Low observable boost-glide trajectory target detection and tracking method under slant range ambiguity condition

Abstract

The present application provides a low observable boost-glide trajectory target detection and tracking method under the condition of slant range ambiguity, belongs to the field of near space hypersonic target detection and tracking, and is configured with an alternate pulse repetition frequency model for radar ranging; defines an extended non-coherent accumulation model in the range-time plane for target detection; configures an S-shaped recursive energy tracking model for target tracking; designs a recursive energy filter, and updates through recursive energy, so that target tracking is always kept under the condition of high signal-to-noise ratio, and the target track is obtained by using a filtering algorithm. The method of the present application designs the pulse repetition frequency in the same sampling period as a constant value, so that it has enough energy for coherent accumulation detection; and designs the pulse repetition frequency in different sampling periods as alternate values, so that it has the condition for solving the slant range ambiguity problem. At the same time, it can provide conditions for solving the slant range ambiguity problem.

Description

Technical Field

[0001] This invention belongs to the field of near-space hypersonic target detection and tracking, and particularly relates to a method for low-observable boost-glide trajectory target detection and tracking under conditions of tilted distance ambiguity. Background Technology

[0002] Currently, near space refers to the airspace at an altitude of 20km-100km. Near-space hypersonic vehicles are atmospheric or suborbital vehicles capable of traveling at speeds exceeding Mach 5 in near space. Unlike traditional aerodynamic and satellite-orbiting targets, near-space targets possess a unique hypersonic boost-glide trajectory, enabling them to rapidly attack any target globally within an hour. In particular, with the successful testing of hypersonic vehicles such as the AGM-183A and X-51A, near-space hypersonic weapons have become the preferred means of implementing global strike strategies. However, existing radar early warning and defense systems are unable to effectively track and intercept these targets.

[0003] To achieve early warning of hypersonic targets, radar needs to detect them at long range. If hypersonic targets can be detected and tracked at long range, radar early warning and defense systems will have sufficient time to respond to this hypersonic weapon threat. However, in long-range detection mode, the problem of ambiguity in tilt range will be introduced into radar ranging. With ambiguity in tilt range, it is difficult to distinguish which transmitted pulse signal the received radar echo originates from, thus making it impossible to obtain the true distance between the target and the radar.

[0004] As a classic method for resolving tilt range ambiguity, the multi-pulse repetition frequency method is widely used in target detection and tracking. Its advantage is that it can solve the tilt range ambiguity problem while performing coherent accumulation detection of the target. Its disadvantage is that because one coherent accumulation period is allocated to multiple pulse repetition frequencies, the echo energy after coherent accumulation is difficult to reach the target detection threshold. In particular, under low signal-to-noise ratio conditions, the tilt range ambiguity problem cannot be solved due to missed target detection.

[0005] However, hypersonic targets inevitably possess certain stealth characteristics. When a target moves at hypersonic speeds, a large amount of shock plasma is generated around it. This shock plasma can strongly absorb, scatter, and reflect radar electromagnetic waves, thus endowing the target with a certain degree of stealth. This also means that it is difficult to obtain the energy required for target detection through coherent accumulation in a short period of time, and therefore, it is impossible to effectively solve the problem of ambiguity at tilted range. Summary of the Invention

[0006] The present invention provides a target detection and tracking method for low observable boost-glide trajectory under tilt distance ambiguity conditions, which can simultaneously solve the target detection and tracking problems caused by the combined effects of tilt distance ambiguity, low observability and boost-glide maneuvering derived from hypersonic target motion.

[0007] The methods include:

[0008] S1: Configure the alternating pulse repetition frequency model for radar ranging;

[0009] ① The fuzzy tilt distance of the target is measured by alternating pulse repetition frequency;

[0010] ②Restore the true distance to the target;

[0011] S2: Define an extended noncoherent accumulation model for target detection in the distance-time plane;

[0012] ① Define the extended noncoherent accumulation model;

[0013] ② Select the distance-time plane;

[0014] ③ Extending the noncoherent accumulation detection method based on distance-time Hough transform;

[0015] ④ Detecting low-observable targets;

[0016] S3: Configure the S-shaped recursive energy tracking model for target tracking;

[0017] ① Configure the S-shaped motion model;

[0018] ② Design a recursive energy filter and update it by recursive energy to keep target tracking under high signal-to-noise ratio conditions. Use the filtering algorithm to obtain the target track.

[0019] It should be further noted that the method of measuring the fuzzy tilt distance of the target by alternating pulse repetition frequency in step S1 also includes:

[0020] Within the same sampling period, the pulse repetition frequency is constant. Let the fuzzy measurement of the target at time k be...

[0021]

[0022] Where, r amb θ(k) is the fuzzy tilt distance, and θ(k) is the azimuth angle. is the pitch angle, and a(k) is the amplitude of the echo pulse.

[0023] It should be further noted that by using three alternating pulse repetition frequencies to design the radar ranging model, the fuzzy tilt range of the target can be expressed as:

[0024]

[0025] in,

[0026]

[0027] Formula (3) calculates the fuzzy tilt distance of the i-th pulse repetition frequency. The calculation is performed in the following manner.

[0028]

[0029] t true (k) is the actual time delay of the echo pulse, mod(·) represents the modulo operation, T i =1 / f i It is the pulse repetition period, f i is the repetition frequency of the i-th pulse, c is the speed of light, and i = 1, 2, 3.

[0030] It should be further noted that the steps to reconstruct the true distance to the target also include:

[0031] The repetition frequency of the i-th pulse based on radar ranging is f. i Then f i The corresponding maximum unambiguous tilt distance is,

[0032] R i =c / 2f i (5)

[0033] If the interval R i For fuzzy tilt distance If we extend the slope, the extension tilt distance is expressed as:

[0034]

[0035] Where, r i j (k) is the i-th extended tilt distance, N i It is the amount of extended tilt distance;

[0036] For example, if the actual distance is less than the radar distance, the amount of extended tilt range is given by the following formula:

[0037] N i =Int(R max / R i (7)

[0038] Among them, R max This represents the radar's ranging range, and Int(·) indicates the rounding operation;

[0039] The extended measurement of the target is given by the following formula:

[0040]

[0041] in, This is the j-th extended measurement of the i-th PRF.

[0042] It should be further noted that the definition of the extended noncoherent accumulation model in step S2 also includes:

[0043] First, multiple assumptions are applied to the alternating multi-pulse repetition frequency measurement; second, non-coherent accumulation detection is performed simultaneously with target coherent accumulation detection, so that the accumulation energy of low-observable targets reaches the target detection threshold; finally, the detection of low-observable targets is completed.

[0044] It should be further noted that the selection of the distance-time plane in step S2 also includes:

[0045] Assuming the target's tilt distance is r = 600 km and the radar angle measurement error is Δα = 0.3°, then the target's position measurement deviation is...

[0046]

[0047] According to the 3δ decision criterion, the maximum deviation of the target's position measurement is 9.45 km, which is much larger than the radar range measurement error of several hundred meters.

[0048] It should be further noted that the extension of the noncoherent accumulation detection method based on the distance-time Hough transform in step S2 also includes: Let (r i j (k),t(k)) is a point in the distance-time plane, where r i j (k) is the pulse repetition frequency f i The j-th extended tilt distance, t(k) is r i j The time stamp of (k) in The unique curve corresponding to the given point in the plane is obtained in the following way.

[0049]

[0050] Where ρ is (r i j The distance from point (k),t(k)) to the origin. It is the angle between the r-axis and the ρ-axis;

[0051] If multiple curves are in If two lines intersect at a single point in a plane, then in the distance-time plane, there exists a straight line that corresponds to multiple curves. This straight line is represented as...

[0052]

[0053] Where, (ρ0, ) represents the intersection of multiple curves, and r and t represent the distance and time variables corresponding to the straight line, respectively.

[0054] It should be further noted that the method for detecting low-observable targets in step S2 also includes: Plane divided into sizes of Several cells allow the target energy to accumulate in one of the cells;

[0055] The center of cell (u,v) is represented as follows:

[0056]

[0057]

[0058] in,

[0059] Δρ=R max / N ρ (14)

[0060]

[0061] N ρ It is the number of ρ units. yes The number of units, R max This refers to the radar's ranging range;

[0062] In the Based on planar discretization, Curves in a plane are represented by the following pair. The mapping is replaced with,

[0063]

[0064] Among them, (r i j (k),t(k)) is a point in the distance-time plane. yes in the plane A set of points ;

[0065] In the A pair of curves in a plane After mapping, point (r) ij The energy in (k),t(k)) will be stored in the cells through which the curve passes, and the energy in cell (u,v) is represented as,

[0066]

[0067] in, Let A(k) be the current energy in cell (u,v), and let A(k) be the energy in cell (r). i j The energy at point (k),t(k));

[0068] If multiple points in the distance-time plane are approximately connected by a straight line, then the energy of these multiple points will be concentrated in the distance-time plane. In a single cell of a plane, a hypothesis test is performed that makes the detection of low-observable targets describe the following:

[0069] H0: The target was detected in cell (u,v);

[0070] H1: No target was detected in cell (u,v);

[0071] Where λ is the energy threshold;

[0072] Under the assumption that H0 holds, the target trajectory is obtained through the following Hough inverse mapping:

[0073]

[0074] Low-observable targets were then detected from the extended tilt range.

[0075] It should be further noted that the method of configuring the S-shaped motion model in step S3 also includes:

[0076] The autocorrelation function of the target acceleration is designed as follows:

[0077]

[0078] Where a(t) is the target acceleration at time t. Let ω0 be the instantaneous covariance of a(t), and ω0 be the angular velocity of the target boost-glide trajectory.

[0079] The power spectrum of the target acceleration is expressed as follows: (The Fourier transform of the autocorrelation function of the target acceleration is given by...)

[0080]

[0081] Configure the approximate whitening filter as follows:

[0082]

[0083] Assumption yes In the time domain, the expression is... The Laplace transform is expressed as

[0084]

[0085] and then The differential equation is expressed as

[0086]

[0087] Where v(t) is a function with zero mean and constant variance. Input white noise;

[0088] Assumption

[0089]

[0090] Let x(t) be the target state vector in the X direction at time t. and These are the target's position, velocity, acceleration, and jerk, respectively, and they have...

[0091]

[0092] Substitute the state phasor X(t) into If the differential equation is given, then the equation of continuous motion of the target is expressed as:

[0093]

[0094] in,

[0095]

[0096] Β=[0 0 0 ω0] T (30)

[0097] By integrating both sides of the continuous equations of motion of the target, we obtain the discrete equations of motion of the target.

[0098]

[0099] The discrete equations of motion of the target are rewritten as follows:

[0100] X(k+1)=ΦX(k)+V(k) (32)

[0101] in

[0102]

[0103] It is the state transition matrix, where T is the time interval.

[0104]

[0105] It has constant variance

[0106]

[0107] Zero-mean Gaussian white noise.

[0108] It should be further noted that the design of the recursive energy filter in step S3 also includes:

[0109] Assume the recursive energy at time k is:

[0110]

[0111] Where a(i) is the energy of the i-th trajectory point, i = k-m+1, k-m+2, ..., k;

[0112] The recursive energy E(k) is introduced into the filtering algorithm to provide a high signal-to-noise ratio for tracking targets with low observability; furthermore, the update of the target trajectory is represented by the following hypothesis test:

[0113] H0: E(k)≥λ, the target trajectory is updated by recursively updating the energy;

[0114] H1: E(k) < λ, the target track is terminated;

[0115] Where λ is the energy threshold, which is the same as the energy threshold for target detection;

[0116] Under the assumption of H0, the target trajectory is updated by the maximum energy measurement in the tracking gate, thus enabling the target to be tracked in real time under low signal-to-noise ratio conditions;

[0117] Assumption

[0118] b(k+1)=max{b1(k+1),b2(k+1),...,b N (k+1)} (37)

[0119] It is the maximum energy measured at the tracking point in the tracking gate, where b i (k+1) is the energy of the i-th candidate measurement in the tracking gate, and N is the number of candidate measurements;

[0120] Introducing b(k+1) into the filtering algorithm, the target trajectory is updated using the measurement point with the highest energy in the tracking gate, and the energy update is recursively calculated as follows.

[0121] E(k+1)=E(k)+b(k+1)-a(k-m+1) (38)

[0122] Where a(k-m+1) is the trajectory point energy at the last moment in the recursive energy;

[0123] By recursively updating the energy, target tracking is always maintained under conditions of high signal-to-noise ratio, and the target trajectory is then obtained using a filtering algorithm.

[0124] As can be seen from the above technical solutions, the present invention has the following advantages:

[0125] 1) The target detection and tracking method for low observable boost-glide trajectory under tilt distance ambiguity conditions provided by the present invention, on the one hand, designs the pulse repetition frequency within the same sampling period as a fixed value, so that it has enough energy for coherent accumulation detection; on the other hand, designs the pulse repetition frequency between different sampling periods as alternating values, so that it has the conditions to solve the tilt distance ambiguity problem, so that it can provide conditions for solving the tilt distance ambiguity problem while detecting and tracking the target.

[0126] 2) The method of the present invention combines extended measurement after multiple hypothesis processing with anti-stealth technology, which can complete the detection of low observable targets while solving the ambiguity of tilt distance; the method of the present invention no longer converts the target measurement into traditional position measurement, but directly detects low observable targets in the distance-time plane, which can effectively avoid the position measurement deviation introduced during long-range detection.

[0127] 3) This invention also addresses the low observability characteristics of targets, going beyond the assumption that the target's trajectory is a straight line. Instead, it utilizes a periodic glide jump method to predict the target's boost-glide trajectory, thus ensuring a high detection probability while also considering the target's maneuverability. Furthermore, considering the boost-glide trajectory characteristics of targets, this method no longer uses the traditional nearest neighbor filtering method for real-time target measurement tracking. Instead, it uses a maximum recursive energy decision method for recursive tracking of target measurements, thereby achieving both real-time tracking of the target's boost-glide trajectory and a high detection probability.

[0128] 4) This invention can simultaneously solve the detection and tracking problems caused by the combined effects of tilt distance ambiguity, low observability, and boost-glide maneuvering resulting from hypersonic motion of the target. Attached Figure Description

[0129] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0130] Appendix Figure 1 This is a flowchart of a low-observable boost-glide trajectory target detection and tracking method under conditions of tilted distance ambiguity;

[0131] Appendix Figure 2 This is a diagram of an alternating pulse repetition frequency ranging model;

[0132] Appendix Figure 3 It is an extended measurement diagram at the repetition frequency of a single pulse;

[0133] Appendix Figure 4 It is an extended measurement diagram at the alternating pulse repetition frequency;

[0134] Appendix Figure 5 This is a design scheme diagram for the extended non-coherent accumulation model;

[0135] Appendix Figure 6 It is a noncoherent accumulation detection map based on distance-time Hough transform;

[0136] Appendix Figure 7 This is the design diagram of the acceleration autocorrelation function of the S-shaped motion model;

[0137] Appendix Figure 8 It is a graph of recursive energy construction;

[0138] Appendix Figure 9 It is a graph of recursive energy updates;

[0139] Appendix Figure 10 It is the maximum energy filtering diagram. Detailed Implementation

[0140] The purpose of the target detection and tracking method for low-observable boost-glide trajectory under tilt range ambiguity conditions provided by this invention is to break through the constraints of traditional target detection and tracking methods, and solve the target detection and tracking problems under the combined effects of tilt range ambiguity, low observability and boost-glide maneuvering, thereby improving the ability of existing radar to detect and track hypersonic targets.

[0141] The low-observable boost-glide trajectory target detection and tracking method provided by this invention can acquire and process related data based on artificial intelligence technology. Specifically, the low-observable boost-glide trajectory target detection and tracking method under inclined distance ambiguity conditions utilizes digital computers or digitally controlled machines to simulate, extend, and expand human intelligence, perceiving the environment, acquiring knowledge, and using that knowledge to obtain optimal results. This includes theories, methods, technologies, and application devices.

[0142] The target detection and tracking method for low-observable boost-glide trajectories under conditions of tilted distance ambiguity involves both hardware and software technologies. The fundamental technologies of this invention generally include sensors, dedicated artificial intelligence chips, cloud computing, distributed storage, big data processing technology, operating / interactive systems, and mechatronics. The software technologies for intelligent diagnostic methods for CNC machine tools mainly include machine learning / deep learning and programming languages. Programming languages ​​include, but are not limited to, object-oriented programming languages—such as Java, Smalltalk, and C++—as well as conventional procedural programming languages—such as C or similar languages.

[0143] The low-observable boost-glide trajectory target detection and tracking method under tilt distance ambiguity conditions is applied to one or more detection terminals. The detection terminal is a device that can automatically perform numerical calculations and / or information processing according to pre-set or stored instructions. Its hardware includes, but is not limited to, microprocessors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.

[0144] The testing terminal can be any electronic product that can interact with the user, such as personal computers, tablets, smartphones, personal digital assistants (PDAs), interactive network television (IPTV), etc.

[0145] The detection terminal may also include network devices and / or user equipment. The network devices include, but are not limited to, a single network server, a server group consisting of multiple network servers, or a cloud based on cloud computing consisting of a large number of hosts or network servers.

[0146] The network where the detection terminal is located includes, but is not limited to, the Internet, wide area network, metropolitan area network, local area network, and virtual private network (VPN).

[0147] The problem to be solved by the low-observable boost-glide trajectory target detection and tracking method under tilt distance ambiguity conditions provided by this invention includes:

[0148] 1) The challenge of joint detection and tracking caused by the ambiguity of tilt distance, low observability and the combined effects of boost-glide maneuvering derived from the hypersonic motion of the target.

[0149] 2) Under the condition of ambiguity of tilt distance, the existing single-pulse repetition frequency ranging method has enough energy for coherent accumulation, but cannot solve the problem of tilt distance ambiguity; while the existing multi-pulse repetition frequency ranging method can solve the problem of tilt distance ambiguity, but cannot provide enough energy for the coherent accumulation detection of the target.

[0150] 3) Under the dual influence of tilt range ambiguity and low observability, existing solutions for tilt range ambiguity and low observability target detection methods are significantly incompatible. On the one hand, most existing low observable target detection methods only discuss the stealth characteristics of the target, without fully considering the problem of low observable target detection under tilt range ambiguity. On the other hand, most existing solutions for tilt range ambiguity are based on the assumption of high signal-to-noise ratio. Under low signal-to-noise ratio conditions, the problem of tilt range ambiguity cannot be solved due to missed detection of targets.

[0151] 4) Under the dual influence of low observability and irregular maneuvering, existing low-observability target tracking methods and maneuvering target tracking methods are no longer applicable, making it difficult to effectively track targets with low-observable boost-glide trajectories. On the one hand, most existing maneuvering target tracking methods are based on the assumption of a high signal-to-noise ratio and do not have the ability to handle stealth targets under low signal-to-noise ratio conditions; on the other hand, most existing low-observable target tracking methods limit the target's motion to a straight line, while the target's actual trajectory is not limited to a single straight line and is not suitable for the target's boost-glide trajectory.

[0152] To address the aforementioned problems, the target detection and tracking method for low-observable boost-glide trajectories under conditions of tilted distance ambiguity provided by this invention includes the following technical measures:

[0153] Step 1: Improve the existing radar ranging method by designing a radar ranging model using pulses with alternating pulse repetition frequencies. In this case, the radar pulse repetition frequency is constant within the same sampling period, but changes alternately during different sampling periods. As a result, the radar echo has enough energy for coherent accumulation within the same sampling period, and has the conditions to resolve tilt range ambiguity during different sampling periods. This also means that this method can provide conditions for solving the tilt range ambiguity problem while simultaneously detecting and tracking targets.

[0154] Step 2: Improve the existing target detection method by directly combining the extended measurement after multi-hypothesis processing with the anti-stealth technology in the range-time plane. Through extended non-coherent accumulation detection in the range-time plane, the problem of low observable target detection under tilted range ambiguity conditions can be effectively solved.

[0155] Step 3: Improve the existing target tracking method. By designing the boost-glide trajectory matching motion model and developing the maximum recursive energy filtering algorithm, it can combine the advantages of real-time processing and anti-stealth, thus effectively solving the target tracking problem under the dual influence of low observability and boost-glide maneuvering.

[0156] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0157] Please see Figure 1 The diagram shows a flowchart of a low-observable boost-glide trajectory target detection and tracking method under tilt distance ambiguity conditions in a specific embodiment. The method includes the following steps:

[0158] S1: Configure the alternating pulse repetition frequency model for radar ranging;

[0159] In one exemplary embodiment, the ranging model of the radar is improved to a new mode of alternating pulse repetition frequency in the ranging stage. In this mode, the pulse repetition frequency is constant within the same sampling period, and the radar echo has sufficient energy for coherent accumulation detection; the alternating pulse repetition frequency between different sampling periods, after multiple assumption processing, can provide conditions for solving the problem of tilt range ambiguity while simultaneously detecting and tracking the target.

[0160] ① The fuzzy tilt distance of the target is measured by alternating pulse repetition frequency;

[0161] The pulse repetition frequency is constant within the same sampling period, but varies alternately during different sampling periods, such as... Figure 2 As shown.

[0162] Assume the fuzzy measurement of the target at time k is,

[0163]

[0164] Where, r amb θ(k) is the fuzzy tilt distance, and θ(k) is the azimuth angle. is the pitch angle, and a(k) is the amplitude of the echo pulse.

[0165] If a radar ranging model is designed using three alternating pulse repetition frequencies, the fuzzy tilt range of the target can be expressed as:

[0166]

[0167] in,

[0168]

[0169] Formula (3) is the fuzzy tilt distance of the repetition frequency of the it-th pulse.

[0170]

[0171] Formula (4) is the ambiguity delay of the echo pulse, t true (k) is the actual time delay of the echo pulse, mod(·) represents the modulo operation, T i =1 / f i It is the pulse repetition period, f i is the repetition frequency of the i-th pulse, c is the speed of light, and i = 1, 2, 3.

[0172] ②Restore the true distance to the target;

[0173] Since the fuzzy tilt distance is not the true distance of the target, the sampling multiple hypothesis processing method extends the fuzzy tilt distance to several uncertain intervals. At this time, the true position of the target can be obtained from one of the uncertain intervals.

[0174] Since the repetition frequency of the i-th pulse in radar ranging is f i Then its corresponding maximum unambiguous tilt distance is,

[0175] R i =c / 2f i (5)

[0176] If we use interval R i For fuzzy tilt distance If we extend it, the extension tilt distance can be expressed as,

[0177]

[0178] Where, r i j (k) is the i-th extended tilt distance, N i It is the amount of extended tilt distance.

[0179] Meanwhile, the actual distance is less than the radar distance, and therefore the amount of extended tilt range can be given by the following formula:

[0180] Ni =Int(R max / R i (7)

[0181] Among them, R max The range of the radar is represented by Int(·), which indicates the rounding operation.

[0182] Furthermore, the extended measurement of the target can be given by the following formula:

[0183]

[0184] in, This is the j-th extended measurement of the i-th PRF.

[0185] Through multi-hypothesis processing, the fuzzy tilt distance is extended to several uncertain intervals. For a single pulse repetition frequency, the true distance of the target can be reconstructed from one of these uncertain intervals, but it is difficult to distinguish which is the true distance of the target, such as... Figure 3 As shown. For situations where the pulse repetition frequency changes alternately, a continuous trajectory can only be formed at the target's actual location, such as... Figure 4 As shown. This means that the true distance to the target can be distinguished simultaneously with target detection and tracking.

[0186] S2: Define an extended noncoherent accumulation model for target detection in the distance-time plane;

[0187] In the detection phase, the target detection model is improved to a new extended noncoherent accumulation mode in the range-time plane. This allows the method of the present invention to not only resolve tilt range ambiguity while detecting low-observable targets, but also effectively avoid position measurement biases introduced by long-range radar detection.

[0188] ① Define the extended noncoherent accumulation model;

[0189] In this embodiment, the problem of tilt distance ambiguity can be solved simultaneously with target parameter accumulation detection through multiple hypothesis processing. However, under low signal-to-noise ratio conditions, the target may be missed because the energy accumulated by the coherent phase does not reach the detection threshold. In this case, the problem of tilt distance ambiguity cannot be solved due to the missed detection of the target.

[0190] Therefore, this implementation example Figure 5 The extended noncoherent accumulation model shown is used to detect low-observable targets while solving the tilt distance ambiguity problem.

[0191] First, multiple assumptions are processed for alternating multi-pulse repetition frequency measurement, creating conditions for solving the problem of tilt distance ambiguity while detecting low observable targets.

[0192] Secondly, while performing coherent accumulation detection on the target, non-coherent accumulation detection is also performed to ensure that the accumulation energy of low-observable targets reaches the target detection threshold.

[0193] Finally, by combining the two approaches, the detection of low-observable targets can be achieved while simultaneously resolving the problem of tilt distance ambiguity.

[0194] ② Select the distance-time plane;

[0195] According to the embodiments of this application, unlike the classic noncoherent accumulation detection method, the extended tilt distance measurement is no longer converted into the traditional position measurement, but is directly performed on the distance-time plane using noncoherent accumulation detection. In this case, the method of the present invention can not only complete the detection of low observable targets while solving the tilt distance ambiguity, but also effectively avoid the position measurement deviation introduced by radar long-range detection.

[0196] Since radar position deviation is mainly caused by radar angle measurement error and is proportional to the target's tilt distance, assuming the target's tilt distance is r = 600 km and the radar angle measurement error is Δα = 0.3°, then the target's position measurement deviation is...

[0197]

[0198] According to the 3δ decision criterion, the target's position measurement deviation can reach up to 9.45 km, which is much larger than the radar range measurement error of several hundred meters.

[0199] In this context, during the noncoherent accumulation detection of targets, replacing traditional position measurements with range-time measurements can effectively avoid the position measurement bias introduced during long-range radar detection. Therefore, the range-time plane is selected for extended noncoherent accumulation detection of targets.

[0200] ③ Extending the noncoherent accumulation detection method based on distance-time Hough transform;

[0201] According to an embodiment of this application, considering that the target trajectory in a short time can be approximated as a straight line, the Hough transform method is selected to design the extended range-time noncoherent accumulation detection method. This is because, by processing the target measurement with the Hough transform, the linear detection problem in a short time can be transformed into an energy accumulation problem, thereby enabling the detection of low-observable targets under the condition of improved signal-to-noise ratio.

[0202] Assume (r) i j (k),t(k)) is a point in the distance-time plane, where r i j (k) is the pulse repetition frequency fi The j-th extended tilt distance, t(k) is r i j The time stamp of (k), and then, in A unique curve corresponding to that point can be obtained in the plane.

[0203]

[0204] Where ρ is (r i j The distance from point (k),t(k)) to the origin. It is the angle between the r-axis and the ρ-axis.

[0205] If multiple such curves are in If curves intersect at a single point in a plane, then there exists a straight line in the distance-time plane that corresponds to these curves. This straight line can be represented as:

[0206]

[0207] Where, (ρ0, ) is the intersection of these curves, and r and t are the distance and time variables corresponding to this straight line, respectively.

[0208] This invention utilizes an energy accumulation method in By finding the intersection points of multiple curves in a plane, low-observable targets can be detected in the distance-time plane, such as... Figure 6 As shown.

[0209] ④ Detecting low-observable targets;

[0210] In the short term, the target trajectory can be approximated as a straight line, but it is not a true straight line. In reality, the target's trajectory... Curves in a plane do not intersect at a single point, but rather converge in a certain region.

[0211] Therefore, here will Plane divided into sizes of The cells are arranged such that the target energy can accumulate within one of them. The center of cell (u,v) can be represented as...

[0212]

[0213]

[0214] in,

[0215] Δρ=R max / N ρ (14)

[0216]

[0217] N ρ It is the number of ρ units. yes The number of units, R max It refers to the radar's ranging range.

[0218] In the Based on planar discretization, A curve in a plane can be represented by the following pair of curves. The mapping is replaced with,

[0219]

[0220] Among them, (r i j (k),t(k)) is a point in the distance-time plane. yes in the plane A set of points .

[0221] In the A pair of curves in a plane After mapping, point (r) i j The energy in (k),t(k)) will be stored in the cells through which the curve passes, and the energy in cell (u,v) can be expressed as,

[0222]

[0223] in, Let A(k) be the current energy in cell (u,v), and let A(k) be the energy in cell (r). i j The energy at point (k),t(k)).

[0224] If some points in the distance-time plane are approximately connected by a straight line, then the energy of those points will be concentrated in... In a single cell within a plane. Therefore, the problem of low-observable target detection can be formulated as a hypothesis test as follows:

[0225] H0: The target was detected in cell (u,v).

[0226] H1: No target was detected in cell (u,v).

[0227] Where λ is the energy threshold.

[0228] Under the assumption that H0 holds, the target trajectory can be obtained through the following Hough inverse mapping.

[0229]

[0230] This allows for the detection of low-observable targets from extended tilt ranges.

[0231] S3: Configure the S-shaped recursive energy tracking model for target tracking;

[0232] In the tracking phase, the target tracking model is improved to a new S-shaped recursive energy tracking mode. In this mode, the target's boost-glide trajectory can be predicted using the S-shaped motion model, and the target's trajectory under low signal-to-noise ratio conditions can be updated using a recursive energy filtering algorithm.

[0233] ① Configure the S-shaped motion model;

[0234] In one exemplary embodiment, the S-shaped motion model is designed to match the boost-glide trajectory characteristic of hypersonic targets. Unlike the classic Singer motion model, the S-shaped motion model does not design the target acceleration as a zero-mean Markov random process with exponential autocorrelation. Instead, it designs the target acceleration as a zero-mean Markov process with cosine autocorrelation, taking full account of the target's periodic motion characteristics. Figure 7 As shown.

[0235] The autocorrelation function of the target acceleration is designed as follows:

[0236]

[0237] Where a(t) is the target acceleration at time t. Let ω0 be the instantaneous covariance of a(t), and let ω0 be the angular velocity of the target boost-glide trajectory.

[0238] The power spectrum of the target acceleration can be expressed as follows: (The Fourier transform of the autocorrelation function of the target acceleration is given by...)

[0239]

[0240] This embodiment can be designed as follows:

[0241]

[0242] Formula (21) is an approximate whitening filter. Given the power spectrum of the input white noise, then The output can be represented as,

[0243]

[0244] contrast And S(jω) can be obtained,

[0245]

[0246] This means that Designing it as an approximate whitening filter is reasonable.

[0247] If this embodiment assumes yes In the time domain, the expression is... The Laplace transform of can be expressed as,

[0248]

[0249] and then The differential equation can be expressed as,

[0250]

[0251] Where v(t) is a function with zero mean and constant variance. Input white noise.

[0252] Assumption

[0253]

[0254] Formula (26) is the target state vector in the X direction at time t, x(t). and These are the target's position, velocity, acceleration, and jerk, respectively, and they have...

[0255]

[0256] Substitute the state phasor X(t) into If the differential equation is given, then the equation of continuous motion of the target can be expressed as:

[0257]

[0258] in,

[0259]

[0260] Β=[0 0 0 ω0] T (30)

[0261] By integrating both sides of the continuous equations of motion of the target, we can obtain the discrete equations of motion of the target.

[0262]

[0263] Rewriting this expression yields...

[0264] X(k+1)=ΦX(k)+V(k) (32)

[0265] in,

[0266]

[0267] Formula (33) is the state transition matrix, and T is the time interval.

[0268]

[0269] Formula (34) is zero-mean Gaussian white noise with constant variance in Formula (35).

[0270]

[0271] ②This embodiment also includes a recursive energy filter;

[0272] Since the target's boost-glide trajectory can be predicted using the designed S-shaped motion model, the remaining task is to design a filter algorithm to update the target's trajectory under low observability conditions.

[0273] It should be noted that recursive energy is introduced in target tracking to transform the problem of tracking low-observable targets into the problem of tracking high-observable targets.

[0274] On the one hand, the recursive energy consists of the energy of m tracking points, thus enabling low-observable targets to be tracked under high signal-to-noise ratio conditions, such as... Figure 8 As shown.

[0275] On the other hand, the recursive energy update is achieved by replacing the tracking point energy at the last moment with the energy of the measurement point, thus enabling real-time tracking of low-observable targets, such as... Figure 9 As shown.

[0276] This embodiment assumes that the recursive energy at time k is,

[0277]

[0278] Where a(i) is the energy of the i-th trajectory point, i = k-m+1, k-m+2, ..., k.

[0279] Introducing the recursive energy E(k) into existing filtering algorithms can provide a high signal-to-noise ratio for tracking targets with low observability. Furthermore, the update of the target trajectory can be represented by the following hypothesis test.

[0280] H0: E(k)≥λ, the target trajectory is updated by recursively updating the energy.

[0281] H1:E(k)<λ, the target track is terminated.

[0282] Where λ is the energy threshold, which is the same as the energy threshold for target detection.

[0283] Under the assumption of H0, the target trajectory is updated by measuring the maximum energy in the tracking gate, thus enabling real-time tracking of the target even under low signal-to-noise ratio conditions. Figure 10 As shown.

[0284] This embodiment is the same as the traditional filtering algorithm. The target trajectory is updated online through the measurement in the tracking gate, so that the target's boost-glide trajectory can be tracked in real time.

[0285] Unlike traditional filtering algorithms, the target trajectory is updated using the measurement point with the maximum energy, rather than the measurement point with the minimum statistical distance. This transforms the problem of tracking low-observable targets into the problem of tracking high-observable targets.

[0286] In this embodiment, it is assumed that formula (37) is the maximum energy of the measurement point in the tracking gate, where b i (k+1) is the energy of the i-th candidate measurement in the tracking gate, and N is the number of candidate measurements.

[0287] b(k+1)=max{b1(k+1),b2(k+1),...,b N (k+1)} (37)

[0288] By introducing b(k+1) into the traditional filtering algorithm, the target trajectory can be updated using the measurement point with the highest energy in the tracking gate. Therefore, the recursive energy update can be performed as follows.

[0289] E(k+1)=E(k)+b(k+1)-a(k-m+1) (38)

[0290] Where a(k-m+1) is the trajectory point energy at the last moment in the recursive energy.

[0291] By recursively updating the energy, target tracking can always be maintained under conditions of high signal-to-noise ratio, and the target trajectory can be obtained using existing filtering algorithms.

[0292] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0293] Thus, the target detection and tracking method for low-observable boost-glide trajectories under tilted range ambiguity conditions, as disclosed in this invention, addresses the challenges of target detection and tracking under the combined influence of tilted range ambiguity, low observability, and boost-glide maneuvers arising from hypersonic target motion. This invention improves upon traditional radar ranging methods by modifying the existing radar ranging model to a new mode of alternating pulse repetition frequencies, providing conditions for resolving tilted range ambiguity while simultaneously detecting and tracking targets. Next, it improves existing target detection methods by combining extended measurements after multiple hypothesis processing with anti-stealth technology in the range-time plane. This not only resolves tilted range ambiguity while detecting low-observable targets but also effectively avoids position measurement biases introduced by long-range radar detection. Finally, it improves existing target tracking methods by designing a boost-glide trajectory matching motion model and developing a maximum recursive energy filtering algorithm, giving it both real-time processing and anti-stealth advantages, thereby effectively solving the target tracking challenges under the combined influence of low observability and boost-glide maneuvers.

[0294] The units and algorithm steps of the various examples described in the embodiments of the low-observable boost-glide trajectory target detection and tracking method under tilt distance ambiguity conditions of the present invention can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of the present invention.

[0295] The features, structures, or characteristics described in the low-observable boost-glide trajectory target detection and tracking method under tilt distance ambiguity conditions of the present invention can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a full understanding of embodiments of the invention. However, those skilled in the art will recognize that the technical solutions of the invention can be practiced without one or more of the specific details, or other methods, components, apparatuses, steps, etc., can be employed. In other instances, well-known methods, apparatuses, implementations, or operations are not shown or described in detail to avoid obscuring aspects of the invention.

[0296] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for detecting and tracking low-observable boost-glide trajectory targets under conditions of tilted distance ambiguity, characterized in that, The methods include, S1: Configure the alternating pulse repetition frequency model for radar ranging; ① The fuzzy tilt distance of the target is measured by alternating pulse repetition frequency; ② Restore the true distance to the target; The steps to restore the true distance to the target also include: The first based on radar ranging The pulse repetition frequency is ,but The corresponding maximum unambiguous tilt distance is, (5) If by interval For fuzzy tilt distance If we extend the slope, the extension tilt distance is expressed as: , (6) in, It is the first One extended tilt distance, It is the amount of extended tilt distance; For example, if the actual distance is less than the radar distance, the amount of extended tilt range is given by the following formula: (7) in, This refers to the radar's ranging range. Indicates the rounding operation; The extended measurement of the target is given by the following formula: (8) in, For the first i The j-th extended measurement of a PRF; S2: Define an extended noncoherent accumulation model for target detection in the distance-time plane; ① Define the extended noncoherent accumulation model; ② Select the distance-time plane; ③ Extending the noncoherent accumulation detection method based on distance-time Hough transform; ④ Detecting low-observable targets; S3: Configure the S-shaped recursive energy tracking model for target tracking; ① Configure the S-shaped motion model; ② Design a recursive energy filter and update it by recursive energy to keep target tracking under a high signal-to-noise ratio condition. Use the filtering algorithm to obtain the target track.

2. The method for detecting and tracking low-observable boost-glide trajectory targets under tilt distance ambiguity conditions according to claim 1, characterized in that, The method of measuring the fuzzy tilt distance of the target by alternating pulse repetition frequency in step S1 also includes: The pulse repetition frequency is constant within the same sampling period. Assume the target is... The fuzzy measurement of time is, (1) in, It is a fuzzy tilt distance. It's the azimuth. It is the pitch angle. It is the amplitude of the echo pulse.

3. The method for detecting and tracking low-observable boost-glide trajectory targets under tilt distance ambiguity conditions according to claim 1, characterized in that, The definition extension of the noncoherent accumulation model in step S2 also includes: First, multiple assumptions are applied to the alternating multi-pulse repetition frequency measurement; second, non-coherent accumulation detection is performed simultaneously with target coherent accumulation detection, so that the accumulation energy of low-observable targets reaches the target detection threshold; finally, the detection of low-observable targets is completed.

4. The method for detecting and tracking low-observable boost-glide trajectory targets under tilt distance ambiguity conditions according to claim 3, characterized in that, The selection of the distance-time plane in step S2 also includes: Assuming the target's tilt distance is The radar angle measurement error is Then the target's position measurement deviation is, (9) According to 3 The judgment criterion is that the maximum deviation of the target's position measurement is The target's position measurement deviation is much greater than the radar distance measurement error of several hundred meters.

5. The method for detecting and tracking low-observable boost-glide trajectory targets under tilt distance ambiguity conditions according to claim 3, characterized in that, Step S2, which extends the noncoherent accumulation detection method based on distance-time Hough transform, also includes: set up It is a point in the distance-time plane, where, It is the pulse repetition frequency. The j One extended tilt distance, yes Time stamp, in The unique curve corresponding to the given point in the plane is obtained in the following way. (10) in, yes The distance from the point to the origin, yes shaft and The angle between the axes; If multiple curves are in If two lines intersect at a single point in a plane, then in the distance-time plane, there exists a straight line that corresponds to multiple curves. This straight line is represented as... (11) in, It is the intersection of multiple curves. and These are the distance and time variables corresponding to the straight line, respectively.

6. The method for detecting and tracking low-observable boost-glide trajectory targets under tilt distance ambiguity conditions according to claim 5, characterized in that, The methods for detecting low-observable targets in step S2 also include: Will Plane divided into sizes of Several cells allow the target energy to accumulate in one of the cells; Cell The center is represented as, (12) (13) in, (14) (15) yes The number of units, yes The number of units, This refers to the radar's ranging range; In the Based on planar discretization, Curves in a plane are represented by the following pair. The mapping is replaced with, (16) in, It is a point in the distance-time plane. yes in the plane A set of points ; In the A pair of curves in a plane After mapping, the point The energy in the curve will be stored in the cells through which the curve passes, and the cells... The energy in is represented as, (17) in, It is a cell The existing energy in it, yes The energy of a point; If multiple points in the distance-time plane are approximately connected by a straight line, then the energy of these multiple points will be concentrated in the distance-time plane. In a single cell of a plane, a hypothesis test is performed that makes the detection of low-observable targets describe the following: : In the cell The target was detected. : In the cell No target was detected. in, Energy threshold; In the assumption Under the given conditions, the target trajectory is obtained through the following Hough inverse mapping: (18) Low-observable targets were then detected from the extended tilt range.

7. The method for detecting and tracking low-observable boost-glide trajectory targets under tilt distance ambiguity conditions according to claim 1, characterized in that, The method of configuring the S-shaped motion model in step S3 also includes: The autocorrelation function of the target acceleration is designed as follows: (19) in, for The target acceleration at any given moment for instantaneous covariance, Angular rate of the target-boosted gliding trajectory; The power spectrum of the target acceleration is expressed as follows: (The Fourier transform of the autocorrelation function of the target acceleration is given by...) (20) Configure the approximate whitening filter as follows: (21) Assumption yes In the time domain, the expression is... The Laplace transform is expressed as (24) and then The differential equation is expressed as (25) in, It has zero mean and constant variance Input white noise; Assumption (26) yes The target state vector in the X direction at time X. , , and These are the target's position, velocity, acceleration, and jerk, respectively, and they have... (27) state phasor Substitution If the differential equation is given, then the equation of continuous motion of the target is expressed as: (28) in, (29) (30) By integrating both sides of the continuous equations of motion of the target, we obtain the discrete equations of motion of the target. (31) The discrete equations of motion of the target are rewritten as follows: (32) in (33) It is the state transition matrix. It is a time interval. (34) It has constant variance (35) Zero-mean Gaussian white noise.

8. The method for detecting and tracking low-observable boost-glide trajectory targets under tilt distance ambiguity conditions according to claim 7, characterized in that, Step S3, designing the recursive energy filter, also includes: Assumption The recursive energy at time step is: (36) in, It is the first i The energy of each trajectory point ; Recursive energy A filtering algorithm is introduced to provide a high signal-to-noise ratio for tracking targets with low observability; therefore, the update of the target trajectory is represented by the following hypothesis test: : The target trajectory is updated by recursively updating the energy. : The target trajectory was terminated; in, This is the energy threshold, which is the same as the energy threshold for target detection. In the assumption Under these conditions, the target trajectory is updated by measuring the maximum energy in the tracking gate, thus enabling the target to be tracked in real time under low signal-to-noise ratio conditions; Assumption (37) It is the maximum energy measured at the tracking gate, where, It is the first in the tracking gate The energy of each candidate measurement It is the number of candidate measurements; Will By introducing a filtering algorithm, the target trajectory is updated using the measurement point with the highest energy in the tracking gate, and the energy update is recursively calculated as follows. (38) in, It is the trajectory point energy at the last moment in the recursive energy; By recursively updating the energy, target tracking is always maintained under conditions of high signal-to-noise ratio, and the target trajectory is then obtained using a filtering algorithm.

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