algorithm, which can improve the calculation efficiency of a detection threshold result and ensure the calculation accuracy of the detection threshold result.
In order to achieve the purpose, the technical scheme of the invention is as follows: the method is used for acquiring the real threshold in a dynamic programming pre-detection tracking DP-TBD method in a radar environment, and comprises the following steps:
path planning is carried out by adopting a greedy approximation algorithm, a value function is constructed for the planned path and is marked as a greedy approximation function, and a probability distribution function of the greedy approximation function is calculated
Figure GDA0003242191930000021
x is solved for IlowProbability distribution function of
Figure GDA0003242191930000031
Of (2).
The lower limit of the true threshold is constructed to be ZlowLet us order
Figure GDA0003242191930000032
Wherein P isfaCalculating Z for a set false alarm ratelow。
Path planning is carried out by adopting a maximum approximation algorithm, a maximum function of a value function is constructed for the planned path and is marked as a maximum approximation function, and a probability distribution function of the maximum approximation function is calculated
Figure GDA0003242191930000033
y is solved for IupProbability distribution function of
Figure GDA0003242191930000034
Of (2).
Constructing the upper limit of the true threshold as order ZupLet us order
Figure GDA0003242191930000035
Calculating Zup。
Then the real threshold is Z ═ epsilon Zlow+(1-ε)Zup。
Wherein epsilon is a set proportionality coefficient
Figure GDA0003242191930000036
And using the real threshold Z for dynamic programming pre-detection tracking by using a dynamic programming pre-detection tracking DP-TBD method in a radar environment.
Further, a greedy approximation algorithm is adopted for path planning, a value function is constructed for the planned path and is marked as a greedy approximation function, and the method specifically comprises the following steps:
and acquiring the corresponding state transition number q, the accumulated frame number m and the noise average power lambda when a DP-TBD (pre-tracking-time tracking delay-time detection) method is used in a radar environment.
Constructing a greedy approximation function of
Figure GDA0003242191930000037
Wherein Y is0To satisfy the random variable of Ga (1, lambda) distribution, YiTo satisfy
Figure GDA0003242191930000038
A random variable of distribution.
Further, solving a probability distribution function of a greedy approximation function
Figure GDA0003242191930000039
Comprises the following steps: calculation of I by moment approximationlowProbability distribution function of
Figure GDA00032421919300000310
Further, the maximum approximation function specifically includes:
maximum approximation function
Figure GDA00032421919300000311
Wherein when a is 1, Ya～Ga(m,λ)
When a is greater than 1, the ratio of a,
Figure GDA0003242191930000041
wherein the parameter k of the shape parameters m-k is determined according to (q-1) (k-1) +1 < a < (q-1) k + 1.
Further, a probability distribution function of a maximum approximation function is calculated
Figure GDA0003242191930000042
The method specifically comprises the following steps: calculation of I by moment approximationupProbability distribution function of
Figure GDA0003242191930000043
Has the advantages that:
the threshold obtaining method for dynamically planning tracking before detection based on the approximate algorithm obtains the lower limit of a real threshold tracked before dynamic planning detection by adopting a greedy approximate algorithm, obtains the upper limit of the real threshold by adopting a maximum value approximate method, and constructs an approximate relation between the upper limit and the lower limit and the real threshold to obtain an accurate estimation value of the real threshold.
Drawings
Fig. 1 is a flowchart of a threshold acquisition method for dynamically planning pre-detection tracking based on an approximation algorithm according to the present invention.
Fig. 2 shows an example of a DP-TBD search path, where the set number of state transitions is 3, and DP accumulation is performed on data of 3 time stages, and the DP-TBD algorithm is actually finding a path to the target position in the third stage.
FIG. 3 is a schematic diagram of a greedy approximation search.
FIG. 4 is a schematic diagram of the maximum method approximation.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a threshold acquisition method for dynamically planning track-before-detection based on an approximate algorithm, which is used for acquiring a real threshold in a DP-TBD method for tracking before-detection by using dynamic planning in a radar environment, wherein the principle of the DP-TBD method is as follows:
the DP-TBD method is essentially that under the condition that the change rate of the target state is constant or small, the state transition of the target between adjacent stages is judged, and the track which the target may experience is obtained by recursion; observations are then accumulated along these trajectories to overcome the target-span cell problem, and a long-term accumulation of the target is achieved, the accumulated observations also being referred to as a value function.
The main body of the DP-TBD idea is how to acquire all possible trajectories that the target may experience and accumulate the value function as such. The general flow of the DP-TBD algorithm is as follows:
1) value function initialization
Assume phase 1, each range binWithin which the target is present. For all states of phase 1
Figure GDA0003242191930000051
(N is the total number of distance units)
Figure GDA0003242191930000052
Wherein
Figure GDA0003242191930000053
When the phase K (1,2, …, K) is shown, the object is in the nth range cell of the one-dimensional range image, namely a state;
Figure GDA0003242191930000054
represents the state of the pair
Figure GDA0003242191930000055
The observed value of (n-th range unit radar echo amplitude squared);
Figure GDA0003242191930000056
called cost function or cumulative observation or value function, and records the state along a certain track (the track, the k stage is
Figure GDA0003242191930000057
) A non-coherent accumulation of the observed values of (a);
Figure GDA0003242191930000058
recording a state of the k-1 stage, wherein the state is most likely to be transferred to obtain the state
Figure GDA0003242191930000059
In the state of (a) to (b),
Figure GDA00032421919300000510
for trace backtracking, the initial value is set to 0, i.e. the starting point of the trace is indicated.
2) Value function accumulation
When K is 2 ≦ K ≦ K, for all states
Figure GDA00032421919300000511
Figure GDA0003242191930000061
Figure GDA0003242191930000062
Indicating that all possible transitions in stage k-1 result in a state
Figure GDA0003242191930000063
The state set of (2) is predicted by using the speed and distance information of the trajectory.
3) Function of screening values
Finding the detection threshold V greater than the value function in the K stageTAnd obtaining a state corresponding to the value function, as shown in the following equation:
Figure GDA0003242191930000064
4) backtracking
For the state found in the third step
Figure GDA0003242191930000065
Starting from phase K
Figure GDA0003242191930000066
Backtrack its complete trajectory:
Figure GDA0003242191930000067
Figure GDA0003242191930000068
indicates a final state of
Figure GDA0003242191930000069
The trace of (c), the state of the kth stage. Greedy approximation algorithm and determination of real threshold lower limit.
As shown in fig. 2, the DP-TBD is essentially searching for a path with the highest energy. Ignoring the boundary of the state, the DP-TBD is regarded as a pure path network searching problem, and the energy of each node is independently distributed in the same way and is exponentially distributed.
Based on the above principle of DP-TBD, the invention provides a threshold acquisition method for dynamically planning track-before-detect based on an approximate algorithm, the flow of which is shown in FIG. 1, and the method comprises the following steps:
s1, planning the path by greedy approximation algorithm, constructing a value function for the planned path, marking as a greedy approximation function, and calculating the probability distribution function of the greedy approximation function
Figure GDA00032421919300000610
x is solved for IlowProbability distribution function of
Figure GDA00032421919300000611
The variable of (1);
the dynamic programming method with the optimal performance can be degraded into a greedy algorithm with suboptimal performance so as to solve the approximate distribution of the value function and the lower limit of the real threshold.
As shown in fig. 3, the greedy approximation algorithm search step: from the end point, the state with the maximum power in the possible transition states of the next stage is selected, and the value function of the noise accumulation can be reduced to:
Ilow＝X1,1+max{X2,1,...,X2,q}+max{X3,1,...,X3,q}+...+max{Xm,1,...,Xm,q} (5)
wherein X1,1,...,Xm,qAre all independently distributed with the same index
Figure GDA0003242191930000071
x > 0.
m ═ K accumulation frame number, q state transition number (K:)
Figure GDA0003242191930000072
Number of middle states), IlowA greedy approximation algorithm.
The equivalent form of equation (5) is shown by the sum of q +1 independently differently distributed gamma variables, i.e.:
Figure GDA0003242191930000073
wherein Y is0To satisfy the random variable of Ga (1, lambda) distribution, YiTo satisfy
Figure GDA0003242191930000074
A random variable of distribution.
Figure GDA0003242191930000075
Refers to gamma distribution
Figure GDA0003242191930000076
m＞1；x,i,λ＞0。
Ga (α, β) α, β are shape and scale parameters, respectively; average power of lambda noise.
With respect to the probability distribution satisfied by the sum of the gamma variables of the plurality of independent different distributions, the approximation can be performed using a moment approximation method:
distribution S for sum of multiple independent gamma variablesn＝R1+R2+...+Rn,Ri～Ga(αi,βi)
Figure GDA0003242191930000077
Wherein:
Figure GDA0003242191930000081
phi (#) and phi (#) represent probability density functions and probability distribution functions of Gaussian distribution respectively; mu, sigma, kappa3Respectively representing the sum distribution S of a plurality of independent gamma variablesnMean, standard deviation, and third order cumulant of (d).
Figure GDA0003242191930000082
By using (6), (7), (8) and (9), I can be obtainedlowProbability distribution function of
Figure GDA0003242191930000083
Step 2, for a given false alarm rate Pfa(set according to actual requirements), and then the threshold Z of the greedy approximation method can be obtained by using the following formulalow：
Figure GDA0003242191930000084
The greedy algorithm ignores part of the possible paths, resulting in that the last path may not be the path with the largest energy, which eventually results in a set value function threshold being smaller. I.e. the false alarm rate is PfaAssuming that the true threshold is Z, the method utilizes
Figure GDA0003242191930000085
The calculated threshold is ZlowThen Z islowZ, and both are true if and only if m 1,2 or q 1. Thus can be used for
Figure GDA0003242191930000086
Lower limit distribution, Z, regarded as true distributionlowIs the lower limit of the true threshold Z.
Step 3, planning the path by adopting a maximum approximation algorithm, constructing a maximum function of the value function aiming at the planned path, and recording the maximum function as the maximum functionMaximum approximation function, probability distribution function for calculating maximum approximation function
Figure GDA0003242191930000091
y is solved for IupProbability distribution function of
Figure GDA0003242191930000092
Of (2).
As shown in fig. 4, the principle of the maximum value approximation method is: assuming that any nodes in adjacent stages can be connected, the maximum value of the value function is the accumulation of the maximum values of the nodes in each stage, that is:
Iup＝X1,1+max{X2,1,...,X2,q}+...+max{Xm,1,...,Xm,(q-1)(m-1)+1} (11)
wherein X1,1,...,Xm,(q-1)(m-1)+1Are independent random variables distributed with the same index.
IupThe sum of the gamma variables, which can be equally (q-1) (m +1) +1 independently different distributions, is the following expression:
Figure GDA0003242191930000093
wherein
Figure GDA0003242191930000094
It is also possible to obtain I by means of a moment approximationupProbability density function of
Figure GDA0003242191930000095
Step 4, for a given false alarm rate PfaThe threshold Z of the maximum value approximation method can be obtained by using the following formulaup：
Figure GDA0003242191930000096
The maximum value approximation method enables any nodes in adjacent stages to be communicated, a part of impossible paths are added, and the approximation finally causes the set value function threshold to be larger. I.e. the false alarm rate is PfaAssuming that the true threshold is Z, the method utilizes
Figure GDA0003242191930000097
The calculated threshold is ZupZ is less than or equal to ZupBoth are true if and only if m 1,2 or q 1. Thus can be used for
Figure GDA0003242191930000098
Upper distribution, Z, considered as true distributionupIs the upper limit of the true threshold Z.
Step 5, the false alarm rate P is respectively obtained through the second step and the third stepfaLower, lower limit Z of true threshold ZlowAnd an upper limit ZupThen, according to the fitting formula:
Z＝εZlow+(1-ε)Zup (14)
wherein the proportionality coefficient
Figure GDA0003242191930000099
I.e. to find the true threshold Z.
And 6, using the real threshold Z for dynamic programming pre-detection tracking by using a dynamic programming pre-detection tracking DP-TBD method in a radar environment.
The following examples illustrate the implementation steps:
in order to verify the threshold calculation method, the DP-TBD threshold calculation is completed by adopting an algorithm for rapidly acquiring the tracking threshold before dynamic programming detection by combining a greedy approximation method and a maximum value approximation method based on simulation data. The simulation parameters are shown in table 1:
TABLE 1
Parameter(s) Value of
Number of state transitions q 9
Accumulated frame number m 100
False alarm rate Pfa 1e-2
Noise power lambda 1
Step one, calculating a real lower threshold limit:
the simulation parameters are brought into (6) to obtain
Figure GDA0003242191930000101
Wherein Y is0To satisfy the random variable of Ga (1,1) distribution, YiTo satisfy
Figure GDA0003242191930000102
A random variable of distribution. Through the calculation of (9), I is obtainedlowThe mean value, the standard deviation and the third-order cumulant of the formula are respectively as follows:
Figure GDA0003242191930000103
will IlowThe mean value, standard deviation and third-order cumulant of (4) are substituted into (7) and (8) to obtain IlowProbability density function ofComprises the following steps:
Figure GDA0003242191930000111
then P is putfa＝10-2And
Figure GDA0003242191930000112
substituting (10) to obtain the corresponding lower threshold limit Zlow：
Zlow＝311.1
Step two, calculating a real upper limit of a threshold:
the simulation parameters are brought (12) to obtain:
Figure GDA0003242191930000113
wherein
Figure GDA0003242191930000114
Then, the calculation of (9) is carried out to obtain IupThe mean value, the standard deviation and the third-order cumulant of the formula are respectively as follows:
Figure GDA0003242191930000115
will IupThe mean value, standard deviation and third-order cumulant of (4) are substituted into (7) and (8) to obtain IupThe probability density function of (a) is:
Figure GDA0003242191930000116
then P is putfa＝10-2And
Figure GDA0003242191930000117
substituting (13) to obtain the corresponding upper threshold limit Zup：
Zup＝654.98
Step three, calculating a real threshold estimation value:
according to Pfa＝10-2And calculating to obtain a scale factor epsilon: 0.8546 for epsilon
Then changing epsilon to 0.8546 and Zlow＝311.1、ZupSubstitution 654.98 into (14) yields the true threshold estimate Z:
Z＝0.8546×311.1+(1-0.8546)×654.98＝361.1
the real threshold estimation value obtained by utilizing the traditional Monte Carlo simulation experiment is 353.5, the difference between the real threshold estimation value and the result obtained by the method provided by the invention is only 2 percent, and the method is very close to the method, thereby simultaneously explaining the accuracy of the algorithm. However, if the example adopts the traditional Monte Carlo simulation experiment, the simulation number is 105In time, more than 40 minutes is needed to obtain a real threshold estimation value, but the method provided by the invention only needs 7-8 seconds. Namely, the method can be applied to the radar DP-TBD to realize the rapid calculation of the detection threshold.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A threshold obtaining method for dynamically planning track-before-detection based on an approximate algorithm is characterized in that the method is used for obtaining a real threshold in a DP-TBD method for dynamically planning track-before-detection in a radar environment, and the real threshold obtaining method comprises the following steps:
path planning is carried out by adopting a greedy approximation algorithm, a value function is constructed for the planned path and is marked as a greedy approximation function, and a probability distribution function of the greedy approximation function is calculated
Figure FDA0003242191920000011
x is solved for IlowProbability distribution function of
Figure FDA0003242191920000012
The variable of (1);
the lower limit of the true threshold is constructed to be ZlowLet us order
Figure FDA0003242191920000013
Wherein P isfaCalculating Z for a set false alarm ratelow；
Path planning is carried out by adopting a maximum approximation algorithm, a maximum function of a value function is constructed for the planned path and is marked as a maximum approximation function, and a probability distribution function of the maximum approximation function is calculated
Figure FDA0003242191920000014
y is solved for IupProbability distribution function of
Figure FDA0003242191920000015
The variable of (1);
the upper limit of the true threshold is constructed to be ZupLet us order
Figure FDA0003242191920000016
Calculating Zup；
Then the real threshold is Z ═ epsilon Zlow+(1-ε)Zup；
Wherein epsilon is a set proportionality coefficient
Figure FDA0003242191920000017
Using the real threshold Z for tracking before dynamic programming detection by using a dynamic programming tracking-before-detection DP-TBD method in a radar environment;
a greedy approximation algorithm is adopted for path planning, a value function is constructed for the planned path and is marked as a greedy approximation function, and the method specifically comprises the following steps:
acquiring a state transition number q, an accumulated frame number m and a noise average power lambda corresponding to a dynamic programming detection pre-tracking DP-TBD method in a radar environment;
constructing a greedy approximation function of
Figure FDA0003242191920000018
Wherein Y is0To satisfy the random variable of Ga (1, lambda) distribution, YiTo satisfy
Figure FDA0003242191920000021
A distributed random variable;
probability distribution function for solving greedy approximation function
Figure FDA0003242191920000022
Comprises the following steps: calculation of I by moment approximationlowProbability distribution function of
Figure FDA0003242191920000023
The maximum approximation function is specifically:
maximum approximation function
Figure FDA0003242191920000024
Wherein when a is 1, Ya～Ga(m,λ)
When a is greater than 1, the ratio of a,
Figure FDA0003242191920000025
wherein the parameter k of the shape parameters m-k is based on
(q-1) (k-1) +1 < a < (q-1) k + 1;
the probability distribution function of the calculated maximum approximation function
Figure FDA0003242191920000026
The method specifically comprises the following steps: calculation of I by moment approximationupProbability distribution function of
Figure FDA0003242191920000027
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