CN102279399A - Dim target frequency spectrum tracking method based on dynamic programming - Google Patents

Abstract

The invention relates to a dim target frequency spectrum tracking method based on dynamic programming. In the method, data association and track detection are completed on a dim target submerged in background noise in a frequency spectrum tracking form. The method comprises the following steps of: determining a line spectrum searching range, calculating all feasible track scores in a line spectrum searching region in a line spectrum distribution form, determining a highest score state as an optimal line spectrum track for the termination of the state, and recovering a line spectrum track by forwardly tracking a state value obtained at each processing stage; and finishing data interconnection and track detection in a single optimizing process by using a dynamically-programmed line spectrum tracking method, so that the identification sensitivity of a target frequency spectrum is enhanced and the detection and tracking of a dim signal are further completed. A score function in practical work is in an additive form, and the score value of a state transition path is calculated by accumulating transition scores. During working, a line spectrum score function is combined with a generalized likelihood ratio, so that the nongaussian noise processing capability is enhanced.

Description

A kind of weak target frequency spectrum tracking based on dynamic programming

Technical field

The present invention relates to microphone array signal processing technology field, particularly a kind of weak target frequency spectrum tracking based on dynamic programming.

Background technology

The walkaway of air high speed moving target is the problem that receives much concern always.The airborne noise of high-speed moving object detects and exists signal to noise ratio (S/N ratio) low, and the big grade of noise line spectrum Doppler shift is difficult for the problem of detection and tracking.Because for moving target, when having relative motion between sound source and the receiving sensor, there is Doppler shift in the signal that sensor receives.Because THE VELOCITY OF SOUND IN AIR velocity of sound in the water, so the signal Doppler shift that sensor received when moving target was measured in air is bigger nearly about 5 times than measurement result in the water, the target speed of related movement is big more, frequency is high more, and Doppler shift is just big more so.Though big Doppler shift is beneficial to the evaluating objects kinematic parameter, the propagation attenuation of sound wave is bigger in the air, is directly proportional with target frequency simultaneously, and the high more acoustic attenuation of frequency is big more, and received signal to noise ratio is low more.

Big Doppler shift and low signal-to-noise ratio have brought difficulty to target detection, make that general line spectrum enhancement techniques result of use is relatively poor.Usually in the low signal-to-noise ratio environment faint motion target detection is adopted self-adaptation line spectrum enhancement techniques.Self-adaptation line spectrum Enhancement Method is the adjustable narrow band filter of a kind of centre frequency from frequency domain, can make system output signal center line spectral component have bigger signal to noise ratio (S/N ratio) effectively.But there is the slow and weak shortcoming of inhibition Gaussian noise ability of speed of convergence.In some nonlinear system, the accidental resonance technology is that signal energy reaches the effect that improves output signal-to-noise ratio by the transform portion noise energy.Self-adaptation line spectrum Enhancement Method based on Higher Order Cumulants has the ability that suppresses gaussian colored noise more by force.But they are when following the tracks of the big Doppler's line spectrum of low signal-to-noise ratio signal, and simulation result shows: said method faces the shortcoming that tracking performance is relatively poor, calculated amount is big.

Summary of the invention

The objective of the invention is to, the present invention proposes a kind of weak target frequency spectrum tracking based on dynamic programming, so that improve because clutter pollutes and the identification sensitivity of ambiguous target spectrum.

For achieving the above object, a kind of weak target frequency spectrum tracking based on dynamic programming, this method is finished data association and track detection to the weak target that is submerged in the ground unrest by frequency spectrum tracking form; At first determine the line spectrum hunting zone, according to the spectral profile form, the feasible track score of all in the calculating line spectral region of search, the top score state can be defined as the optimum line spectrum track that this state stops, by follow the trail of forward each the processing stage state value that drawn, can recover the line spectrum track; The concrete steps of this method comprise:

Step 1): obtain the microphone array data-signal, the data-signal that receives is carried out pre-service, then the time-frequency spectrum of signal calculated;

Step 2): determine the band limits that line spectrum is followed the tracks of according to the time-frequency spectrum distribution of described step 1) acquisition and the priori of target noise, and determine the track-while-scan zone thus;

Step 3): according to described step 2) the line spectrum energy in the track-while-scan zone that obtains is determined line spectrum intensity detection threshold value; With line spectrum intensity detection threshold value serves as according to the start-stop moment of judging that line spectrum is followed the tracks of;

Step 4): priori and movement velocity thereof according to target are estimated its Doppler shift size, determine the spectral trace distribution function;

Step 5): the spectral trace distribution function of determining according to described step 4) carries out line spectrum detection tracking; In the spectrogram of time-frequency spectrum, line spectrum is represented signal formed track of amplitude peak in the frequency domain scope.Accumulate the inevitable maximum of gained signal energy along target trajectory, definable line spectrum tracking problem for finding the solution the decision problem of optimum state metastasis sequence, promptly by trying to achieve branch functional K (J) maximal value, obtains the line spectrum variation track thus.

$K\left(J\right)=\underset{J}{\max }K\left(J\right)---\left(1\right)$

J={s (0) wherein, s (1) ..., s (n) }.S (i) represents i target spectrum state vector constantly, satisfies Markovian process;

The new breath of target spectrum state is pressed markov random walk process model building, solve the exhaustive search problem of target detection by the segmentation optimization.For first order modeling, the omnidistance score functional of line spectrum track J can be decomposed into

$K\left(J\right)=g_1(s\left(0\right),s\left(1\right))+g_2(s\left(1\right),s\left(2\right))+...+g_n(s(n-1),s\left(n\right))=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{g}_i(s(i-1),s\left(i\right))---\left(2\right)$

$K\left(J\right)=\underset{J}{\max }K\left(J\right)=\underset{s\left(n\right)}{\max }\left[\underset{s(n-1)}{\max }\right[g_n(s(n-1),s\left(n\right))+\underset{s(n-2)}{\max }[g_{n-1}(s(n-2),s(n-1))+---\left(3\right)$

$...+\underset{s\left(1\right)}{\max }\left[\begin{array}{cc}{g}_2(s\left(1\right),s\left(2\right))+\underset{s\left(0\right)}{\max }& g_1(s\left(0\right),s\left(1\right))\end{array}\right]\·\·\·\left]\right]]$

In formula (2) and the formula (3), the score functional of the n time search when gn represents linear search.Dynamic programming solution procedure formula (3) specifically can be calculated stage by stage by formula (4), formula (5) and formula (6):

$K_0\left(s\left(1\right)\right)=\underset{s\left(0\right)}{\max }{g}_1(s\left(0\right),s\left(1\right))---\left(4\right)$

$K_{i-1}\left(s\left(i\right)\right)=\underset{s(i-1)}{\max }[g_i(s(i-1),s\left(i\right))+K_{i-2}\left(s(i-1)\right)]---\left(5\right)$

$K\left(J\right)=\underset{s\left(n\right)}{\max }{K}_{n-1}\left(s\left(n\right)\right)---\left(6\right)$

The design of line spectrum tracing process score functional K (J) is defined as based on the posteriority detection probability

$K\left(J\right)=\log \left[\frac{P_{n|n}(s\left(0\right),s\left(1\right),...,s\left(n\right)|Z^n)}{P_{n|n}\left(H_0\right|Z^n)}\right]---\left(7\right)$

In the formula (7), definition H ₁=s (0), s (1) ...., s (n) } be to be the hypothesis that the specific line spectrum track of termination occurs with state s (n) up to n observation cycle, H ₀Be zero line spectrum hypothesis, Z ⁿIt is the metric data collection till n the observation cycle; The score functional of above type is considered simultaneously and is supported and oppose the situation that target occurs.

Formula (7) is used the Bayes principle and utilized single order Markov model characteristic, and final the derivation obtains the score functional expression formula of recursive form:

$K_{i-1}\left(s\left(i\right)\right)=\log \left[\frac{P\left(Z^i\right|s\left(i\right))}{P\left(Z^i\right|H_0)}\right]+\underset{s(i-1)}{\max }[\log P\left(s\left(i\right)\right|s(i-1))+K_{i-2}\left(s(i-1)\right)]---\left(12\right)$

In the formula (12), K _I-1(s (i)) is the feasible line spectrum track score that stops with state s (i) in the i step.The search of s (i) got in s (i-1) quantized value is no more than the rectangular neighborhood of Doppler shift Δ f resolution unit carry out.A stage i in office by the state of search generation top score, can determine the most probable line spectrum track that stops at this state.

Step 6): the state of determining according to described step 5) stops most probable line spectrum track constantly.By follow the trail of forward each the processing stage the high state value that drawn recover line spectrum track history, finish the tracing process that target spectrum changes.

In the described step 1), pre-service mainly comprises data filtering.According to priori design low-pass filter, the outer clutter of filtering band.

In the described step 1), to the cyclic spectrum of digital signal according to the following formula signal calculated;

$S\left(e^{\mathrm{jw}}\right)=\frac{{\left|\underset{l=1}{\overset{n}{\mathrm{\Σ}}}{x}_l\left(e^{-\mathrm{jwl}}\right)\right|}^2}{n}$

Wherein, x _l(e ^-jwl) be the Fourier transform of described data-signal, l is discrete data sequence l ∈ [1 n].

The invention has the advantages that the line spectrum tracking by dynamic programming utilizes a kind of single optimizing process to finish the interconnected and track of data and surveys, thus the identification sensitivity that improves target spectrum, and then finish Detection of weak and tracking.Score functional in the real work can add form, and the score value that gets of a bar state transfer path is calculated by each score that shifts that adds up.In the work line spectrum track score functional is combined with Generalized Likelihood Ratio to strengthen the ability that it handles non-Gaussian noise.

Description of drawings

Fig. 1 is the line spectrum track following algorithm flow chart based on dynamic programming;

Fig. 2 sensor for speaker measurement aircraft noise frequency spectrum the time lays synoptic diagram

Fig. 3 is that certain type helicopter is crossed the frequency spectrum course in the flight course of top;

Fig. 4 is the time-frequency spectrum after certain type helicopter is handled based on dynamic programming algorithm.

Embodiment

Describe the present invention below in conjunction with accompanying drawing and instantiation.

In fact the line spectrum tracking problem can be regarded as a multistage decision optimization problem, and this problem can be found the solution with dynamic programming algorithm.PROBLEM DECOMPOSITION with research during processing is the several subproblems that interknit.Value at each certain variable of stage requirement selection makes overall process reach optimum by given criterion.Dynamic programming method does not use pre-thresholding wave filter, keeps all the weak signal information in the original metric data.This method utilizes a kind of single optimizing process to finish the interconnected and flight path detection of data, thereby improves because clutter pollutes and the identification sensitivity of ambiguous target spectrum.It comes the tracking signal frequency spectrum by the exhaustive search of all the feasible state transition paths on the signal time-frequency combination is distributed.Show the robustness that target spectrum is existed big doppler phenomenon.State transitions sequence score functional can add form in the algorithm, and the score value that gets of a bar state transfer path is calculated by each score that shifts that adds up.Utilize the markov single order model theory of moving about that higher-dimension score functional is decomposed into one group of one dimension or low-dimensional functional sum, can effectively reduce calculated amount.

Based on epimere statement, characteristics of the present invention are: signal line spectrum enhancing problem is converted into the optimization problem of a multistage decision, adopts dynamic programming algorithm to handle; And the detection and tracking of target line spectrum are merged into the single optimizing process that relates to line spectrum variation track, ground unrest and clutter statistical model.Specifically, at first determine the line spectrum hunting zone, according to the spectral profile form, the feasible track score of all in the calculating line spectral region of search, the top score state can be defined as the most probable line spectrum track that this state stops.By follow the trail of forward each the processing stage optimum state value that drawn, can recover the line spectrum track.

A kind of weak target frequency spectrum tracking process flow diagram based on dynamic programming, as shown in Figure 1.Comprise in conjunction with Fig. 1 detailed process:

Step 10), obtain the microphone array data-signal, the time-frequency spectrum of signal calculated distributes;

Step 20), determine the band limits that line spectrum is followed the tracks of, and determine the track-while-scan zone thus according to priori.

Step 30), according to line spectrum intensity detection threshold value, judge that start-stop that line spectrum follows the tracks of is constantly.

Step 40), according to the priori of target noise, determine the spectral trace distribution function.

Step 50), to all the feasible state transition paths in the line spectrum region of search, promptly the line spectrum track carries out exhaustive search, determines at the most probable track of following the tracks of under the final state;

Step 60), pass through forward direction back tracking method, recovery line spectrum track course.

Wherein, step 10) also comprises: the data-signal that receives is carried out pre-service, the logarithm period spectrum of signal calculated.

Wherein, step 10) is used formula Calculate the cyclic spectrum feature of described data-signal, x _l(e ^-jwl) be the Fourier transform of described data-signal, l is discrete data sequence l ∈ [1n].

Wherein, step 50) function described in comprises finds the solution the state transitions sequence, i.e. line spectrum track J={s (0), and s (1) ..., s (n-1) }, and make score functional K (J) maximum of sequence.

$K\left(J\right)=\underset{J}{\max }K\left(J\right)$

1, line spectrum increased dynamic planning form

In the spectrogram of time-frequency spectrum, line spectrum is the sequence of a continuous point, its expression signal formed track of amplitude peak in the frequency domain scope.It is inevitable maximum to accumulate the gained energy along target trajectory, and definable line spectrum tracking problem for finding the solution the decision problem of optimum state metastasis sequence, promptly by trying to achieve branch functional K (J) maximal value, obtains the line spectrum variation track thus.

$K\left(J\right)=\underset{J}{\max }K\left(J\right)---\left(1\right)$

J={s (0) wherein, s (1) ..., s (n) }.S (i) represents i target spectrum state vector constantly, satisfies Markovian process.During the track-while-scan of target line spectrum, definition i region of search constantly is R (i); When finding the solution dynamic programming line spectrum tracing process exact solution, generally must all line spectrum tracks of limit.To the situation of m value quantification state, n observation cycle, feasible acquisition track number is m ⁿ, calculated amount is with the increase exponential increase of observation data.

The new breath of target spectrum state is pressed markov random walk process model building, solve the exhaustive search problem of target detection by the segmentation optimization.For first order modeling, the omnidistance score functional of line spectrum track J can be decomposed into:

$K\left(J\right)=g_1(s\left(0\right),s\left(1\right))+g_2(s\left(1\right),s\left(2\right))+...+g_n(s(n-1),s\left(n\right))=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{g}_i(s(i-1),s\left(i\right))---\left(2\right)$

Then

$K\left(J\right)=\underset{J}{\max }K\left(J\right)=\underset{s\left(n\right)}{\max }\left[\underset{s(n-1)}{\max }\right[g_n(s(n-1),s\left(n\right))+\underset{s(n-2)}{\max }[g_{n-1}(s(n-2),s(n-1))+---\left(3\right)$

$...+\underset{s\left(1\right)}{\max }\left[\begin{array}{cc}{g}_2(s\left(1\right),s\left(2\right))+\underset{s\left(0\right)}{\max }& g_1(s\left(0\right),s\left(1\right))\end{array}\right]\·\·\·\left]\right]]$

Wherein, g _nThe score functional of the n time search when representing linear search.Dynamic programming solution procedure formula (3) computation process is stage by stage described by formula (4), formula (5) and formula (6):

$K_0\left(s\left(1\right)\right)=\underset{s\left(0\right)}{\max }{g}_1(s\left(0\right),s\left(1\right))---\left(4\right)$

$K_{i-1}\left(s\left(i\right)\right)=\underset{s(i-1)}{\max }[g_i(s(i-1),s\left(i\right))+K_{i-2}\left(s(i-1)\right)]---\left(5\right)$

$K\left(J\right)=\underset{s\left(n\right)}{\max }{K}_{n-1}\left(s\left(n\right)\right)---\left(6\right)$

The calculated amount of above dynamic programming solution procedure after by markov random walk process model building is decomposed into n linear search problem by the n dimension search of describing in the formula (1), each quantized value to the target spectrum state, the calculated amount of this linear search is proportional to m, and the amount of calculation is proportional to m ²N.Saved m than exhaustive search ^N-2/ n the time doubly.

2, the design of score functional and corresponding dynamic planning solution

The design of line spectrum tracing process scoring function is defined as based on the posteriority detection probability

$K\left(J\right)=\log \left[\frac{P_{n|n}(s\left(0\right),s\left(1\right),...,s\left(n\right)|Z^n)}{P_{n|n}\left({\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000407558600013.png,HSA00000407558600014.png"\; state="\{\{state\}\}">H</figure-callout>}}_0\right|Z^n)}\right]---\left(7\right)$

Wherein, H ₁=s (0), s (1) ..., s (n) } be to be the hypothesis that the specific objective line spectrum track of termination occurs with state s (n) up to n observation cycle, H0 is a zero line spectrum hypothesis, Z ⁿIt is the metric data collection till n the observation cycle.The score functional of above type is considered support simultaneously and is opposed that situation appears in target.

Algorithm is at first used the Bayes principle to the molecule denominator of K (J) formula logarithmic function, and functional form becomes:

$\frac{P_{n|n}(s\left(0\right),s\left(1\right),...,s\left(n\right)|Z^n)}{P_{n|n}\left({\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000407558600013.png,HSA00000407558600014.png"\; state="\{\{state\}\}">H</figure-callout>}}_0\right|Z^n)}=\frac{P\left(Z^n\right|s\left(n\right))}{P\left(Z^n\right|H_0)}\&CenterDot;\frac{P_{n|n-1}(s\left(0\right),...,s\left(n\right)|Z^{n-1})}{P_{n-1|n-1}\left({\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000407558600013.png,HSA00000407558600014.png"\; state="\{\{state\}\}">H</figure-callout>}}_0\right|Z^{n-1})}---\left(8\right)$

Wherein, P (Z ⁿ| s (n)) and P (Z ⁿ| H ₀) be respectively under target line spectrum hypothesis and zero line spectrum assumed condition, the probability density of the metric data on the n observation cycle.Then to forward direction transition probability function P _N|n-1The definition of application conditions probability, P _N|n-1Satisfy:

P _n|n-1(s(0)，...，s(n)|Z ^n-1)＝P(s(n)|s(0)，...，s(n-1))P _n-1|n-1(s(0)，...，s(n-1)|Z ^n-1) (9)

Because the target spectrum state satisfies the single order markov model that moves about, so formula (9) can be written as:

P _n|n-1(s(0)，...，s(n)|Z ^n-1)＝P(s(n)|s(n-1))P _n-1|n-1(s(0)，...，s(n-1)|Z ^n-1) (10)

Formula (8) to formula (10) substitution formula (7), is obtained following recursive form:

$\log \left[\frac{P_{n|n}(s\left(0\right),s\left(1\right),...,s\left(n\right)|Z^n)}{P_{n|n}\left({\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000407558600013.png,HSA00000407558600014.png"\; state="\{\{state\}\}">H</figure-callout>}}_0\right|Z^n)}\right]=\log [\frac{P\left(Z^n\right|s\left(n\right))}{P\left({|Z}^n\right|H_0)}\&CenterDot;P\left(s\left(n\right)\right|s(n-1))\&CenterDot;\frac{P_{n-1|n-1}(s\left(0\right),...,s\left(n\right)|Z^{n-1})}{P_{n-1|n-1}\left({\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000407558600013.png,HSA00000407558600014.png"\; state="\{\{state\}\}">H</figure-callout>}}_0\right|Z^{n-1})}]---\left(11\right)$

According to formula (11), iterative algorithm formula (5) becomes:

$K_{i-1}\left(s\left(i\right)\right)=\log \left[\frac{P\left(Z^i\right|s\left(i\right))}{P\left(Z^i\right|H_0)}\right]+\underset{s(i-1)}{\max }[\log P\left(s\left(i\right)\right|s(i-1))+K_{i-2}\left(s(i-1)\right)]---\left(12\right)$

K _I-1(s (i)) is the score with the feasible line spectrum track of state s (i) termination in the i step.A stage i in office can determine the most probable line spectrum track that stops at this state by the state s (i) of search generation top score.By follow the trail of forward each the processing stage optimum state value that drawn, can return to the line spectrum track history till the i observation cycle.

3, the design of optimum search strategy

Formula (12) is carried out in certain suitably big or small neighborhood R (s (i-1)) of s (i-1) actual only need of the search of s (i), and this is enough little because suitably select R (s (i-1)) can make in the score of its outside, consequently can not cause high score.Follow the tracks of in the application at the target line spectrum, get R (s (i-1)) for be no more than the rectangular neighborhood of Doppler shift resolution unit around s (i-1) quantized value.

4, the determining of distribution function in the step 4)

The objective definition line spectrum measures model:

Wherein, A (i) is the true amplitude of target line spectrum, and w (i) is the additional noise of known statistical model, and n (i) is the random series of known statistical model.Target likelihood ratio then:

P(Z ⁱ|s(i))/P(Z ⁱ|H ₀)＝P _T(z(i)-A)/P _n(z(i))

Wherein, P _TAnd P _nBe respectively the amplitude distribution of line spectrum and noise, A is the valuation of line spectrum amplitude.

For simulating the output characteristics that some clutter suppresses module, P (z) adopts mixed Gaussian to distribute, then

P(Z ⁱ|s(i))/P(Z ⁱ|H ₀)＝[(1-ε)G ₁(z(i)-A)+εG ₂(z(i)-A)]/[(1-ε)G ₁(z(i))+εG ₂(z(i))] (13)

G _iBe the zero-mean Gaussian distribution, variance is

Common ε＜＜1, standard deviation sigma ₁＜＜σ ₂According to the line spectrum characteristic of target state, σ _iValue and the size of line spectrum Doppler shift be close.

The design of state transitions scoring function need be considered target line spectrum Doppler's variation characteristic.It is the function of mathematical expectation and line spectrum virtual condition absolute difference, promptly

log?P(s(i)|s(i-1))＝log?P(|s(i)-s(i|i-1)|) (14)

Wherein, step 60) behind the most probable line spectrum track of having determined under the final state N.By follow the trail of forward each the processing stage optimum state value that drawn, can return to the line spectrum track till the N observation cycle.

Certain type helicopter sea examination data instance analysis

Fig. 2 be in June, 2002 in the Tobago marine site far from the sea when 1 meter is with speaker measurement aircraft noise frequency spectrum sensor lay synoptic diagram.Noise spectrum when Fig. 3 crosses the top for aircraft, aircraft fundamental frequency 83.3Hz, spectral resolution 2.44Hz.Average flight speed 53m/s during test, 66 meters of flying heights.There is bigger Doppler shift in the aircraft line spectrum among the figure, and with tangible harmonic wave.Crossing top moment target and sensor does not have relative velocity, and the Doppler shift amount is zero.Aircraft is crossed the top and constantly is labeled as 0 among the figure, meets to fly over journey and be labeled as constantly negatively, and the backward flight process is labeled as the positive moment.

The main source of aircraft far-field radiation noise is that screw propeller rotates the air vibration noise that the disturbance air produces.The dominant frequency of propeller noise is relevant with the speed of blade rotation, is the periodicity of blade rotation p.s..Propeller noise comprises main screw rotational noise and empennage rotational noise.Frequency spectrum medium and low frequency section main screw rotational noise in the highest flight; The Mid Frequency noise mainly comes from tail-rotor rotational noise and harmonic wave thereof.The target flying speed is very fast, can cause bigger Doppler shift in the medium-high frequency section, can obtain target velocity and location parameter effectively according to the Doppler shift size.But useful signal almost completely was submerged in the ground unrest when neighbourhood noise was very big, needed the utilization dynamic programming method that the aircraft noise frequency spectrum is carried out line spectrum and detected tracking.Algorithm is at first determined detection threshold according to detection probability and false-alarm probability, and frequency-division section carries out the line spectrum tracking then.According to the previous moment target location, the rectangular neighborhood of selecting to be no more than this frequency range Doppler shift resolution unit carries out track-while-scan.Because each frequency range Doppler varies in size, thus line spectrum variation range difference to some extent, frequency is high more, and Doppler is big more.The line spectrum variation range was less when target was far away; And near crossing the top constantly, the line spectrum variation range is bigger.Target is crossed the top and the period can be differentiated according to the power of signal, and signal intensity was met and flown strong with backward flight when target was crossed the top; Can meet according to target simultaneously and fly to judge the top period with backward flight sound intensity difference; Also can differentiate according to the speed that the target azimuth changes.To carry out the parameter correction according to handling frequency range and period in the practical application.Fig. 4 can be clear that the high-frequency signal of being covered by clutter for the aircraft noise frequency spectrum of line spectrum after strengthening.Doppler departs from natural frequency about 15%, and is consistent with the ratio of the air velocity of sound of the flying speed of 53m/s and 340m/s.Dynamic programming method also has higher detection sensitivity to aircraft noise low-frequency range line spectrum.Doppler is less for the aircraft noise low-frequency range, and the Doppler of HFS is big than low frequency part, and the spectral line of high frequency aircraft noise is strengthened and analyzes, and more helps according to its Doppler's size, estimates the parameters of target motion such as the position of aircraft and flying speed.

It should be noted last that above embodiment is only unrestricted in order to technical scheme of the present invention to be described.Although the present invention is had been described in detail with reference to embodiment, those of ordinary skill in the art is to be understood that, technical scheme of the present invention is made amendment or is equal to replacement, do not break away from the spirit and scope of technical solution of the present invention, it all should be encompassed in the middle of the claim scope of the present invention.

Claims (3)

1. weak target frequency spectrum tracking based on dynamic programming, this method is to being submerged in weak target in the ground unrest and finishing data association by frequency spectrum tracking form and track being surveyed; At first determine the line spectrum hunting zone, according to the spectral profile form, the feasible track score of all in the calculating line spectral region of search, the top score state can be defined as the optimum line spectrum track that this state stops, by follow the trail of forward each the processing stage state value that drawn, can recover the line spectrum track; The concrete steps of this method comprise:

Step 1): obtain the microphone array data-signal, the data-signal that receives is carried out pre-service, then the time-frequency spectrum of signal calculated;

Step 2): determine the band limits that line spectrum is followed the tracks of according to the time-frequency spectrum distribution of described step 1) acquisition and the priori of target noise, and determine the track-while-scan zone thus;

Step 3): according to described step 2) the line spectrum energy in the track-while-scan zone that obtains is determined line spectrum intensity detection threshold value; With line spectrum intensity detection threshold value serves as according to the start-stop moment of judging that line spectrum is followed the tracks of;

Step 4): determine the spectral trace distribution function according to target priori and movement velocity estimating target Doppler shift size thereof;

Step 5): the spectral trace distribution function of determining according to described step 4) carries out line spectrum detection tracking; Promptly defining the line spectrum tracking problem is to find the solution the decision problem of optimum state metastasis sequence; Obtain the line spectrum variation track by trying to achieve branch functional K (J) maximal value;

$K\left(J\right)=\underset{J}{\max }K\left(J\right)---\left(1\right)$

In the formula (1), J={s (0), s (1) ..., s (n) }, s (i) represents i target spectrum state vector constantly, satisfies Markovian process;

The new breath of target spectrum state is pressed markov random walk process model building, solve the exhaustive search problem of target detection by the segmentation optimization; For first order modeling, the omnidistance score functional of line spectrum track J can be decomposed into:

$K\left(J\right)=g_1(s\left(0\right),s\left(1\right))+g_2(s\left(1\right),s\left(2\right))+...+g_n(s(n-1),s\left(n\right))=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{g}_i(s(i-1),s\left(i\right))---\left(2\right)$

$K\left(J\right)=\underset{j}{\max }K\left(J\right)=\underset{s\left(n\right)}{\max }\left[\underset{s(n-1)}{\max }\right[g_n(s(n-1),s\left(n\right))+\underset{s(n-2)}{\max }[g_{n-1}(s(n-2),s(n-1))+---\left(3\right)$

$...+\underset{s\left(1\right)}{\max }\left[\begin{array}{cc}{g}_2(s\left(1\right),s\left(2\right))+\underset{s\left(0\right)}{\max }& g_1(s\left(0\right),s\left(1\right))\end{array}\right]\&CenterDot;\&CenterDot;\&CenterDot;\left]\right]]$

In formula (2) and the formula (3), g _nThe score functional of the n time search when representing linear search;

Dynamic programming solution procedure formula (3) specifically can be calculated stage by stage by formula (4), formula (5) and formula (6):

$K_0\left(s\left(1\right)\right)=\underset{s\left(0\right)}{\max }{g}_1(s\left(0\right),s\left(1\right))---\left(4\right)$

$K_{i-1}\left(s\left(i\right)\right)=\underset{s(i-1)}{\max }[g_i(s(i-1),s\left(i\right))+K_{i-2}\left(s(i-1)\right)]---\left(5\right)$

$K\left(J\right)=\underset{s\left(n\right)}{\max }{K}_{n-1}\left(s\left(n\right)\right)---\left(6\right)$

The score functional K (J) of line spectrum tracing process is defined as based on the posteriority detection probability:

$K\left(J\right)=\log \left[\frac{P_{n|n}(s\left(0\right),s\left(1\right),...,s\left(n\right)|Z^n)}{P_{n|n}\left(H_0\right|Z^n)}\right]---\left(7\right)$

In the formula (7), definition H ₁=s (0), s (1) ..., s (n) } be to be the hypothesis that the specific line spectrum track of termination occurs with state s (n) up to n observation cycle, H ₀Be zero line spectrum hypothesis, Z ⁿIt is the metric data collection till n the observation cycle; The score functional of above type is considered simultaneously and is supported and oppose the situation that target occurs;

Formula (7) is used the Bayes principle and is utilized final derivation of single order Markov model characteristic to obtain the score functional expression formula of recursive form:

$K_{i-1}\left(s\left(i\right)\right)=\log \left[\frac{P\left(Z^i\right|s\left(i\right))}{P\left(Z^i\right|H_0)}\right]+\underset{s(i-1)}{\max }[\log P\left(s\left(i\right)\right|s(i-1))+K_{i-2}\left(s(i-1)\right)]---\left(12\right)$

In the formula (12), K _I-1(s (i)) is the feasible line spectrum track score that stops with state s (i) in the i step, the search of s (i) got in s (i-1) quantized value is no more than the rectangular neighborhood of Doppler shift Δ f resolution unit carry out, the state that a stage i in office produces top score by search is determined the most probable line spectrum track that stops at this state;

Step 6): the state of determining according to described step 5) stops most probable line spectrum track constantly, by follow the trail of forward each the processing stage state value that drawn recover line spectrum track history, finish the tracing process that target spectrum changes.

2. the weak target frequency spectrum tracking based on dynamic programming according to claim 1 is characterized in that in the described step 1), pre-service comprises data filtering.

3. the weak target frequency spectrum tracking based on dynamic programming according to claim 1 is characterized in that, in the described step 1), to the cyclic spectrum of digital signal according to the following formula signal calculated;

$S\left(e^{\mathrm{jw}}\right)=\frac{{\left|\underset{l=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_l\left(e^{-\mathrm{jwl}}\right)\right|}^2}{n}$

Wherein, x _l(e ^-jwl) be the Fourier transform of described data-signal, l is discrete data sequence l ∈ [1 n].

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