An adaptive pulse compression method suitable for off-grid targets

Abstract

The application provides an adaptive pulse compression method suitable for off-grid targets, which comprises the following steps: firstly, an echo signal model of off-grid targets is established, and the echo signal is matched filtered; then, an iterative adaptive filter suitable for off-grid targets is constructed, and the matched filtering result is filtered; according to the iterative result, the off-grid amount of the target is estimated, the off-grid amount is brought into the iterative adaptive filter, and the matched filtering result is filtered again; after multiple iterative treatments, the method can effectively suppress the range sidelobe of the off-grid target, and can accurately estimate the range and power of the target; the matched filtering result is iteratively filtered by using the adaptive filter suitable for off-grid targets, the amplitude of L range units and the off-grid amount estimation result obtained in the last iteration are used as the prior information of the current iteration in each iteration, the filter of the current iteration is adaptively updated, the amplitude of each unit is estimated, and the off-grid amount of each unit is calculated by using the amplitude estimation result.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of signal processing, and particularly relates to an adaptive pulse compression method suitable for off-grid targets. BACKGROUND

[0002] In a pulse radar system, matched filtering of echo signals will produce severe range sidelobes. When there are multiple targets in the observation scene, the range sidelobes of strong targets may mask weak targets or be mistaken as false targets to cause false alarms. In the article "Adaptive pulse compression via MMSE estimation" published by Shannon D. blunt et al. in IEEE Transactions on Aerospace and Electronic Systems, Vol. 42, No. 2, pp. 572-584, 2006, an adaptive pulse compression method (APC) based on the minimum mean square error criterion is proposed. This method can effectively suppress range sidelobes by adaptively constructing filters for each range cell. In the article "Dimensionality reduction techniques for efficient adaptive pulse compression" published by Shannon D. blunt et al. in IEEE Transactions on Aerospace and Electronic Systems, Vol. 46, No. 1, pp. 349-362, 2010, a fast adaptive pulse compression method (FAPC) is proposed. This method processes echoes in segments to reduce computational complexity. In the article "Fast adaptive pulse compression based on matched filter outputs" published by Li Zhengzheng et al. in IEEE Transactions on Aerospace and Electronic Systems, Vol. 51, No. 1, pp. 548-564, 2015, a fast adaptive pulse compression method based on matched filter outputs (MF-RMMSE) is proposed. This method uses a shorter filter to filter the matched filter outputs, thereby greatly reducing the computational load. However, in the off-grid target scene, the sidelobe suppression performance of the above three methods will be severely deteriorated due to the mismatch of the signal model caused by the off-grid of the target. SUMMARY

[0003] Therefore, the present application aims to provide an adaptive pulse compression method suitable for off-grid targets, which can effectively suppress the range sidelobes of off-grid targets, and then accurately estimate the distance and power of the targets.

[0004] An adaptive pulse compression method suitable for off-grid targets, comprising the following steps:

[0005] Step 1: Establishing an echo signal model of off-grid targets, performing matched filtering processing on the echo signal, and the specific method is as follows:

[0006] Step 2: Constructing an iterative adaptive filter suitable for off-grid targets, performing iterative filtering on L distance units, and the specific method is as follows:

[0007] The minimum mean square error cost function is represented as:

[0008]

[0009] Wherein, E[·] represents an expectation function, and w(l) represents a filter coefficient;

[0010]

[0011] K l and K r respectively represent the number of units before and after the element x MF (l) contained in the vector x ; x(l) represents an element at a corresponding position in the vector x;

[0012]

[0013]

[0014] To minimize the cost function, it is required to solve

[0015] d[J(l)] / d[w H (l)]=0 (12)

[0016] The obtained iterative adaptive filter is represented as

[0017]

[0018] Assuming that each unit distance image is independent and unrelated to noise, and the noise is a Gaussian white noise with a power spectral density of σ 2 , then

[0019]

[0020] Wherein, R Kl+N (Δ l ) represents R(Δl ) of (K) l +N) columns,

[0021]

[0022]

[0023] Therefore, the estimated value of the range image impulse response of the l-th cell is expressed as:

[0024]

[0025] The estimated value of element x(l) is obtained according to formula (17). By traversing l∈[0,L-1], we obtain the estimated values ​​of each element in x, and thus form the estimated value of x. At this point, the estimated value is used. Update x;

[0026] Step 3: Calculate the displacement of L distance cells. The specific steps are as follows:

[0027] The total number of off-grid cells after the qth iteration of the k0th unit. Represented as:

[0028]

[0029] Where x(k0+r) represents the element at position k0+r in the current x; This represents the out-of-cell quantity of the k0th unit in the previous iteration; when |x (q) (k0+1)|≤|x (q) When (k0-1)|, r = -1; otherwise, r = 1.

[0030] According to formula (18), we get Traverse k0∈[0,L-1] to obtain the values ​​of each element in Δ. As an estimate of Δ Using estimated values Update Δ;

[0031] Step 4: Repeat steps 2 and 3 for a set number of iterations, then output x and the off-grid value Δ to complete the range sidelobe suppression and obtain the range image impulse response.

[0032] Preferably, in the first iteration, the initial distance image impulse response is: The initial amount of off-grid is Δ (0) =0.

[0033] Preferably, the set number of iterations is 6.

[0034] Preferably, step 1 specifically includes the following steps:

[0035] Assume that the number of pulse sampling points is N, there are L distance cells, and the aliasing amount is represented as:

[0036] Δ = [Δ0 Δ1 … Δ L-1 ] T ,Δ l ∈(-0.5,0.5] (1)

[0037] Wherein each element in Δ represents the aliasing amount corresponding to each distance cell;

[0038] Assume that the transmitted pulse signal is s = [s0 s1 … s N-1 ] T Wherein each sampling point is represented as:

[0039]

[0040] The N continuous sampling vectors corresponding to the lth distance cell of the baseband echo signal are represented as y(l) = [y(l) y(l+1) … y(l+N-1)] T

[0041]

[0042] Wherein each element in y(l) represents the echo signal of each sampling point;

[0043]

[0044]

[0045]

[0046] G is an N × (2N-1) dimensional transmitted signal matrix, G'(Δ l ) and G''(Δ l ) are phase mismatching matrices caused by target aliasing, x is an L × 1 dimensional range image vector, x(l) is a subvector composed of the first N-1 to the last N-1 elements of the lth element in x, is a (2N-1) × 1 dimensional vector, and v(l) is an N × 1 dimensional noise vector;

[0047] The echo signal is subjected to matched filtering processing, and the matched filtering result of the lth distance cell is represented as:

[0048]

[0049] Wherein r(Δ l ) = (s H Q(Δ l ))​T ; the s H Q(Δ l ) calculation results are represented as: r -N+1 (Δ l ), r -N+2 (Δ l )...r N-1 (Δ l ), then

[0050] r(Δ l ) = (s H Q(Δ l )) T = [r -N+1 (Δ l ) r -N+2 (Δ l )... r N-1 (Δ l )] T .

[0051] Preferably, the pulse sampling point number is N=32, and there are L=100 distance units.

[0052] The present application has the following beneficial effects:

[0053] The present application provides an adaptive pulse compression method suitable for off-grid targets. The method first establishes an echo signal model of off-grid targets, and performs matched filtering on the echo signal. Then, an iterative adaptive filter suitable for off-grid targets is constructed, and the matched filtering result is filtered. The off-grid amount of the target is estimated according to the iteration result, and the off-grid amount is brought into the iterative adaptive filter, and the matched filtering result is filtered again. After multiple iterations, the method can effectively suppress the range sidelobes of off-grid targets, and can accurately estimate the range and power of the target.

[0054] The matched filtering result is iteratively filtered by using the adaptive filter suitable for off-grid targets. In each iteration, the amplitude and off-grid amount estimation result of the L distance units obtained in the last iteration are used as the prior information of the current iteration, the filter of the current iteration is adaptively updated, the amplitude of each unit is estimated, and the off-grid amount of each unit is calculated using the amplitude estimation result. Generally, six iterations can successfully suppress the range sidelobes of off-grid targets, and accurately estimate the range and power of the target. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 A flowchart of an adaptive pulse compression method robust to off-grid targets of the present application;

[0056] Figure 2 The matched filtering result and the iterative filtering result of the embodiment of the present application. DETAILED DESCRIPTION

[0057] The application will be described in detail below with reference to the accompanying drawings and examples.

[0058] Step 1: Establishing an echo signal model of the off-grid target, and performing matched filtering processing on the echo signal, the specific method is as follows:

[0059] Suppose the pulse sampling point number is N, there are L distance units, and the off-grid amount can be expressed as:

[0060] Δ=[Δ0 Δ1 … Δ L-1 ] T ,Δ l ∈(-0.5,0.5] (1)

[0061] Wherein, each element in Δ represents the off-grid amount corresponding to each distance unit;

[0062] Suppose the transmitted pulse signal is s=[s0 s1 … s N-1 ] T , wherein each sampling point can be expressed as:

[0063]

[0064] The N continuous sampling vectors y(l)=[y(l) y(l+1)… y(l+N-1)] corresponding to the lth distance unit of the baseband echo signal can be expressed as: T

[0065]

[0066] Wherein, each element in y(l) represents the echo signal of each sampling point;

[0067]

[0068]

[0069]

[0070] G is a transmitted signal matrix of N×(2N-1) dimensions, G'(Δ l ) and G''(Δ l ) are phase mismatching matrices caused by the off-grid of the target, x is a distance image vector of L×1 dimensions, x(l) is a subvector composed of the first N-1 to the last N-1 elements of the lth element in x, which is a (2N-1)×1 dimension vector, and v(l) is a noise vector of N×1 dimensions.

[0071] Performing matched filtering processing on the echo signal, the matched filtering result of the lth distance unit can be expressed as​

[0072]

[0073] wherein r(Δ l ) = (s H Q(Δ l )) T ; each term of the calculation result of s H Q(Δ l ) is represented as r -N+1 (Δ l ), r -N+2 (Δ l )...r N-1 (Δ l ), then

[0074] r(Δ l ) = (s H Q(Δ l )) T = [r -N+1 (Δ l ) r -N+2 (Δ l )... r N-1 (Δ l )] T .

[0075] Step 2: Construct an iterative adaptive filter suitable for the off-grid target, and perform iterative filtering on L distance cells, in particular as follows:

[0076] The minimum mean square error cost function is represented as:

[0077]

[0078] wherein E[·] represents an expectation function, and w(l) represents a filter coefficient;

[0079]

[0080] K l and K r represent the number of cells before and after the element x MF (l) in the vector x , respectively; x(l) represents an element at a corresponding position in the vector x;

[0081]

[0082]

[0083] To minimize the cost function, the following equation needs to be solved:

[0084] d[J(l)] / d[w H (l)]=0 (12)

[0085] The iterative adaptive filter is expressed as follows:

[0086]

[0087] Assuming that the distance images of each cell are uncorrelated and uncorrelated with the noise, and that the noise has a power spectral density of σ... 2 Gaussian white noise, then has

[0088]

[0089] Where R Kl+N (Δ l ) represents R(Δ l ) of (K) l +N) columns,

[0090]

[0091]

[0092] Therefore, the estimated range image impulse response of the l-th cell can be expressed as:

[0093]

[0094] The estimated value of element x(l) can be obtained according to formula (17). By traversing l∈[0,L-1], we can obtain the estimated values ​​of each element in x, and thus form the estimated value of x. At this point, the estimated value is used. Update x.

[0095] Step 3: Calculate the displacement of L distance cells. The specific steps are as follows:

[0096] The total number of off-grid cells after the qth iteration of the k0th unit. It can be represented as:

[0097]

[0098] Where x(k0+r) represents the element at position k0+r in the current x; This represents the out-of-cell quantity of the k0th unit in the previous iteration; when |x (q) (k0+1)|≤|x (q) When (k0-1)|, r = -1; otherwise, r = 1.

[0099] According to formula (18), we get By traversing k0∈[0,L-1], we can obtain the values ​​of each element in Δ. as an estimate of Δ with the estimate update Δ.

[0100] Step 4: repeat step 2 and step 3, after multiple iterations, output x and the out-of-grid amount Δ, the range image impulse response can be obtained.

[0101] Let the initial range image impulse response be Let the initial out-of-grid amount be Δ (0) = 0, repeat step 2 and step 3, after multiple iterations, the range sidelobes can be suppressed, and the range image impulse response can be accurately estimated.

[0102] Embodiment:

[0103] In this example, the transmit pulse width is T P = 4 μs, the bandwidth is B = 4 MHz, the linear frequency modulation pulse, the sampling rate is f s = 8 MHz, the number of sampling points in the pulse is N = 32, the number of distance units is L = 100, the carrier frequency is f c = 3 GHz, there are three targets in the scene, respectively located at the positions corresponding to the 46.8, 50.3 and 54.3 distance units, the signal-to-noise ratios are 20 dB, 50 dB and 20 dB respectively, and a filter with a length of K l = 3 and K r = 3 is used.

[0104] After six iterations, the range sidelobes of the out-of-grid targets can be effectively suppressed, and the SNR estimates of the three targets are 19.96 dB, 50 dB and 19.98 dB respectively, and the position estimates are 46.8, 50.3 and 54.3 respectively.

[0105] In summary, the above is only a preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. An adaptive pulse compression method suitable for off-grid targets, characterized in that, The method comprises the following steps: Step 1: establishing an echo signal model of the off-grid target, and performing matched filtering on the echo signal, and the specific method is as follows: Assuming that the pulse sampling point number is N, there are L distance units, and the off-grid amount is represented as: Δ = [Δ0 Δ1... Δ L-1 ] T ,Δ l ∈(-0.5,0.5] (1) Wherein, each element in Δ represents the off-grid amount corresponding to each distance unit; Assume the transmitted pulse signal is s = [s0 s1... s N-1 ] T where each sample point is represented as: The N continuous sampling vectors corresponding to the 1th distance unit of the baseband echo signal y(l) = [y(l) y(l+1) … y(l+N-1)] T is represented as: Wherein, each element in y(l) represents the echo signal of each sampling point; G is an N x (2N - 1) dimensional transmit signal matrix, G'(Δ l ) and G"(Δ l ) are the phase mismatch matrices due to target misregistration, x is an L x 1 dimensional range image vector, x(l) is a subvector of the first N - 1 to the last N - 1 elements of the lth element of x, x(l) is a (2N - 1) x 1 dimensional vector, v(l) is an N x 1 dimensional noise vector; Performing matched filtering on the echo signal, and the matched filtering result of the lth distance unit is represented as: where r(Δ l ) = (s H Q(Δ l )) T ; and the results of the calculation of each of s H Q(Δ l ) are represented as r -N+1 (Δ l ), r -N+2 (Δ l )...r N-1 (Δ l ), respectively, then r(Δ l ) = (s H Q(Δ l ) ) T = [r -N+1 (Δ l ) r -N+2 (Δ l ) … r N-1 (Δ l )] T ; Step 2: constructing an iterative adaptive filter suitable for the off-grid target, and performing iterative filtering on the L distance units, and the specific method is as follows: The minimum mean square error cost function is represented as: Wherein, E[·] represents an expected function, and w(l) represents a filter coefficient; K l and K r Representing vectors respectively Contains element x MF (l) represents the number of elements before and after it; x(l) represents the element at the corresponding position in vector x; In order to minimize the cost function, it is required to solve d[J(l)] / d[w H (l)] = 0 (12) The iterative adaptive filter is obtained as Assuming that the cells are uncorrelated and that the noise is white Gaussian noise with power spectral density σ 2 , then we have wherein represents the (K l +N)th column of R(Δ l ), Therefore, the distance image pulse response estimation value of the lth unit is represented as According to formula (17), the estimated value of element x(l) is obtained The estimated value of each element in x is obtained by traversing l∈[0,L-1], thereby forming the estimated value of x At this time, the estimated value x is updated; Step 3: calculating the off-grid amount of the L distance units, and the specific steps are as follows: total amount of out-of-cell after the qth iteration of the k0th unit is represented as: where x(k0+r) represents the element at position k0+r in the current x; represents the residual of the k0th element at the last iteration; when |x (q) (k0+1) |≤ |x (q) (k0-1) |, r = -1, otherwise r = 1; According to equation (18), we have Traverse k0∈[0,L-1], get the value of each element in Δ As the estimated value of Δ Use the estimated value Update Δ; Step 4: repeating step 2 and step 3, outputting x and the off-grid amount Δ after a set number of iterations, completing distance sidelobe suppression, and obtaining a distance image pulse response.

2. A method for adaptive pulse compression for off-grid targets as claimed in claim 1, wherein, At the first iteration, the initial distance image impulse response is The initial distance from the grid is Δ (0) = 0.

3. A method for adaptive pulse compression for off-grid targets as claimed in claim 1, wherein, The set number of iterations is 6 times.

4. The method of claim 1, wherein the method is applied to off-grid targets. The pulse sampling point number is N=32, and there are L=100 distance units.

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