CN112763981A - Detection method and system for radar pulse signal - Google Patents

Detection method and system for radar pulse signal Download PDF

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CN112763981A
CN112763981A CN202011471055.2A CN202011471055A CN112763981A CN 112763981 A CN112763981 A CN 112763981A CN 202011471055 A CN202011471055 A CN 202011471055A CN 112763981 A CN112763981 A CN 112763981A
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CN112763981B (en
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吴日恒
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Shandong Agricultural University
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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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/285—Receivers

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Abstract

The invention belongs to the technical field of radar pulse signal detection, and discloses a method and a system for detecting a radar pulse signal. In radar and electronic reconnaissance systems, the electromagnetic signals of an interested target area need to be scanned and monitored uninterruptedly so as to find abnormality and detect the radiation source signals which are suddenly started up most quickly, and the method has very important value and significance in both military fields and civil fields.

Description

Detection method and system for radar pulse signal
Technical Field
The invention belongs to the technical field of radar pulse signal detection, and particularly relates to a method and a system for detecting a radar pulse signal.
Background
Currently, the current state of the art commonly used in the industry is such that:
in the field of radar signal detection, a common criterion is the nemann-pearson criterion, but this technique is based on a binary assumption: either a signal is present or a signal is not present, and in practice, it is unknown whether and when a radar signal is present, so the usual signal detection criterion, the nemann-pearson criterion, cannot be implemented.
In modern war, in order to increase attack efficiency to enemy military target and improve survival probability of own battlefield radar, the own military radar in war keeps radio silence for most of time, under the support of necessary military information, the military radars can be quickly started up, guide own guided weapon to attack enemy high-value target, and quickly shut down in extremely short time, so as to avoid attack of enemy anti-radiation missile. In the fight system, in order to increase the attack efficiency on the anti-radiation missile of the enemy, the sensor system of the own party is inevitably required to be capable of quickly detecting the radar pulse signal of the quick start-up of one side of the enemy in the shortest time, and the anti-radiation missile of the own party is guided to quickly attack the detected radar target of the enemy.
Due to the specificity of the application context, conventional signal detection methods such as the Neyman-pearson (np) criterion, the idea is: the signal parameters are known and the signal is a stationary signal, so that the criterion of maximizing the correct detection probability is met under a certain false alarm rate, and the thought of the method does not consider practical application scenes such as non-stationary signals or sudden change of the statistical characteristics of the signal. Under the condition that parameters are unknown, the conventional NP criterion firstly estimates unknown parameters by using methods such as MLE (Multi level iterative optimization) and the like, and then executes a detection task after PDF (Portable document Format) is known, the process is carried out according to the front-back sequence, and the parameter estimation value of each new data sample can be changed, so that all data sample spaces have to be reused for estimating the unknown parameters, the calculated amount is too complex, the instantaneity cannot be met, and the war victory or defeat is greatly restricted and influenced due to the complexity of high-dimensional parameter estimation, and even the trend of a warfare station is decisively influenced. On the other hand, for modern high-intensity wars, it is unrealistic to expect that enemies have longer radar startup working time, the real situation is often to improve the survival rate of the radar, and the startup working time of enemy battlefield surveillance radars is extremely short, which means that own sensors can only collect a small number of signal samples and carry out joint rapid detection and unknown parameter estimation in real time, and under the situation, the conventional radar signal detection and estimation method based on the NP criterion is difficult to detect rapidly changing signals in real time.
In summary, the problems of the prior art are as follows:
(1) under the condition that parameters are unknown, the traditional NP criterion estimates unknown parameters, the calculated amount is too complex, the instantaneity cannot be met, and signals with rapid changes are difficult to detect in real time.
(2) Whether the radar works or not and when the radar starts to work are unknown, and binary hypothesis judgment cannot be carried out by applying NP (number-of-cycles) criteria.
(3) The working time of the radar is uncertain, and the working may not be continuous, so that it is difficult to ensure that the sensor can collect enough samples, and the NP criterion cannot be applied.
The significance of solving the technical problems is as follows: the problems often appear in engineering application, the conventional NP criterion is adapted to an ideal environment and cannot meet the application requirements of environments such as passive sensing and electronic reconnaissance, the introduction of the fastest detection theory can adapt to the battle environment with dynamic time variation in a battlefield, a solid theory and technology realization foundation is laid for developing the application under passive sensing, the method has very important significance for guaranteeing the national ownership, the safety and the integrity of territory, and powerful technical support is provided for winning high-technology wars under modern wars conditions.
The two methods provided by the invention can realize joint rapid detection of radar pulse signals and parameter estimation by using a small amount of samples under a certain false alarm probability condition.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method and a system for detecting a radar pulse signal.
The invention is realized in such a way that a method for detecting radar pulse signals comprises the following steps:
in the radar pulse signal detection, grid search is not carried out, the radar pulse amplitude statistic accumulation iterative GLRT method is embedded into the accumulation sum method by using the structural characteristics of the radar pulse signal, and online real-time joint detection and radar pulse amplitude estimation are synchronously realized.
Further, the method for detecting the radar pulse signal further includes:
handle [ Amin,Amax]Dividing the grid into m grids with equal intervals, and estimating A by using a parallel accumulation and iteration method when m is large enoughaveDetecting a radar pulse signal; for new data set, continuously obtaining increment of GLRT by recursive iterative solution form of parallel accumulation and method when parallel accumulation and iterative solution are one discrete AaveWhen GLRT corresponding to the estimated value of (A) first meets a threshold condition, iteration is automatically stopped, and discrete AaveEstimate is the most accurate AaveAnd detecting a corresponding radar pulse signal.
Further, the method for detecting the radar pulse signal specifically includes:
step one, the number of samples tends to infinity, and the average pulse amplitude AaveWill converge progressively; a generalized log-likelihood ratio of
Figure RE-GDA0003002473360000031
Step two, for H1Average pulse amplitude A under the conditionsaveStatistics calculation Structure, pair AaveAnd performing iterative statistic cumulative calculation.
Figure RE-GDA0003002473360000032
Step three, taking the average pulse amplitude A of the log-likelihood functionaveThe derivative of (a) of (b),
Figure RE-GDA0003002473360000033
step four, making the log-likelihood function related to the average pulse amplitude AaveIs equal to 0, the MLE maximum likelihood estimate is calculated, quantized to a recursive solution,
Figure RE-GDA0003002473360000034
in the fifth step, the step of,
Figure RE-GDA0003002473360000035
threshold value h → ∞ embedded in the accumulation sum method to obtain
Figure RE-GDA0003002473360000036
Gradual unbiased optimal estimator;
Figure RE-GDA0003002473360000041
further, the radar pulse signal is characterized by the structural feature of H1Under the condition of AaveStatistics calculation structure of (1):
H0:x(t)＝n(t) t＝0,…,v-1
H1:x(t)＝Aave+n(t),t＝v,v+1,...；
in the above formula, v represents the time T at which the change occurs at the v-th time0(changetime) the radar pulse signal starts to appear steadily at time v, A represents the unknown radar pulse amplitude, and the average pulse amplitude is measured
Figure RE-GDA0003002473360000042
AaveVaries with the propagation distance between the receiving antenna and the radar radiation source target, etc.; a. theaveIs a steady determination signal within the sampling interval, satisfies Aave∈[Amin,Amax]，Amin＞0，AmaxIs the highest pulse amplitude input to the receiver limited by the action of the limiter, u (-) represents a unit step function; t ispriThe pulse repetition interval PRI of radar pulse signal, tau pulse width PW, both of which vary with radar type, and T for the same radarpriτ is a fixed known parameter, and n (t) represents the additive white gaussian noise independent of the signal.
Further, the accumulation sum method includes:
firstly, setting a uniform detection threshold h;
secondly, calculating the sum of log-likelihood ratios; the likelihood ratio function is si，
Figure RE-GDA0003002473360000043
Figure RE-GDA0003002473360000044
Thirdly, obtaining a decision function through an accumulation and recursion iteration mode,
Figure RE-GDA0003002473360000045
the fourth step, judging the discrete AaveDetecting whether GLRT meets a threshold condition or not by using a generalized likelihood function ratio corresponding to the estimated value; whether the sum of the cumulative log-likelihood ratios is equal to or greater than a threshold value;
and fifthly, stopping iteration when the threshold value is larger than or equal to the threshold value.
Further, the radar pulse amplitude statistic accumulation iterative GLRT method comprises the following steps:
when the number of samples tends to infinity, the unknown parameter A is correctedaveWill progressively converge to a least-square unbiased MVU estimate with a generalized log-likelihood ratio of
Figure RE-GDA0003002473360000051
Figure RE-GDA0003002473360000052
The stopping criterion is
T*＝ess inf{k:gk≥h}；
The probability density function PDF of the received signal sequence is
Figure RE-GDA0003002473360000053
In the above formula, N is the number of samples, σ2Is known as white Gaussian noise n (t)The variance of (c).
Further, the accumulation and method parallel accumulation and CUSUM method iterative solution comprises:
setting a uniform detection threshold h, judging that the radar pulse signal is reliably detected when the sum of the cumulative log-likelihood ratios is equal to or greater than the threshold h, and designating this time as a stop time T*I.e. the stopping criterion of the accumulation sum method is
T*＝ess inf{k:Sk≥h}；
In the above formula, ess inf {. cndot } represents an intrinsic infinitive sign, and the decision function SkIs composed of
Figure RE-GDA0003002473360000054
Likelihood ratio function siIs defined as
Figure RE-GDA0003002473360000055
In the above formula, the first and second carbon atoms are,
Figure RE-GDA0003002473360000056
when H occurs1Event and AaveFor the probability density function PDF when known,
Figure RE-GDA0003002473360000057
to generate H0Probability density function PDF at event; let T be0When the decision criterion occurs at the 0 th moment, the decision criterion is defined as
d＝sup(si,0)；
In the above formula, sup (-) denotes a supremum symbol; for on-line real-time calculation, a recursive iterative form solution is written to obtain
Figure RE-GDA0003002473360000061
And S 00; recursive iterative formSolve at hypothesis AaveThe fastest detection solution obtained when the solution is accurately known;
when A isaveWhen unknown, [ A ]min,Amax]Divided into m sufficiently fine equally spaced grids, then m +1 discrete values are represented as
Aave,j,j＝1,2,…,m+1；
And A isave,1＝Amin，Aave,n+1＝AmaxThen the stopping criterion in the parallel accumulation and iteration method becomes
Figure RE-GDA0003002473360000062
Figure RE-GDA0003002473360000063
Figure RE-GDA0003002473360000064
J-th average amplitude Aave,jIs in the form of a recursive iterative solution of the decision function
Figure RE-GDA0003002473360000065
In the formula (I), the compound is shown in the specification,
Figure RE-GDA0003002473360000066
when H occurs1Event and Aave＝Aave,jThe probability density function PDF of time.
Another object of the present invention is to provide a detection control system for implementing radar pulse signals.
In summary, the advantages and positive effects of the invention are:
1) the invention can detect whether the radar works or not, can detect when the radar starts to work, and can realize the detection in the shortest time.
2) The reliability of the radar working state detection of the invention completely depends on the judgment of a user on a specific application environment, and the larger the set threshold value is, the higher the reliability is, but the longer the required detection time is.
3) The method can detect the signal change trend of the radar during working as soon as possible, and also provides the time when the signal changes during the working of the radar, which is decisive for the influence of wars.
4) Under the condition that the radar parameters are unknown, the invention provides a composite form combining parameter iterative estimation and a fastest detection recursion algorithm, which not only can estimate the unknown parameters of the radar on line, but also realizes the fastest online detection, and the fastest detection time depends on the number of samples and the signal-to-noise ratio, thereby bringing great convenience to the real-time calculation of engineering.
5) After the radar radiation source is detected on line and the estimation of the unknown parameters of the radar is obtained through synchronous iteration, the radar source can be accurately positioned, and the accurate attack of the fighting weapon is facilitated.
6) The invention only aims at the fastest detection and parameter estimation of the radar implemented by a single antenna, and the technical basis and principle of the invention can be easily expanded to the situation of an antenna array, thereby greatly improving the practical value of the invention in engineering.
In radar and electronic reconnaissance systems, the electromagnetic signals of an interested target area need to be continuously scanned and monitored so as to find abnormality and quickly detect radiation source signals which are suddenly started up, and the method has very important value and significance in both military fields and civil fields.
The present invention assumes that the Pulse Width (PW) and pulse repetition Period (PRI) of the radar pulse signal are known, and this information can be provided by intelligence agencies, which are parameters that determine magnitude and do not vary with distance, azimuth and time of the radar. The amplitude (a) of the radar pulse signal is unknown and varies with the range, time and azimuth of the radar. The traditional radar pulse signal Detection method firstly estimates the amplitude A, generally adopts a Generalized Likelihood Ratio Test (GLRT) or Maximum Likelihood Estimation (MLE) based method, then adopts a fastest Detection (Quickest Detection: QD) theory to detect the amplitude change time, and is a sequential method with a sequential execution sequence. GLRT or MLE are computationally expensive because they cannot perform fast iterative operations, and it is difficult for such strategies to perform fast detection and parameter estimation of targets simultaneously in real time in the context of the above-mentioned applications. The invention provides two methods, can carry out combined rapid detection and parameter estimation on the pulse radar signal, really integrates the thought of detection in estimation, and can realize online real-time rapid detection and parameter estimation under the condition of small samples.
Drawings
Fig. 1 is a flowchart of an iterative solution of a parallel accumulation sum (CUSUM) method according to an embodiment of the present invention.
Fig. 2 is a recursive flow chart of an iterative Generalized Likelihood Ratio (GLR) method provided by an embodiment of the present invention.
FIG. 3 is an estimated value of the mean amplitude of m +1 radar pulses at different SNR according to an embodiment of the present invention
Figure RE-GDA0003002473360000081
Fastest detection time T*Figure (a).
In the figure: (a) when the signal-to-noise ratio is 1dB, the pulse amplitude estimated value
Figure RE-GDA0003002473360000082
Fastest detection time T*(ii) a (b) When the signal-to-noise ratio is 5dB, the pulse amplitude estimated value
Figure RE-GDA0003002473360000083
Fastest detection time T*(ii) a (c) When the signal-to-noise ratio is 10dB, the pulse amplitude estimated value
Figure RE-GDA0003002473360000084
Fastest detection time T*。
FIG. 4 is a recursive solution, estimation, provided by an embodiment of the present invention using an iterative GLR method developed by the present inventionAverage value of radar pulse amplitude
Figure RE-GDA0003002473360000085
Fastest detection time T*Figure (a).
In the figure: (a) the detection threshold h is 400, under different signal-to-noise ratios, the pulse amplitude estimation value
Figure RE-GDA0003002473360000086
Fastest detection time T*(ii) a (b) The detection threshold h is 300, under different signal-to-noise ratios, the pulse amplitude estimation value
Figure RE-GDA0003002473360000087
Fastest detection time T*。
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Under the condition that parameters are unknown, the traditional NP criterion estimates unknown parameters, the calculated amount is too complex, the instantaneity cannot be met, and signals with rapid changes are difficult to detect in real time.
In order to solve the problems of the prior art, the following embodiments describe the present invention in detail.
The method for detecting the radar pulse signal provided by the embodiment of the invention comprises the following steps:
in the radar pulse signal detection, grid search is not carried out, the radar pulse amplitude statistic accumulation iterative GLRT method is embedded into the accumulation sum method by using the structural characteristics of the radar pulse signal, and online real-time joint detection and radar pulse amplitude estimation are synchronously realized.
As a preferred embodiment of the present invention, the method for detecting a radar pulse signal further includes:
handle [ Amin,Amax]Dividing the grid into m grids with equal intervals, and estimating by using a parallel accumulation and iteration method when m is large enoughCalculate out AaveDetecting a radar pulse signal; for new data set, continuously obtaining increment of GLRT by recursive iterative solution form of parallel accumulation and method when parallel accumulation and iterative solution are one discrete AaveWhen GLRT corresponding to the estimated value of (A) first meets a threshold condition, iteration is automatically stopped, and discrete AaveEstimate is the most accurate AaveAnd detecting a corresponding radar pulse signal.
In an embodiment of the present invention, the signal modeling involved in the method for detecting a radar pulse signal provided in the embodiment of the present invention includes:
the present invention illustrates the method and principles in a single antenna configuration, but this method can be easily extended to multiple antenna configurations, assuming that the receiving sensor is an antenna, which may be a multiple antenna or a single antenna configuration.
The invention first establishes a binary hypothesis problem: assuming that the signal received by the antenna is x (t) in the time slot t, the model of x (t) has two cases
Figure RE-GDA0003002473360000091
In the above formula, v represents the time T at which the change occurs at the v-th time0(change time), i.e. the radar pulse signal starts to appear steadily at time v, a represents the unknown radar pulse amplitude, the average pulse amplitude is measured
Figure RE-GDA0003002473360000092
AaveAs a function of the propagation distance between the receiving antenna and the radar radiation source target, etc. So the binary assumption equation (1) can be rewritten
Figure RE-GDA0003002473360000093
Suppose AaveIs a steady determination signal within the sampling interval, satisfies Aave∈[Amin,Amax]，Amin＞0，AmaxIs the highest pulse amplitude input to the receiver limited by the action of the limiter, u (-) represents a unit step function. T ispriIs the Pulse Repetition Interval (PRI) of the radar pulse signal, tau is the Pulse Width (PW), both of which vary with radar type, but for the same radar, let T be assumedpriτ is a fixed known parameter, and n (t) represents additive white gaussian noise, which is independent of the signal.
In an embodiment of the present invention, a method for detecting a radar pulse signal provided in an embodiment of the present invention includes:
1) one method is to mix [ A ]min,Amax]The method is divided into m grids with equal intervals, and the method can accurately estimate A by utilizing a parallel accumulation and iteration method as long as m is large enoughaveAnd the radar pulse signal can be detected quickly. For a new data set, the likelihood function is definitely changed, but the invention does not need to reuse the grid method for searching, and continuously obtains the increment of GLRT through the recursive iterative solution form of parallel accumulation and method when a discrete A in the parallel accumulation and iterative solutionaveWhen GLRT corresponding to the estimated value of (A) first meets a threshold condition, iteration is automatically stopped, and the discrete AaveThe estimate is the most accurate AaveThe corresponding radar pulse signal is detected fastest. The other method is characterized in that a grid search method is not needed, structural features of radar pulse signals are developed, a radar pulse amplitude statistic accumulation iterative GLRT method is provided and is embedded into an accumulation sum method, and online real-time combined fastest detection and radar pulse amplitude estimation are synchronously realized.
In the embodiment of the present invention, the iterative solution of the parallel accumulation sum (CUSUM) method includes:
setting a uniform detection threshold h (the threshold is related to false alarm probability), and judging that the radar pulse signal is reliably detected when the sum of the cumulative log-likelihood ratios is equal to or greater than the threshold h, wherein the moment is called stop time T*(Stopping time), i.e. the cumulative sumThe stopping criterion of the method is
T*＝ess inf{k:Sk≥h} (3)
In the above formula, ess inf {. cndot } represents an intrinsic infinitive sign, and the decision function SkIs composed of
Figure RE-GDA0003002473360000101
Likelihood ratio function siIs defined as
Figure RE-GDA0003002473360000102
In the above formula, the first and second carbon atoms are,
Figure RE-GDA0003002473360000103
when H occurs1Event and AaveAs a Probability Density Function (PDF) when known,
Figure RE-GDA0003002473360000104
to generate H0Probability Density Function (PDF) at event. Due to the invention to T0Do not estimate and for unknown amplitude AaveIs estimated and T0The previous data are not related, so without loss of generality, the invention assumes T0When the decision criterion occurs at the 0 th moment, the decision criterion is defined as
d＝sup(si,0) (6)
In the above formula, sup (-) denotes a supremum symbol. For on-line real-time calculation, writing (4) into a recursive iterative form solution to obtain
Figure RE-GDA0003002473360000111
And S 00. The recursive iterative formal solution is described above under the assumption AaveIs the fastest detection solution obtained when accurately known. When A isaveWhen unknown, the invention willmin,Amax]Is divided into m feetA fine enough grid of equal intervals, then m +1 discrete values are represented as
Aave,j,j＝1,2,…,m+1 (8)
And A isave,1＝Amin，Aave,n+1＝AmaxThen the stopping criterion in the parallel accumulation and iteration method becomes
Figure RE-GDA0003002473360000112
Figure RE-GDA0003002473360000113
Figure RE-GDA0003002473360000114
J-th average amplitude Aave,jIs in the form of a recursive iterative solution of the decision function
Figure RE-GDA0003002473360000115
In the formula (I), the compound is shown in the specification,
Figure RE-GDA0003002473360000116
when H occurs1Event and Aave＝Aave,jProbability Density Function (PDF). In the invention, the structural characteristics of radar pulse signals are developed, and a statistic accumulation iteration GLRT method is provided, namely an estimation AaveThe iterative incremental MLE method is embedded into an accumulation sum method, and online real-time combined fastest detection and radar pulse amplitude estimation are synchronously realized.
As shown in fig. 1, an iterative solution of a parallel accumulation sum (CUSUM) method provided by an embodiment of the present invention includes:
a uniform detection threshold h (this threshold is related to the false alarm probability) is set S101.
S102, calculating pairsThe sum of the number likelihood ratios. The likelihood ratio function is si，
Figure RE-GDA0003002473360000121
Figure RE-GDA0003002473360000122
S103, obtaining a decision function of the order of the first time through an accumulation and recursion iteration form,
Figure RE-GDA0003002473360000123
s104, judging the discrete AaveAnd detecting whether GLRT meets a threshold condition or not by using the generalized likelihood function ratio corresponding to the estimated value. I.e., whether the sum of the cumulative log-likelihood ratios is equal to or greater than a threshold value.
And S105, stopping iteration when the threshold value is larger than or equal to the threshold value.
2) In an embodiment of the invention, a recursive solution of an iterative Generalized Likelihood Ratio (GLR) method comprises:
the maximum likelihood ratio estimation (MLE) is characterized by the fact that the unknown parameter A is estimated when the number of samples tends to infinityaveWill progressively converge to a least-square unbiased (MVU) estimate when the generalized log-likelihood ratio becomes
Figure RE-GDA0003002473360000124
Figure RE-GDA0003002473360000125
The stopping criterion is
T*＝ess inf{k:gk≥h} (15)
To derive a solution to the cumulative sum (CUSUM) method and to eliminate the high complexity and non-existence of traditional MLE due to high-dimensional computationThe invention develops the equation (2) in which H is1Under the condition of AaveThe statistic calculation structure of (1), can be applied to AavePerforming iterative statistic accumulation calculation without performing AaveA high complexity MLE estimation is performed. The Probability Density Function (PDF) of the received signal sequence is
Figure RE-GDA0003002473360000126
In the above formula, N is the number of samples, σ2Is the variance of known white gaussian noise n (t). Taking log-likelihood function about AaveDerivative of (A) to
Figure RE-GDA0003002473360000131
Make it equal to zero to obtain MLE
Figure RE-GDA0003002473360000132
MLE is an effective estimator. Forming (18) into a recursive solution form
Figure RE-GDA0003002473360000133
And is
Figure RE-GDA0003002473360000134
Therefore, when the detection threshold h → ∞ is detected, that is, the number of samples N → ∞ is detected, the detection threshold is obtained by the formula (19)
Figure RE-GDA0003002473360000135
Is a progressive unbiased optimal estimator, so equation (19) provides an estimation method of an unknown parameter iterative MLE for the specific research problem of the invention. Handle
Figure RE-GDA0003002473360000136
Embedded in the accumulation sum method (13) to (15) to obtain
T*＝ess inf{k:Sk≥h}(20)
Figure RE-GDA0003002473360000137
As shown in fig. 2, the parallel computing process can be briefly described as follows:
s201, the number of samples tends to be infinite, and the average pulse amplitude AaveThe estimate of (c) will converge progressively. A generalized log-likelihood ratio of
Figure RE-GDA0003002473360000138
S202, for H1Average pulse amplitude A under the conditionsaveStatistics calculation Structure, pair AaveAnd performing iterative statistic cumulative calculation.
Figure RE-GDA0003002473360000139
S203, taking the log likelihood function about the average pulse amplitude AaveThe derivative of (a) of (b),
Figure RE-GDA00030024733600001310
s104 relating the log-likelihood function to the average pulse amplitude AaveIs equal to 0, the MLE maximum likelihood estimate is calculated, quantized to a recursive solution,
Figure RE-GDA0003002473360000141
S205:
Figure RE-GDA0003002473360000142
threshold value h → ∞ embedded in the accumulation sum method to obtain
Figure RE-GDA0003002473360000143
A progressive unbiased optimal estimator.
Figure RE-GDA0003002473360000144
Compared with the first inventive method, this method does not require grid search, i.e. is very suitable for applications where there is no a priori knowledge of the pulse amplitude. The two methods provided by the invention can synchronously realize online combined fastest detection and pulse amplitude estimation, and the second method can carry out iterative estimation and can also achieve progressive optimization.
The invention is further described below in connection with simulation analysis.
Experiment 1: in the experiment, the invention sets the detection threshold h as 280 and the true value of the mean value of the pulse amplitude as Aave＝2.6，Amin＝1.0，AmaxThe invention uses the average value of 1000 Monte Carlo simulation results as the performance comparison basis, and the estimated value of the average value of m +1 radar pulse amplitudes under different SNR
Figure RE-GDA0003002473360000145
Fastest detection time T*As shown in fig. 3. Fig. 3 (a): pulse amplitude estimation at a signal-to-noise ratio of 1dB
Figure RE-GDA0003002473360000146
Fastest detection time T*. Fig. 3 (b): pulse amplitude estimation at 5dB SNR
Figure RE-GDA0003002473360000147
Fastest detection time T*. Fig. 3 (c): pulse amplitude estimation at a signal-to-noise ratio of 10dB
Figure RE-GDA0003002473360000148
Fastest detection time T*。
As can be seen from the simulation results in FIG. 3, the iterative solution of the first method proposed in the present invention, namely the parallel accumulation sum (CUSUM) method, can not only accurately and stably estimate the unknown pulse amplitude
Figure RE-GDA0003002473360000149
And near the accurate estimation value, the fastest detection time is shortest, so that the 'detection in estimation' is really realized. On the other hand, the invention also shows that under the condition that the detection threshold is not changed, the fastest detection time is less and less along with the increase of the signal-to-noise ratio, and the improvement of the signal-to-noise ratio can obviously increase the value of the decision function, so that the detection threshold is quickly approached, and the fastest detection time is faster. This method is particularly suitable for use when there is a priori knowledge of the pulse amplitude.
Experiment 2: in the experiment, the detection threshold h set by the invention is 300,400, and the true value of the pulse amplitude mean value is AaveThe signal-to-noise ratio is set to-10 dB, -5dB,0dB,5dB and 10dB respectively, the average value of 1000 Monte Carlo simulation results is used as a performance comparison reference basis, and the estimated mean value of the radar pulse amplitude is estimated by using the recursion solution of the iterative GLR method developed by the invention under different signal-to-noise ratios
Figure RE-GDA0003002473360000151
Fastest detection time T*As shown in fig. 4. Fig. 4 (a): the detection threshold h is 300, under different signal-to-noise ratios, the pulse amplitude estimated value
Figure RE-GDA0003002473360000152
Fastest detection time T*. Fig. 4 (b): the detection threshold h is 400, under different signal-to-noise ratios, the pulse amplitude estimated value
Figure RE-GDA0003002473360000153
Fastest detection time T*。
For the recursive solution of the iterative GLR method, in order to achieve the gradual unbiased estimation performance of the radar pulse amplitude mean, either the detection threshold h is required to be large enough, or the system is required to work under a low signal-to-noise ratio, so that the purpose of obtaining a sufficient number of sample samples is required to facilitate the gradual unbiased estimation performance of the radar pulse amplitude mean
Figure RE-GDA0003002473360000154
The estimation of the method achieves the performance of gradual unbiased estimation, and only the pairing solution obtained by solving the method
Figure RE-GDA0003002473360000155
Is optimal. The second inventive method is therefore particularly suitable for: is not provided with
Figure RE-GDA0003002473360000156
A priori knowledge of the signal to noise ratio, and very low signal to noise ratio.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (8)

1. A method for detecting a radar pulse signal, the method comprising:
in the radar pulse signal detection, grid search is not carried out, the radar pulse amplitude statistic accumulation iterative GLRT method is embedded into the accumulation sum method by using the structural characteristics of the radar pulse signal, and online real-time joint detection and radar pulse amplitude estimation are synchronously realized.
2. The method of detecting a radar pulse signal according to claim 1, wherein the method of detecting a radar pulse signal further comprises:
handle [ Amin,Amax]Dividing the grid into m grids with equal intervals, and estimating A by using a parallel accumulation and iteration method when m is large enoughaveDetecting a radar pulse signal; for new data set, continuously obtaining increment of GLRT by recursive iterative solution form of parallel accumulation and method when parallel accumulation and iterative solution are one discrete AaveWhen GLRT corresponding to the estimated value of (A) first meets a threshold condition, iteration is automatically stopped, and discrete AaveEstimate is the most accurate AaveAnd detecting a corresponding radar pulse signal.
3. The method for detecting a radar pulse signal according to claim 1, wherein the method for detecting a radar pulse signal specifically includes:
step one, the number of samples tends to infinity, and the average pulse amplitude AaveWill converge progressively; a generalized log-likelihood ratio of
Figure RE-FDA0003002473350000011
Step two, for H1Average pulse amplitude A under the conditionsaveStatistics calculation Structure, pair AaveCarrying out iteration statistic cumulative calculation;
Figure RE-FDA0003002473350000012
step three, taking the average pulse amplitude A of the log-likelihood functionaveThe derivative of (a) of (b),
Figure RE-FDA0003002473350000013
step four, making the log-likelihood function related to the average pulse amplitude AaveIs equal to 0, the MLE maximum likelihood estimate is calculated, quantized to a recursive solution,
Figure RE-FDA0003002473350000014
in the fifth step, the step of,
Figure RE-FDA0003002473350000021
threshold value h → ∞ embedded in the accumulation sum method to obtain
Figure RE-FDA0003002473350000022
Gradual unbiased optimal estimator;
Figure RE-FDA0003002473350000023
4. the radar pulse signal detection method according to claim 1,
the radar pulse signal has a structural characteristic of H1Under the condition of AaveStatistics calculation structure of (1):
Figure RE-FDA0003002473350000024
in the above formula, v represents the time T at which the change occurs at the v-th time0(change time) the radar pulse signal starts to appear steadily at time v, A represents the unknown radar pulse amplitude, and the average pulse amplitude is measured
Figure RE-FDA0003002473350000025
AaveVaries with the propagation distance between the receiving antenna and the radar radiation source target, etc.; a. theaveIs a steady determination signal within the sampling interval, satisfies Aave∈[Amin,Amax]，Amin＞0，AmaxIs the highest pulse amplitude input to the receiver limited by the action of the limiter, u (-) represents a unit step function; t ispriThe pulse repetition interval PRI of radar pulse signal, tau pulse width PW, both of which vary with radar type, and T for the same radarpriτ is a fixed known parameter, and n (t) represents the additive white gaussian noise independent of the signal.
5. The method of detecting a radar pulse signal according to claim 1, wherein the accumulation sum method includes:
firstly, setting a uniform detection threshold h;
secondly, calculating the sum of log-likelihood ratios; the likelihood ratio function is si，
Figure RE-FDA0003002473350000026
Figure RE-FDA0003002473350000027
Thirdly, obtaining a decision function through an accumulation and recursion iteration mode,
Figure RE-FDA0003002473350000031
the fourth step, judging the discrete AaveDetecting whether GLRT meets a threshold condition or not by using a generalized likelihood function ratio corresponding to the estimated value; whether the sum of the cumulative log-likelihood ratios is equal to or greater than a threshold value;
and fifthly, stopping iteration when the threshold value is larger than or equal to the threshold value.
6. The method of detecting a radar pulse signal of claim 1, wherein the radar pulse amplitude statistic accumulating iterative GLRT method comprises:
when the number of samples tends to infinity, the unknown parameter A is correctedaveWill progressively converge to a least-square unbiased MVU estimate with a generalized log-likelihood ratio of
Figure RE-FDA0003002473350000032
Figure RE-FDA0003002473350000033
The stopping criterion is
T*＝ess inf{k:gk≥h}；
The probability density function PDF of the received signal sequence is
Figure RE-FDA0003002473350000034
In the above formula, N is the number of samples, σ2Is the variance of known white gaussian noise n (t).
7. The radar pulse signal detection method of claim 2, wherein the accumulation and method parallel accumulation and CUSUM method iterative solution comprises:
setting a uniform detection threshold h, judging that the radar pulse signal is reliably detected when the sum of the cumulative log-likelihood ratios is equal to or greater than the threshold h, and designating this time as a stop time T*I.e. the stopping criterion of the accumulation sum method is
T*＝ess inf{k:Sk≥h}；
In the above formula, ess inf {. cndot } represents an intrinsic infinitive sign, and the decision function SkIs composed of
Figure RE-FDA0003002473350000041
Likelihood ratio function siIs defined as
Figure RE-FDA0003002473350000042
In the above formula, the first and second carbon atoms are,
Figure RE-FDA0003002473350000043
when H occurs1Event and AaveFor the probability density function PDF when known,
Figure RE-FDA0003002473350000044
to generate H0Probability density function PDF at event; let T be0When the decision criterion occurs at the 0 th moment, the decision criterion is defined as
d＝sup(si,0)；
In the above formula, sup (-) denotes a supremum symbol; for on-line real-time calculation, a recursive iterative form solution is written to obtain
Figure RE-FDA0003002473350000045
And S00; recursive iterative formal solution on hypothesis AaveThe fastest detection solution obtained when the solution is accurately known;
when A isaveWhen unknown, [ A ]min,Amax]Divided into m sufficiently fine equally spaced grids, then m +1 discrete values are represented as
Aave,j,j＝1,2,…,m+1；
And A isave,1＝Amin，Aave,n+1＝AmaxThen the stopping criterion in the parallel accumulation and iteration method becomes
Figure RE-FDA0003002473350000046
Figure RE-FDA0003002473350000047
Figure RE-FDA0003002473350000048
J-th average amplitude Aave,jIs in the form of a recursive iterative solution of the decision function
Figure RE-FDA0003002473350000049
In the formula (I), the compound is shown in the specification,
Figure RE-FDA00030024733500000410
when H occurs1Event and Aave＝Aave,jThe probability density function PDF of time.
8. A radar pulse signal detection control system for implementing the radar pulse signal detection method according to claim 1.
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