CN118859119A - A three-feature time series detection method using modified burg algorithm - Google Patents

Abstract

The invention relates to a three-feature time sequence detection method applying a correction burg algorithm, and belongs to the technical field of radar signal processing. The method comprises the following steps: step 1: extracting target features; step 2: AR modeling of the features; step 3: feature fusion; step 4: and (5) detecting performance analysis. According to the invention, the spectral stability factor is added when the reflection coefficient is pushed down, so that the pole is far away from the unit circle, the phenomenon of 'pseudo peak' is avoided, and the clutter characteristic prediction effect is more accurate.

Description

A three-feature time series detection method using modified burg algorithm

Technical Field

The invention relates to a three-feature time series detection method using a modified burg algorithm, and belongs to the technical field of radar signal processing.

Background Art

The ocean environment is complex and changeable. Due to the influence of sea clutter, the echo signals of marine targets, especially small targets such as buoys and small boats, are often submerged in the clutter signals. The detection of such targets requires the use of advanced radar signal processing technology to separate the target from the clutter. As an emerging signal processing technology, feature detection technology can not only make full use of the rich echo information of high-resolution radar, but also simplify radar target detection into a classification problem through feature extraction, thereby reducing the complexity of detection. When using features, only the feature values of the current frame are often considered, while the time series information of the historical frames is ignored. At present, relevant research has performed AR time series modeling on the historical frame data of the features, which effectively optimized the performance of the feature detector.

However, due to the complex formation mechanism of sea clutter and the numerous influencing factors, the characteristic model of sea clutter changes over time. If the conventional Yule-Walker equation method is used to directly perform AR prediction, the deviation between the model and the true value will be too large, affecting the accuracy of time series prediction.

Summary of the invention

Based on radar target detection, the present invention proposes a three-feature time series detection method using a modified Burg method. This method adds a spectral stability factor when deducing the reflection coefficient, so that the pole is far away from the unit circle, avoiding the phenomenon of "pseudo peaks" and making the prediction effect of clutter characteristics more accurate.

A three-feature time series detection method using a modified burg algorithm, which is special in that it includes the following steps:

Step 1: Target feature extraction:

The echo data after pulse compression processing is used to extract features and obtain the observation features required for time series modeling;

Step 2: AR modeling of features:

Effect of Stability Factor on Reflection Coefficient in Burg Method Correction , and use the corrected Recursively derive AR parameters, model the features of a historical frame before the current frame and predict it in one step to obtain the predicted features;

Step 3: Feature fusion:

Perform weighted fusion of the predicted features and the observed features of the current frame to form fused features;

Step 4: Detection performance analysis:

Two sets of public data sets are used to analyze the impact on the separability of fused features. According to the given false alarm probability, the fused features of sea clutter samples are processed in the three-dimensional feature space to obtain the judgment area. The existence of the target is judged based on whether the three-dimensional fused features of the sample to be tested belong to the judgment area.

Preferably, the specific steps of step 1 are as follows:

The three features of RAA, FPAR and RPH are selected and described as follows:

The calculation method of RAA feature is as follows:

(1);

in,

(2);

Represents radar echo data; and Respectively represent the echo data of the unit under test and the reference unit. The calculation method of RDPH characteristics is as follows:

(3);

in,

(4);

(5);

In the formula, is to make The Doppler frequency with the largest amplitude, Determined by the average Doppler bandwidth of sea clutter, Determined by the guard interval of the Doppler peak, Represents in the interval The number of Doppler cells within;

The calculation method of FRAR characteristics is as follows:

(6);

express through The amplitude spectrum obtained by point discrete Fourier transform;

Through feature extraction, we get the RAA observation sequence consisting of M features ,

RDPH observation sequence ,

FRAR observation sequence .

Preferably, in step 2, the reflection coefficient During the derivation process, a stability factor is added to obtain the corrected reflection coefficient As shown in formula (9):

(9);

(10).

Preferably, the specific steps of step 3 are as follows:

Under the condition that the observed features and predicted features are obtained in step 1) and step 2), the two are fused to obtain a new feature, namely the feature fusion value. The specific fusion method is as follows:

(19);

in, Fusion features for the current frame; is the observation feature of the current frame; is the predicted feature of the current frame, obtained by performing AR fitting on the feature sequence of the historical frames and prediction in step 1; , are weighted coefficients, which respectively represent the influence of the current frame data and the historical frame data on the fusion features of the current frame.

Compared with the prior art, the three-feature time series detector using the modified Burg method described in the technical solution has the following beneficial effects:

(1) The method proposed in the present invention utilizes feature history frames as time series information, increases the amount of information contained in the features, improves the separability of clutter and target features, and optimizes the detection performance of the detector.

(2) The modified Burg method is used to avoid the problem of “pseudo-peaks” caused by improper order selection. A higher AR order can be given, which simplifies the steps of determining the AR order using a priori criteria. The distribution of the model poles can be adaptively adjusted to make the establishment of the sea clutter characteristic model more accurate.

(3) Under IPIX data, the average detection probability of the proposed method for the target is 70.19% when using 128 pulses, which is 20.45% higher than the original three-feature detector and 4.09% higher than the original yule three-feature time series detector. Under the high sea state data of the Naval Aviation University, the average detection probability of the target is 58.72%, which is 19.33% higher than the original three-feature detector and 4.33% higher than the original yule three-feature time series detector. The detection effect is still significantly improved when using 64 pulses and 256 pulses.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1: The extreme point change diagram of the AR model before and after the addition of the stabilizing factor; Figure 1 (a) shows the extreme point change diagram of the AR model before the addition of the stabilizing factor, and Figure 1 (b) shows the extreme point change diagram of the AR model after the addition of the stabilizing factor;

Figure 2: Comparison of three-feature prediction curve and observation curve;

Figure 3: Flowchart for feature fusion using prior information;

Figure 4: is a graph showing the variance change of features after fusion; Figure 4 (a) shows the feature variance change graph of HH polarization, and Figure 4 (b) shows the feature variance change graph of VV polarization;

Figure 5: Comparison of Bhattacharyya distances between features of different methods; Figure 5 (a) shows the comparison of HH polarization; Figure 5 (b) shows the comparison of VV polarization;

Figure 6: is a curve diagram showing the change of Bhattacharyya distance with the increase of AR order;

Figure 7: The curves of sea clutter and target variances changing with AR order; Figure 7 (a) shows the curve of clutter variance changing with order, and Figure 7 (b) shows the curve of target variance changing with order;

Figure 8: A graph showing how the average detection probability changes with the increase in AR order after feature fusion.

DETAILED DESCRIPTION

The present invention will be described in detail below with reference to the accompanying drawings.

1) Target feature extraction:

This embodiment is a three-feature time series detector using the modified Burg method, which selects three features, RAA, FPAR, and RPH, which have good separability and stability. The three features are described as follows:

1. The calculation method of RAA feature is as follows:

(1);

in,

(2);

Represents radar echo data; and Respectively represent the echo data of the unit under test and the reference unit.

2. The calculation method of RDPH characteristics is as follows:

(3);

in,

(4);

(5);

In the formula, is to make The Doppler frequency with the largest amplitude, Determined by the average Doppler bandwidth of sea clutter, Determined by the guard interval of the Doppler peak, Represents in the interval The number of Doppler cells in .

3. The calculation method of FRAR characteristics is as follows:

(6);

express through The amplitude spectrum is obtained by discrete Fourier transform of the point.

Through feature extraction, we get the RAA observation sequence consisting of M features ,

RDPH observation sequence ,

FRAR observation sequence .

2) AR modeling of features:

Previous feature detection usually only considers the current frame information and ignores the feature information in the period before the frame. The AR model, as a method of using historical data to predict future data, solves the problem of insufficient utilization of feature time series information. , the general expression of the decentralized AR model is:

(7);

Among them, the model order is a known quantity, is the Gaussian white noise model parameter is the parameter to be estimated, and its estimated value It can be calculated by equation (9):

(8);

, are the forward and backward prediction errors of the input data, which is also called the Burg method of parameter estimation. However, when the order does not match, the AR model is prone to problems such as "pseudo peaks" that affect the stability of the model. Therefore, this embodiment uses a method of model stability to derive the reflection coefficient When adding the stability factor, the corrected reflection coefficient is obtained As shown in formula (9):

(9);

(10);

The specific derivation process is as follows:

Minimize the arithmetic mean of the forward and backward forecast error variance estimates to find ,Right now:

(11);

in:

(12);

(13);

The prediction error satisfies the following recursive formula:

(14);

(15);

We can get:

(16);

Add stabilizing factor have to:

(17);

(18);

in To stabilize the parameters, it is related to the characteristics of the data itself. is the discrete Fourier transform of the p -order AR coefficient. The role of adding the stability factor is to add stability constraints when solving the reflection coefficient. Taking the partial derivative and setting it to 0, we can obtain the solution in (9) that satisfies the minimization of the arithmetic mean of the forward and backward prediction error variance estimates. . Useful The estimated parameters are calculated by (8) and the estimated parameters are used Establish a characteristic AR model. The pole distribution of the AR model of a section of sea clutter characteristic data with a stabilization factor added and the pole distribution of the model without a stabilization factor added are shown in Figure 1. (a) and (b) respectively represent the pole distribution before and after adding the stabilization factor. It can be seen that after adding the stabilization factor, the poles of the AR model will be far away from the unit circle, and the stability of the model is improved.

Regarding the selection of the order p , the original Yule-Walker method uses a fifth-order AR model to model the sea clutter characteristics. Since the present embodiment can adaptively adjust the distribution of the model poles, the order value can be larger than that of the original method. Experience shows that The AR fitting result is better when it is around 0.005~0.2. In high sea conditions, the value can be appropriately increased according to the prior conditions, and in low sea conditions, the value can be appropriately reduced. For the convenience of the experiment, this embodiment takes a unified value. Taking p = 10, the AR model of sea clutter characteristics is established for one-step prediction. The prediction effect is shown in Figure 2. It can be seen that the prediction effect is good and the prediction curve is more stable. The average relative error of the three features predicted by the modified Burg method and the original Yule-Walker equation method using the IPIX data set is shown in Table 1. Features The relative error of the prediction It can be calculated by (19):

(19);

in, yes The predicted value of the corresponding frame.

Table 1 Average relative error of different AR prediction methods

;

It can be seen that in the case of 10th-order AR prediction, the average relative error of the modified Burg method for the three feature predictions is higher than that of the Yule-Walker equation method. The reason is that the stability factor can adaptively adjust the distribution of the AR model poles, avoiding the occurrence of "pseudo-peaks" and other phenomena, and increasing the prediction accuracy. The features at each moment are predicted to obtain the RAA prediction sequence composed of M features. , the RDPH prediction sequence can also be obtained , FRAR prediction sequence .

3) Feature fusion:

Under the condition that the observed features and predicted features are obtained in step 1) and step 2), the two are fused to obtain a new feature, which is called the feature fusion value. The reason for feature fusion is that the observed features reflect the echo information of the current frame, and the predicted features contain the echo information of the historical frames. Fusion of the two increases the amount of information of the features, which can better distinguish the target from the sea clutter, thereby improving the detection performance. The flowchart of using prior information to fuse features is shown in Figure 3, and the specific fusion method is as follows:

(20);

in, Fusion features for the current frame; is the observation feature of the current frame; is the prediction feature of the current frame, which is obtained by AR fitting and 1-step prediction of the historical frame feature sequence; , are weighted coefficients, which respectively represent the influence of the current frame data and the historical frame data on the fusion features of the current frame. The fusion of the observed features and the predicted features can generally be done by taking the average of the two (i.e. ), or adjust the parameters according to the sea state level. When the sea state is higher, the predicted features are considered more valuable, and the corresponding When the sea state is lower, the observed features are considered more valuable. Compared with the original three features, the variance of the fused features is reduced as shown in Figure 4. Figure 4 (a) shows the variance change of the HH polarization features, and Figure 4 (b) shows the variance change of the VV polarization features, which also indicates that the data separability is enhanced and the detection performance will be improved.

Pick , get the fusion features Calculate the fusion features at each moment to get the RAA fusion sequence Similarly, the FPAR fusion sequence can be obtained and RDPH fusion sequence .

4) Performance analysis:

The fusion sequence of the test data set is calculated using the first three steps to perform data separability analysis and detection performance analysis. This embodiment uses the IPIX data set as verification data one, using 9 sets of data collected in 1993, each set of data contains 4 polarization mode data of HH, VV, HV, and VH. During data collection, the radar operates in staring mode, the staring time is about 131 s, the pulse repetition frequency is 1 kHz, the range resolution is 30 m, and the target is a floating ball with a diameter of 1 m wrapped in metal wire. For more detailed data introduction, see Table 2. The high sea state data from the shared data set of the Naval Aviation University is used as verification data two, and the data information is shown in Table 3.

Table 2 IPIX dataset information table

Table 3 Naval Aviation University shared dataset information table

1. Data separability analysis:

Data separability refers to the separability of two types of data samples, which plays an important role in the detection performance of the detector. This embodiment uses the method of calculating the Bhattacharyya distance (B-distance) between clutter and target to measure the separability of the two. The calculation method is as follows:

First, calculate the mathematical expectation vector of the two types of sample sets and the covariance matrix ,

(twenty one);

(twenty two);

in, represents the mean operator, Represents the covariance operator.

Then the Bhattacharyya distance in the feature space can be estimated using formula (22):

(twenty three);

Here, det represents the determinant operator.

In the IPIX data set, 128 pulses are used to extract feature values, and the AR prediction order is p = 10. The Bhattacharyya distance of the fused features of the modified Burg method is calculated and compared with the Yule-Walker equation method and the original three features as shown in Figure 5. Figure 5 (a) shows the comparison diagram of HH polarization, and Figure 5 (b) shows the comparison diagram of VV polarization.

It can be seen that the target and clutter fusion features calculated by the modified Burg method have a higher Bhattacharyya distance than the Yule-Walker equation method and the original three features, which indicates that the detection performance of the method of this embodiment is better than the original method. In addition, it is found that with the increase of the AR order, the data Bhattacharyya distance is improved as shown in Figure 6. The analysis of the target and sea clutter with variance as a breakthrough is shown in Figure 7. Figure 7 (a) shows the curve of the change of clutter variance with the order, and Figure 7 (b) shows the curve of the change of target variance with the order. It is found that with the increase of the AR order, the sea clutter variance is decreasing, and the target variance is increasing, making the fused clutter features more stable, while the target features are more chaotic, thereby increasing the separability of the two. Therefore, the detection performance may also improve with the increase of the AR order.

2. Detector performance analysis:

This embodiment uses a convex hull detection algorithm to construct a detector. The convex hull detection algorithm is a three-dimensional feature detection algorithm for small targets at sea. The three-dimensional feature values of sea clutter and the target are known, and a three-dimensional detection convex hull is constructed. The specific steps are:

(1) Initialization: Set the feature set of small targets and sea clutter The number of eigenvectors of is , set the false alarm rate to , calculate the number of false alarms as .

(2) Find The one farthest from the large target sample cluster area sample points and remove them.

(3) Generate the convex hull decision area using the sea clutter feature points after removing the sample points .

(4) Calculate the number of target feature points that fall outside the decision area and divide it by the number of target feature points to obtain the detection probability Pd.

First, the inference in the separability analysis is verified. The number of pulses is 128, the AR order p = 10, and 50 features are used for one-step prediction. The average detection probability of the modified Burg method under different orders is tested by the convex hull algorithm. As shown in Figure 8, the inference is established. However, the detection performance will not improve with the continuous increase of the order, and the calculation process will become more complicated with the increase of the order. Therefore, the AR order can be appropriately increased under the method of this embodiment. In the following verification, the order p = 40 is taken in this embodiment.

Other conditions remain unchanged, 64, 128, and 256 pulses are used to extract features, and the false alarm probability PFA = 0.001 is taken. The convex hull algorithm is used to test the target detection probability of three methods: no time series fusion, time series fusion using the Yule-Walker equation method, and time series fusion using the modified Burg method. The detection results of the IPIX dataset are shown in Table 4, and the detection results of the Naval Aviation University shared dataset are shown in Table 5.

Table 4 IPIX data detection results

;

Table 5. Test results of the Naval Aviation University shared dataset

It can be seen that under the detection of the two sets of data sets, the detection performance of the modified Burg method is significantly improved compared with the Yule-Walker equation method and the original three-feature detector, and the method is applicable when using different numbers of pulses. In addition, the performance improvement in sea state level 5 is better than that in sea state level 4. The main reason is that the higher the sea state level, the more drastic the sea clutter changes, and the modified Burg method has a more obvious effect on model stability.

The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims (4)

1. A three-feature time series detection method using a modified burg algorithm, characterized by comprising the following steps: Step 1: Target feature extraction: The echo data after pulse compression processing is used to extract features and obtain the observation features required for time series modeling; Step 2: AR modeling of features: Effect of Stability Factor on Reflection Coefficient in Burg Method Correction , and use the corrected Recursively derive AR parameters, model the features of a historical frame before the current frame and predict it in one step to obtain the predicted features; Step 3: Feature fusion: Perform weighted fusion of the predicted features and the observed features of the current frame to form fused features; Step 4: Detection performance analysis: Two sets of public data sets are used to analyze the impact on the separability of fused features. According to the given false alarm probability, the fused features of sea clutter samples are processed in the three-dimensional feature space to obtain the judgment area. The existence of the target is judged based on whether the three-dimensional fused features of the sample to be tested belong to the judgment area. 2. According to the three-feature time series detection method using the modified burg algorithm of claim 1, the specific steps of step 1 are as follows: The three features of RAA, FPAR and RPH are selected and described as follows: The calculation method of RAA feature is as follows: (1); in, (2); Represents radar echo data; and Respectively represent the echo data of the unit under test and the reference unit. The calculation method of RDPH characteristics is as follows: (3); in, (4); (5); In the formula, is to make The Doppler frequency with the largest amplitude, Determined by the average Doppler bandwidth of sea clutter, Determined by the guard interval of the Doppler peak, Represents in the interval The number of Doppler cells within; The calculation method of FRAR characteristics is as follows: (6); express through The amplitude spectrum obtained by point discrete Fourier transform; Through feature extraction, we get the RAA observation sequence consisting of M features , RDPH observation sequence , FRAR observation sequence . 3. A three-feature time series detection method using a modified burg algorithm according to claim 1, characterized in that in step 2, the reflection coefficient During the derivation process, a stability factor is added to obtain the corrected reflection coefficient As shown in formula (9): (9); (10). 4. According to the three-feature time series detection method using the modified burg algorithm of claim 1, the specific steps of step 3 are as follows: Under the condition that the observed features and predicted features are obtained in step 1) and step 2), the two are fused to obtain a new feature, namely the feature fusion value. The specific fusion method is as follows: (19); in, Fusion features for the current frame; is the observation feature of the current frame; is the predicted feature of the current frame, obtained by performing AR fitting on the feature sequence of the historical frames and prediction in step 1; , are weighted coefficients, which respectively represent the influence of the current frame data and the historical frame data on the fusion features of the current frame.