CN111398945A - Sparse moving target detection method based on slow time sliding window filter - Google Patents

Abstract

The invention provides a sparse moving target detection method based on a slow time sliding window filter, which belongs to the field of radar moving target detection methods. The invention aims to provide a brand-new radar moving target detection method in a sparse target environment, which introduces the concept of a generalized fuzzy function, simplifies the moving target detection processing flow and enhances the sparse moving target detection capability in a given Doppler range by designing a secondary modulation pulse repetition interval sequence and a corresponding slow time matched filter.

Description

Sparse moving target detection method based on slow time sliding window filter

Technical Field

The invention relates to the field of radar moving target detection methods, in particular to a sparse moving target detection method based on a slow-time sliding window filter.

Background

Under a sparse target detection scene, the non-uniform PRI sequence has excellent electronic impedance performance based on the asymmetry of information, and a Doppler filter NUDFT and NUFFT applied to target echo detection of the non-uniform PRI sequence has the problem that the response of the Doppler filter fluctuates periodically, so that the target detection performance in a given Doppler range is influenced to a certain extent.

Disclosure of Invention

The invention aims to provide a brand-new radar moving target detection method in a sparse target environment, which introduces the concept of a generalized fuzzy function, simplifies the moving target detection processing flow and enhances the sparse moving target detection capability in a given Doppler range by designing a secondary modulation pulse repetition interval sequence and a corresponding slow time matched filter. Firstly, a pulse repetition interval sequence optimization problem with the optimal accumulation of regional Doppler tolerance as a criterion is designed based on a generalized fuzzy function, and then obtains an optimal solution through problem transformation and finally a golden region search method. The invention is realized by the following technical scheme:

the sparse moving target detection method based on the slow time sliding window filter specifically comprises the following steps:

step 1: determining a target Doppler range to be considered;

step 2: obtaining a generalized fuzzy function, and calculating the accumulated peak level of the generalized fuzzy function in the target Doppler range;

and step 3: forming an optimization problem of a quadratic PRI sequence design based on the minimum unambiguous detection distance, the minimum duty ratio and the generalized fuzzy function accumulation peak level;

and 4, step 4: and obtaining the optimal solution of the secondary PRI sequence design parameters based on a gold search method, and improving the detection capability of the general interested Doppler range target.

Further, the step 1 specifically comprises:PRI sequence is by T_i＝T+a(iT)²N-1 is modulated twice, the PRI sequence interval T_iDepending on the parameters a and T, when a>0, the sequence interval becomes gradually larger with i, when having the Doppler frequency f_d0The target of (2) appears in a certain range bin, noise and interference are not considered, the echo amplitude is normalized, the initial phase is set to zero, and the ideal echo is expressed as:

then the ideal slow time matched filter can be expressed as:

c＝r^*， (2)

wherein, (.)^*Representing conjugate operation, a spike occurs at the zero delay position of the filter, assuming the target echo passes through filter c.

Further, the step 2 specifically comprises: based on the quadratic modulation of PRI sequence, when the Doppler frequency of a target is f_d0At + l Δ f, the output of the filter will spike at another delay location.

Further, the step 3 specifically includes: a generalized blur function is defined to interpret the filtered output:

when k is>0, where k ∈ is the slow time delay, Δ f is the Doppler step size, l Δ f is the Doppler frequency, f₀Is the starting frequency, (.)^*Representing a conjugate operation, when k ≦ 0, the above equation becomes:

the accumulated peak level of the generalized ambiguity function can show the overall doppler margin characteristic, which can be expressed as:

l limits the doppler tolerance range to be considered, so that the target echo with unknown velocity has doppler mismatch loss during matched filtering, we design the staggered sequence to minimize the loss of doppler mismatch statistically, and PRI modulation changes the average pulse train duty ratio, i.e. the radar resource utilization rate is affected, and the cost function is expressed as:

wherein D (a) directly affects the utilization rate of radar resources and can not take any small value, therefore, consider D (a)>D_l,D_lIs the minimum allowable duty factor and, in addition, the minimum maximum unambiguous distance R_maxThere must also be a limit to the number of,

finally, the joint optimization problem of a (a) and d (a) can be expressed as:

where λ s is a weight of two terms, k ═ 100 is a scale factor, and by analyzing the objective function, it is easy to find T + a (it) regardless of the value of a²Proportional to i, i ∈ (0.., N-1), assuming for simplicity that a>0, D (gamma) ═ Dl, and the PRI minimum satisfies T>2Rmax/c, so the original problem is equivalent to:

by derivation, P₂Can be further expressed as:

notice P₃The objective function of (2) includes an accumulation of exponential functionsIn addition form, it is difficult to obtain an analytic solution, and the problem is a continuous problem of variable a, and an optimal solution can be obtained through a gold search method.

The invention has the beneficial effects that: according to the invention, through modulating the PRI sequence, the radial uniform velocity target echo is modulated into quadratic linear phase modulation, the original MTD problem is converted into a parameter estimation problem for solving linear frequency modulation signals while various types of deceptive interference are inhibited, and a calculation method is provided. The non-uniform PRI sequence has significant electronic countermeasure advantages with information asymmetry. And the detection of the target in the interested Doppler frequency range is converted into novel matched filtering processing by utilizing the Doppler tolerance characteristic of the secondary PRI sequence modulation and optimizing the modulation parameters. It should be noted that the filter is designed according to the central doppler frequency, i.e. it is assumed that the application scenario is that the doppler frequency of the target is in a stable range. The experimental result proves that the Doppler frequency response performance is obviously improved compared with an FFT filter in a wider parameter setting range.

Drawings

FIG. 1 shows linear Doppler phases sampled by a twice modulated PRI interval, and the resulting phases of the respective samples;

FIG. 2 shows a center frequency f_d0Three at 600Hz (a) a-5; (b) a is 10; (c) a 15 the doppler tolerance and slow time delay characteristics of the slow time filter, with the center frequency corresponding to 0Hz in the figure;

FIG. 3 shows the cumulative Doppler margin level and average duty cycle versus a;

fig. 4 shows the variation of the weighted (sub-) objective function with respect to λ;

FIG. 5 shows the Doppler response of a quadratic PRI sequence slow time filter with NUDFT, NUFFT at different a;

fig. 6 shows the doppler response of a slow time matched filter with NUDFT, NUFFT at different center doppler frequencies of N-64.

Detailed Description

To further describe the technical solution of the present invention, the present invention will be further explained with reference to the accompanying drawings and the detailed description below:

examples

1. Sequence of remodulated pulse repetition intervals

The conventional burst transmit signal is represented as:

where N is a pulse number, which may be assumed to be 0, Ti (i ═ 1.., N-1) represents the pulse interval of the ith and (i +1) th pulses, and T is_pIs the pulse width, u (T) is the baseband equivalent representation of the pulse signal, rect (·) is a rectangular window function, defining T as a fixed PRI constant when T is_iT, (i ≠ j, i, j ∈ [ 1., N-1), the signal model falls to the uniform PRI case]When T is_i≠T_jThe signal model is a non-uniform PRI case.

Chirp L FM has an excellent doppler margin characteristic because it is linear in time and frequency, quadratic in time and phase, and is applied to the slow time dimension, as shown in fig. 1, which shows that the linear doppler phase is sampled by the quadratic modulation PRI interval and the phases obtained from the respective samples.

Designing the PRI sequence and corresponding filter with good doppler tolerance characteristics can improve the doppler frequency response characteristics of a radar target for a given doppler range.

In particular, the PRI sequence is via T_i＝T+a(iT)²N-1 is modulated twice, the PRI sequence interval T_iDepending on the parameters a and T, when a>0, the sequence interval becomes gradually larger with i, when having the Doppler frequency f_d0The target of (2) appears in a certain range bin, noise and interference are not considered, the echo amplitude is normalized, the initial phase is set to zero, and the ideal echo is expressed as:

then the ideal slow time matched filter can be expressed as:

c＝r^*， (2)

wherein, (.)^*Representing conjugate operation, assuming that the echo of a target passes through the filter c, a peak appears at the zero-delay position of the filter, based on the quadratic modulation of the PRI sequence, when the Doppler frequency of a target is f_d0At + l Δ f, the output of the filter will spike at another delay location. This is the key to the slow time filter and is quite different from the conventional FFT filter. As shown in FIG. 2, the center frequency f is shown_d0The doppler tolerance and slow time delay characteristics of three slow time filters at 600Hz, with the center frequency corresponding to 0Hz in the figure. In fact, for a Doppler frequency of f_d∈[500,700]For Hz targets, the output appears as a sloping ridge shape along the slow time delay cell. The negative slope ridge is nearly linear, providing the detection capability of mismatched doppler targets. Note that the oblique ridges represent the difference as the different parameters a take on values.

2. Problem formation and sequence design

We focus on the quadratic PRI sequence design with the most doppler tolerant characteristic for a given doppler range, thereby improving the overall doppler range of interest target examination capability. Specifically, a generalized blur function is defined to interpret the filtered output:

when k is>0, where k ∈ is the slow time delay, Δ f is the Doppler step size, l Δ f is the Doppler frequency, f₀Is the starting frequency, (.)^*Representing a conjugate operation, when k ≦ 0, the above equation becomes:

the accumulated peak level of the generalized ambiguity function can show the overall doppler margin characteristic, which can be expressed as:

l limits the doppler tolerance range to be considered, so that the target echo with unknown velocity has doppler mismatch loss during matched filtering, we design the staggered sequence to minimize the loss of doppler mismatch statistically, and PRI modulation changes the average pulse train duty ratio, i.e. the radar resource utilization rate is affected, and the cost function is expressed as:

wherein D (a) directly affects the utilization rate of radar resources and can not take any small value, therefore, consider D (a)>D_l,D_lIs the minimum allowable duty factor, and, in addition, the minimum maximum unambiguous distance Rmax must also be limited,

finally, the joint optimization problem of a (a) and d (a) can be expressed as:

where λ s is a weight of two terms, k ═ 100 is a scale factor, and by analyzing the objective function, it is easy to find T + a (it) regardless of the value of a²Proportional to i, i ∈ (0.., N-1), assuming for simplicity that a>0,D(γ)＝D_lAnd the PRI minimum satisfies T>2R_max/c,

The original problem is therefore equivalent to:

by derivation, P₂Can be further expressed as:

notice P₃The target function of (2) comprises the accumulation sum form of exponential functions, and an analytic solution is difficult to obtain, and the problem is a continuous problem of a variable a, and an optimal solution can be obtained by a gold search method.

3. Simulation result

We analyzed the performance of the designed sequence in terms of doppler tolerance and average duty cycle. In particular, we assume the Doppler frequency f of the object of interest_dSubject to uniform distribution, i.e.

Wherein f is_max，f_minIs the maximum, minimum doppler frequency considered. Center frequency

Table 1 below gives the relevant simulation parameters fig. 3 shows the performance of the accumulated doppler margin level and the function of the average duty cycle and the weighted objective function with respect to the modulation rate a when λ is 0.7 as expected, the average duty cycle decreases with increasing a, additionally IDT L reaches a maximum at a 10 and the global objective function reaches its maximum 50.8 at a 5.

TABLE 1

Carrier	300MHz	Light speed	3×108m/s
				Pulse number N	64	Weight coefficientλ	0.3
Pulse width Tp	50μs	PRImin	0.001s
				step length Δf	2Hz	central Doppler fdo	600Hz
fmin	500Hz	fmax	700Hz

Fig. 4 shows the relationship of the two sub-terms of the objective function with respect to λ. It can be seen that for λ 0 ≦ 0.5, the weight sparseness has almost no effect on both terms, whereas at λ 0.5 ≦ 1, both terms change monotonically. The doppler tolerance characteristic is optimized and the average pulse duty cycle coefficient reaches a minimum value of 39.55. Fig. 5 shows the doppler response at different values of a, with the overall fluctuation amplitude less than both NUDFT and NUFFT. Fig. 6 shows the doppler frequency response of the quadratic modulation sequence matched filter and NUDFT, NUFFT. Given center Doppler frequency f_d0The matched filtered frequency response of the quadratic modulation sequence is smoother than the other two (showing periodic fluctuations). For detecting targets in a certain speed range of interest, matched filtering has obvious advantages compared with NUDFT and NUFFT. In addition, the frequency response is a, f_d0And a doppler frequency range. In other words, a can be adjusted under different scenariosTo achieve a globally optimal frequency response.

And (4) conclusion: the method modulates the radial uniform-speed target echo into quadratic linear phase modulation by modulating the PRI sequence, converts the original MTD problem into a parameter estimation problem for solving linear frequency modulation signals while inhibiting various types of deceptive interference, and provides a calculation method. The non-uniform PRI sequence has significant electronic countermeasure advantages with information asymmetry. And the detection of the target in the interested Doppler frequency range is converted into novel matched filtering processing by utilizing the Doppler tolerance characteristic of the secondary PRI sequence modulation and optimizing the modulation parameters. It should be noted that the filter is designed according to the central doppler frequency, i.e. assuming the application scenario that the doppler frequency of the target is in a stable range. The experimental result proves that the Doppler frequency response performance is obviously improved compared with an FFT filter in a wider parameter setting range.

The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that are not thought of through the inventive work should be included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope defined by the claims.

Claims (4)

1. The sparse moving target detection method based on the slow time sliding window filter is characterized by comprising the following steps:

step 1: determining the Doppler range to be considered according to the aerodynamic characteristics of the considered target;

step 2: obtaining a generalized fuzzy function, and calculating the accumulated peak level of the generalized fuzzy function in the target Doppler range;

and step 3: forming an optimization problem of a quadratic PRI sequence design based on the minimum unambiguous detection distance, the minimum duty ratio and the generalized fuzzy function accumulation peak level;

and 4, step 4: and obtaining the optimal solution of the secondary PRI sequence design parameters based on a gold search method, and improving the detection capability of the general interested Doppler range target.

2. The method for detecting the sparse moving object based on the slow time sliding window filter according to claim 1, wherein the step 1 specifically comprises: PRI sequence is by T_i＝T₊a(iT)²N-1 is modulated twice, the PRI sequence interval T_iDepending on the parameters a and T, when a>0, the sequence interval becomes gradually larger with i, when having the Doppler frequency f_d0The target of (2) appears in a certain range bin, noise and interference are not considered, the echo amplitude is normalized, the initial phase is set to zero, and the ideal echo is expressed as:

then the ideal slow time matched filter can be expressed as:

c＝r^*， (2)

wherein, (.)^*Representing conjugate operation, a spike occurs at the zero delay position of the filter, assuming the target echo passes through filter c.

3. The method for detecting sparse moving objects based on the slow-time sliding window filter according to claim 1, wherein the step 2 specifically comprises: based on the quadratic modulation of PRI sequence, when the Doppler frequency of a target is f_d0At + l Δ f, the output of the filter will spike at another delay location, defining a generalized blur function to interpret the filtered output:

when k is>0, where k ∈ is the slow time delay, Δ f is the Doppler step size, l Δ f is the Doppler frequency, f₀Is the starting frequency, (.)^*Representing a conjugate operation, when k ≦ 0, the above equation becomes:

the accumulated peak level of the generalized ambiguity function can show the overall doppler margin characteristic, which can be expressed as:

where L limits the range of doppler tolerance that needs to be considered, then the target echo with unknown velocity will have doppler mismatch loss when matched filtered, and we design the ragging sequence to minimize the loss of doppler mismatch in a statistical sense.

4. The method for detecting sparse moving objects based on the slow-time sliding window filter according to claim 1, wherein the step 3 specifically comprises: PRI modulation will change the average burst duty cycle, i.e. affect the radar resource utilization, the cost function is expressed as:

wherein D (a) directly affects the utilization rate of radar resources and can not take any small value, therefore, consider D (a)>D_l,D_lIs the minimum allowable duty factor and, in addition, the minimum maximum unambiguous distance R_maxThere must also be a limit to the number of,

finally, the joint optimization problem of a (a) and d (a) can be expressed as:

where λ s is the weight of two terms, k 100 is a scale factor, and analysis of the objective function is easy to implementNow, no matter what value a takes, T + a (iT)²Proportional to i, i ∈ (0.., N-1), assuming for simplicity that a>0, D (gamma) ═ Dl, and the PRI minimum satisfies T>2Rmax/c, so the original problem is equivalent to:

by derivation, P₂Can be further expressed as:

notice P₃The target function of (2) comprises the accumulation sum form of exponential functions, and an analytic solution is difficult to obtain, and the problem is a continuous problem of a variable a, and an optimal solution can be obtained by a gold search method.

Images