Tracking method before three-dimensional valuation of low-altitude maneuvering target under multipath condition

Abstract

The invention provides a multipath condition low-altitude maneuvering target three-dimensional valuation pre-tracking method, and relates to the technical field of radar target tracking, and the method comprises the steps: building a system model of a maneuvering target to be tracked under a three-dimensional coordinate system; dividing the height into a plurality of monotone intervals according to the monotonicity of the monopulse ratio on the height, and searching in each monotone interval to obtain a possible initial state of the target; establishing filters corresponding to the number of possible motion modes of the target in each monotonic interval, and dynamically fusing filtering results of the filters in the interval by applying a dynamic multi-model framework to obtain state estimation in the monotonic interval; and taking the state estimation as a model in the static multi-model again, performing static fusion on the state estimation results of all the segmented intervals to obtain target state estimation, and realizing three-dimensional tracking of the low-altitude target. According to the scheme, the three-dimensional tracking effect on the low-altitude flight maneuvering target can be effectively improved.

Description

Technical Field

[0001] The invention relates to the technical field of radar target tracking, and in particular to a three-dimensional pre-estimation tracking method for a low-altitude maneuvering target under multipath conditions. Background Art

[0002] Low-flying targets such as drones are characterized by low flying altitude, high speed, and flexibility. They are easily affected by the multipath effect in complex environments, which causes the target's radar echo signal to be mixed with the environmental reflection signal, making it difficult for the radar system to accurately detect and track the target.

[0003] In the related art, the traditional filtering tracking method often needs to estimate the pitch angle using a single pulse ratio before tracking the target, and when the target is in a maneuvering state, the tracking effect will be greatly reduced.

[0004] Based on this, there is an urgent need for a three-dimensional pre-estimation tracking method for low-altitude maneuvering targets under multipath conditions to solve the above technical problems. Summary of the invention

[0005] The embodiment of the present invention provides a three-dimensional pre-estimation tracking method for low-altitude maneuvering targets under multipath conditions, which can effectively improve the tracking effect of low-altitude flying maneuvering targets.

[0006] In a first aspect, an embodiment of the present invention provides a method for tracking a low-altitude maneuvering target under multipath conditions before three-dimensional estimation, comprising:

[0007] Establishing a system model of a maneuvering target to be tracked in a three-dimensional coordinate system; wherein the observation equation of the system model is a function of the measurement data with respect to the three-dimensional Cartesian coordinate state of the target, and the measurement data includes radial distance, real single pulse ratio and azimuth;

[0008] According to the monotonicity of the single pulse ratio in altitude, the altitude is divided into multiple monotonic intervals, and the possible initial state of the target is searched in each monotonic interval;

[0009] In each monotonic interval, a filter corresponding to the number of possible motion modes of the target is established, and the filtering results of each filter in the interval are dynamically fused using a dynamic multi-model framework to obtain the state estimation in the monotonic interval;

[0010] The state estimation is re-used as a model in the static multi-model, and the state estimation results of all segmented intervals are statically fused to obtain the target state estimation, thereby realizing three-dimensional tracking of low-altitude targets.

[0011] The embodiment of the present invention provides a three-dimensional pre-estimation tracking method for low-altitude maneuvering targets under multipath conditions. First, the observation equation of radial distance, real single pulse ratio and azimuth angle and the three-dimensional state vector of the maneuvering target to be tracked is established in a three-dimensional Cartesian coordinate system, and the single pulse ratio is determined as the observation quantity; then the monotonic interval is divided according to the height value of the single pulse ratio, and the initial state of each monotonic interval is determined; then the initial state is filtered under different motion models to obtain the state update of each motion model; finally, all state update vectors are dynamically fused and statically fused in turn to obtain the target state of the maneuvering target to be tracked. This method can not only avoid the error caused by estimating the pitch angle through the single pulse ratio, but also avoid the filter divergence caused by the sudden maneuver of the target, so as to achieve the tracking of the maneuvering target and greatly improve the tracking accuracy and tracking effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0013] Figure 1 It is a flow chart of a method for tracking a low-altitude maneuvering target under multipath conditions before three-dimensional estimation provided by an embodiment of the present invention;

[0014] Figure 2 It is a schematic diagram of initialization height interval division provided by an embodiment of the present invention;

[0015] Figure 3 is a two-dimensional schematic diagram of multipath geometric relationship provided by an embodiment of the present invention;

[0016] Figure 4 is a three-dimensional schematic diagram of multipath geometric relationship provided by an embodiment of the present invention;

[0017] Figure 5 It is a schematic diagram of a state vector fusion process provided by an embodiment of the present invention;

[0018] Figure 6 is a schematic diagram of the distribution of the real single pulse ratio in horizontal distance and height provided by an embodiment of the present invention;

[0019] Figure 7 It is a noisy single pulse ratio observation corresponding to the trajectory of the maneuvering target to be tracked provided by an embodiment of the present invention;

[0020] Figure 8 It is a schematic diagram of a single three-dimensional tracking result of a pre-estimation tracking method provided by an embodiment of the present invention;

[0021] Fig. 9 It is a schematic diagram of a single height tracking result of a pre-estimation tracking method provided by an embodiment of the present invention;

[0022] Fig.10 is a schematic diagram of weights of two filters correctly initialized according to an embodiment of the present invention;

[0023] Fig.11 It is a schematic diagram of height tracking results of two correctly initialized filters provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0025] As mentioned above, existing tracking technologies often use a single pulse ratio to estimate the pitch angle before tracking the target. At the same time, the target's motion trajectory is relatively simple during target tracking experiments, and the tracking results are difficult to meet the tracking requirements for maneuvering targets under actual conditions.

[0026] Based on this, the concept of the present invention is to establish a three-dimensional Cartesian coordinate relationship between the radial distance, real single pulse ratio and azimuth angle and the target state to avoid estimating the pitch angle, and at the same time set filters of different motion models in each monotonic interval of filtering processing to achieve efficient tracking of maneuvering targets.

[0027] The specific implementation of the above concept is described below.

[0028] Please refer to Figure 1 The embodiment of the present invention provides a method for tracking a low-altitude maneuvering target under multipath conditions before three-dimensional estimation, the method comprising:

[0029] Step 100, establishing a system model of the maneuvering target to be tracked in a three-dimensional coordinate system; wherein the observation equation of the system model is a function of the measurement data with respect to the three-dimensional Cartesian coordinate state of the target, and the measurement data includes radial distance, real single pulse ratio and azimuth;

[0030] Step 102, dividing the altitude into a plurality of monotonic intervals according to the monotonicity of the single pulse ratio in altitude, and searching for a possible initial state of the target in each monotonic interval;

[0031] Step 104, in each monotonic interval, a filter corresponding to the number of possible motion modes of the target is established, and the filtering results of each filter in the interval are dynamically fused using a dynamic multi-model framework to obtain a state estimation in the monotonic interval;

[0032] Step 106, the state estimation is re-used as a model in the static multi-model, and the state estimation results of all segmented intervals are statically fused to obtain the target state estimation, so as to realize the three-dimensional tracking of the low-altitude target.

[0033] In the embodiment of the present invention, firstly, the observation equation of radial distance, real single pulse ratio and azimuth angle and the three-dimensional state vector of the maneuvering target to be tracked is established in a three-dimensional Cartesian coordinate system, and the single pulse ratio is determined as the observation quantity; then, the monotonic interval is divided according to the height value of the single pulse ratio, and the initial state of each monotonic interval is determined; then, the initial state is filtered under different motion models to obtain the state update of each motion model; finally, all state update vectors are dynamically fused and statically fused in turn to obtain the target state of the maneuvering target to be tracked. This method can not only avoid the error caused by estimating the pitch angle through the single pulse ratio, but also avoid the filter divergence caused by the sudden maneuver of the target, so as to achieve the tracking of the maneuvering target and greatly improve the tracking accuracy and tracking effect.

[0034] Described below Figure 1 How the various steps are performed.

[0035] First, with respect to step 100 , a system model of the maneuvering target to be tracked is established in a three-dimensional coordinate system.

[0036] In an embodiment of the present invention, the system model includes a state transfer model and an observation equation of the maneuvering target to be tracked, wherein the observation equation is a function of the measurement data with respect to the three-dimensional state vector of the target, and the measurement data includes the radial distance, real single pulse ratio and azimuth angle of the maneuvering target to be tracked, and these data can be obtained in real time through the measuring equipment.

[0037] Specifically, the state transition model of the target is:

[0038] x k =Fx k-1 +Γv k-1

[0039] in, x k ,y k and z k are the position components of the target along the x, y and z directions in the three-dimensional Cartesian coordinate system, and They represent the velocity components of the target along the x, y and z directions in the three-dimensional Cartesian coordinate system at time k respectively.

[0040] F is the state transfer matrix, Γ is the process noise distribution matrix, v k-1 is the process noise vector, the process noise is assumed to be zero-mean Gaussian white noise, and its covariance matrix is ​​Q k-1 :

[0041]

[0042] Furthermore, by taking the real part of the single pulse ratio obtained by the observation radar as the measurement, the observation equation at time k can be established as shown in the following formula:

[0043]

[0044] in,

[0045]

[0046] Therefore, the observation equation can be rewritten as the following formula, which is a function of the measurement data on the target three-dimensional state vector:

[0047]

[0048] In the formula, ρk, Re{r k}and are the radial distance, real single pulse ratio and azimuth angle of the target observed at time k, respectively, and h r is the radar altitude, and is the noise measured at the corresponding time k.

[0049] Assuming that the measurement noise is independent zero-mean Gaussian white noise, the noise covariance matrix is:

[0050]

[0051] h ratio (·) is a function that characterizes the relationship between the real single pulse ratio measurement and the state vector.

[0052] The single pulse ratio is obtained from the target state vector by the following expression to characterize this functional relationship:

[0053]

[0054] where g s and g d are the voltage gain directivity functions of the radar and beam and the difference beam respectively; θ is the angle of the target offset from the antenna boresight; ψ is the angle of the mirror target offset from the antenna boresight; θ0 is the antenna boresight elevation angle; θ a is the off-axis angle of the upper and lower beams; φ rIt is the phase difference caused by the path length difference between the reflected path and the direct path; λ is the wavelength of the electromagnetic wave.

[0055] v is the reflection coefficient. The multipath reflection caused by the sea surface is divided into two parts: specular reflection and diffuse reflection. Therefore, the reflection coefficient consists of two parts:

[0056] v=v s +v d

[0057] where v s is the specular reflection coefficient, v d is the diffuse reflection coefficient. Specular reflection generally refers to satisfying the Rayleigh criterion, that is:

[0058]

[0059] Among them, Δh is the change in the height of the reflecting surface. When the wave height is lower than the right side, it is determined that the reflection component is mainly specular reflection. The sea surface specular reflection coefficient is defined as the ratio of the reflected electric field vector to the incident electric field vector. It is a complex number. Its amplitude is generally considered to be between 0 and 1, and the phase range is 0 to π. The coefficient ν s The Fresnel reflection coefficient ρ0, the divergence factor D and the specular scattering factor ρ s The product of is:

[0060] ν s =ρ0Dρ s

[0061] The Fresnel reflection coefficient ρ0 is usually the radar operating frequency, polarization mode, and ground rubbing angle ψ g And the function of factors such as surface dielectric constant. The mirror reflection coefficients under vertical polarization and horizontal polarization conditions are:

[0062]

[0063] where ∈ c is the complex dielectric constant:

[0064]

[0065] ∈ / ∈0 is the relative dielectric constant, σ is the conductivity. Specular scattering factor ρ s for:

[0066]

[0067] Among them, σ his the mean square value of the wave height, which is determined by the sea conditions; Γ is the surface roughness factor. The divergence factor D is the result of considering the influence of the earth's curvature. The reflected wave shines on the convex earth surface and causes scattering, which causes the electromagnetic wave energy density to decay. When a flat earth model is assumed, the divergence factor is 1. Since the energy of diffuse reflection decays quickly, while the energy of specular reflection is relatively concentrated, in the low-altitude field mentioned in the embodiment of the present invention, only the influence of specular reflection is considered, while diffuse reflection is ignored.

[0068] Then, for step 102, the altitude is divided into a plurality of monotonic intervals according to the monotonicity of the single pulse ratio in altitude, and a possible initial state of the target is searched in each monotonic interval.

[0069] After the observation equation is established through the above steps, the single pulse ratio will be selected as the observation quantity. For the single pulse ratio, since one single pulse ratio corresponds to multiple heights when the radial distance is constant, it is necessary to solve the problem of height initialization ambiguity first. The embodiment of the present invention introduces a static multi-model framework, that is, multiple static models are established at different heights, and each model corresponds to a filter for filtering. These filters can perform filtering at the same time, thereby solving the problem of initialization ambiguity.

[0070] Generally speaking, the static multi-model framework can establish a filter at all possible heights for filter tracking. However, for some single pulse ratio observations, the corresponding height values ​​may be large, and it is unrealistic to establish a filter at each height. Therefore, in order to ensure the feasibility of the above method, it is necessary to divide the height into several monotonic intervals according to the monotonic distribution of the single pulse ratio in height, and search in each interval for the height value that is closest to the calculated single pulse ratio and the single pulse ratio measurement as the initial height value of the filter in the monotonic interval. That is to say, only one static multi-model filter is set in a monotonic interval, and each monotonic interval represents a static sub-model in the static multi-model, so as to ensure that it will not be missed and reduce the amount of calculation. Finally, the binary search method is used to quickly search for the value to complete the initialization of the filter height.

[0071] Specifically, we first need to divide the monotonic interval used to set the filter, including the following steps:

[0072] First determine the search range of the target pitch angle: select the angle range within which the target can be observed within the half-power beam width of the antenna. When the lower boundary of the half-power beam width of the antenna is irradiated below the sea surface (this usually happens in the horizon reflection area), the lower boundary is adjusted to the pitch angle at the sea level, that is, the pitch angle search range (θ min ,θ max )for:

[0073]

[0074] Then according to the pitch angle value θ within the search range i and the direct path length ρ, the reflection path length l with a path difference equal to an integer multiple of half the wavelength is calculated i for:

[0075]

[0076] Where i = 1, 2, ..., m, m is the number of monotonic intervals, θ i In the interval (θ min ,θ max ) are arranged from small to large;

[0077] The difference between the reflected path length and the direct path length corresponding to these reflection points is:

[0078] Δρ i = l i -ρi=1,2,…,m

[0079] Since the difference is an integer multiple of half a wavelength, the relationship between the reflection paths of adjacent segment endpoints is:

[0080] l i+1 = l i +0.5λi=1,2,…,m-1

[0081] According to the reflection path length l i The path difference Δρ from the direct path length ρ i , the number of monotonic intervals m is calculated as:

[0082]

[0083] Where λ is the wavelength of the electromagnetic wave, m is a positive integer, and only [·] here is rounded down;

[0084] It can be seen that the higher the radar frequency, the more the phase changes under the same path difference, the more monotonic intervals are divided, and the boundary height value z of the divided monotonic interval is i for:

[0085]

[0086] Among them, h r is the radar height, the height interval (z0, z n ) is divided into multiple monotonic intervals (z0, z1)(z1, z2), (z2, z3), ..., (z m-1 , z m ),like Figure 2 shown.

[0087] Then, after dividing the monotonic intervals, the possible initial state of the target can be searched in each monotonic interval, including the following steps: calculating the difference between each single pulse ratio and the single pulse ratio measurement in the monotonic interval, and taking the height value corresponding to the single pulse ratio whose first difference meets the single pulse ratio error range as the initial height value of the filter in the monotonic interval.

[0088] Specifically, the binary search method is used to quickly search for the height value corresponding to the single pulse ratio in each subinterval. The difference function f(z)=Re{r(z)}-Re{r} is constructed, where Re{r} is the single pulse ratio measurement and Re{r(z)} is the single pulse ratio corresponding to point z. The subinterval is halved until f(z) is less than the allowable error, and then the heights of the two filters are determined.

[0089] It is worth noting that, for special cases, after comparing the points on a monotonic curve with the single pulse ratio measurement, there is no point that meets the single pulse ratio within the error range. At this time, the height value corresponding to the point with the smallest error in the same measurement comparison is selected as the height of the filter.

[0090] After the filter height is determined, the radial distance, azimuth and all the initial height values ​​can be used, such as Figure 3 and Figure 4 As shown, the initial position of the maneuvering target to be tracked in each monotonic interval is obtained by calculating the geometric relationship, thereby determining the initial state at the initial moment. The specific calculation process is well known to those skilled in the art and will not be described in detail here.

[0091] Finally, the initial position of the maneuvering target to be tracked corresponding to all filters at the initial time k = 1, 2 is obtained as:

[0092]

[0093] After coordinate transformation, it is expressed in polar coordinates as:

[0094]

[0095] The initial state vector is:

[0096]

[0097] The initial state covariance matrix is:

[0098]

[0099] The covariance of the transformed measurement error is:

[0100]

[0101] The elements are:

[0102]

[0103]

[0104] The compensation factor and for:

[0105]

[0106] in is the equation of the pitch angle measurement error of the i-th sub-filter at the k-th step, is the variance of the azimuth measurement error.

[0107] For step 104, filters corresponding to the number of possible motion modes of the target are established in each monotonic interval, and the filtering results of each filter in the interval are dynamically fused using a dynamic multi-model framework to obtain a state estimate in the monotonic interval.

[0108] For the maneuvering target studied in the embodiment of the present invention, the target has two or more motion modes and mode switching exists, and it is necessary to additionally combine the dynamic multi-model algorithm framework to handle the possible mode interactions of the target. Therefore, the embodiment of the present invention adds a second filter on the basis of the original one filter in each monotonic interval. The two filters are located at the same height but belong to two different motion models in the dynamic multi-model. In this way, the filtering of the second motion mode of the maneuvering target can be achieved, and the two motion models together constitute a static sub-model of the static multi-model.

[0109] Since there are two motion modes of the maneuvering target to be tracked in this embodiment, there are two different motion models corresponding to them, namely, a near-uniform motion model and an approximately constant turning rate motion model. Therefore, the interaction of the two motion models needs to be considered before filtering. Take the two motion models of the rth static sub-model Mr as an example:

[0110] The transition probability of the target from mode a to mode b is p ab , and p ab It is known in advance that the target state mode transition probability matrix with two motion modes can be expressed as:

[0111]

[0112] Among them, p 11 Indicates that the target moves from mode 1 to mode 1, that is, maintains the original movement mode, p 12It means that the target changes from mode 1 to mode 2, that is, mode interaction occurs. Similarly, the matrix can be obtained. Both motion mode a and motion mode b include mode 1 and mode 2. In this matrix, the sum of each row must be 1, that is, the sum of the transition probabilities of any given state must be 1.

[0113] After determining the mode transition probability, the state vector and covariance of the previous moment can be applied to the dynamic multi-model for interaction to obtain the state estimation vector and estimated covariance of each mode after the interaction process at the previous moment.

[0114] Specifically, the total probability that the maneuvering target to be tracked is in motion mode b after the interaction at the last moment is calculated as:

[0115]

[0116] in, is the probability of motion mode a in the rth static sub-model Mr of the static multi-model at the previous moment, r = 1, 2, …, m.

[0117] For example, assuming that b is mode 1, it means that the maneuvering target is in mode 1 after the interaction. The total probability of being in mode 1 calculated by the above formula includes: the probability of maintaining mode 1 and the probability of changing from mode 2 to mode 1; the same applies when b is mode 2.

[0118] According to the total probability and the probability of motion mode a at the previous moment, the conditional probability of the maneuvering target to be tracked changing from any of the two modes to the determined mode during the interaction process at the previous moment is calculated. for:

[0119]

[0120] According to the conditional probability and the state vector and covariance of the previous moment, the state estimation vector of each mode after the interaction process at the previous moment is calculated. and the estimated covariance They are:

[0121]

[0122] in, and They are the state vector and covariance of the previous moment respectively.

[0123] Furthermore, since two filters exist simultaneously in the same monotonic interval during the initialization process, when filtering the initial state vector, it is necessary to update the state estimation vector using state transition models of different motion modes.

[0124] According to the above steps, for the nearly constant turn (NCV) model, the state transfer matrix F is:

[0125]

[0126] Where T is the radar sampling time interval;

[0127]

[0128] For a near constant turn rate (NCT) model with a known turning rate in the vertical plane, the state transfer matrix F is:

[0129]

[0130] where ω is the turning rate in the numerical plane, is the target azimuth.

[0131] In the implementation of the present invention, each state estimation vector and estimated covariance obtained are filtered by applying an insensitive Kalman filter corresponding to different motion models, and the state update vector and update covariance of each motion model at the next moment are obtained in turn, including:

[0132] The state prediction and state covariance prediction based on the NCV motion model and the NCT motion model are:

[0133]

[0134] The state transfer matrix of the two motion models is abbreviated as F bk-1 :

[0135]

[0136] Status Update:

[0137]

[0138] Where l = 0, 1, ... 2n, n is the dimension of the state vector, where:

[0139]

[0140] in Representation Matrix The g-th row or g-th column of

[0141] The weights associated with the mean and covariance are:

[0142]

[0143] In this formula, λ is the scale parameter:

[0144] λ=α 2 (n+κ)-n

[0145] Where α, β and κ are the sampling parameters of the sigma point;

[0146] The measurement prediction is:

[0147]

[0148] The autocorrelation matrix of the observation vector is:

[0149]

[0150] The covariance matrix of the observation vector and the state vector is:

[0151]

[0152] The filter gain of motion mode b is:

[0153]

[0154] The state update vector and update covariance are:

[0155]

[0156] Among them, z k is the actual measurement data at time k.

[0157] like Figure 5 As shown in the figure, for a static sub-model in a monotonic interval, the state update vectors corresponding to the two dynamic models are obtained after filtering. Therefore, before performing static multi-model fusion, it is necessary to perform dynamic model fusion on each static sub-model first, that is, to fuse the two state update vectors into one as the state vector of the static sub-model.

[0158] Specifically, the state update vectors and update covariances of the two motion models in the monotonic interval are dynamically fused using the dynamic multi-model after probability update, and the fused state vector and fused covariance of the monotonic interval are obtained in turn:

[0159] According to the updated dynamic multi-model probability The state update vector corresponding to each motion model Fusion is performed and the fusion state vector is calculated

[0160]

[0161] in,

[0162]

[0163] is the likelihood function of the dynamic multi-model;

[0164]

[0165] According to the updated dynamic multi-model probability The updated covariance corresponding to each motion model Fusion is performed and the fusion covariance is calculated for:

[0166]

[0167] With respect to step 106, the state estimation is re-used as a model in the static multi-model, and the state estimation results of all segmented intervals are statically fused to obtain the target state estimation, thereby realizing three-dimensional tracking of low-altitude targets.

[0168] Specifically, the static multi-model probability is first updated according to the updated dynamic multi-model probability; then the fusion states of all monotonic intervals are statically fused using the static multi-model after probability update, and the target state vector and target covariance of the maneuvering target to be tracked are obtained in turn.

[0169] The likelihood function of the rth sub-model of the static multi-model is:

[0170]

[0171] The static multi-model probability is updated as:

[0172]

[0173] The probability of a single motion model in a dynamic multi-model is updated as:

[0174]

[0175] According to the updated static multi-model probability The fused state vectors corresponding to all monotonic intervals are merged to calculate the final state vector for:

[0176]

[0177] According to the updated static multi-model probability The fused covariances corresponding to all monotonic intervals are fused to calculate the final covariance P k|k for:

[0178]

[0179] In order to demonstrate the effectiveness of the method proposed in the embodiment of the present invention, a corresponding simulation scenario was set up to verify the method of the embodiment of the present invention.

[0180] A. Simulation Parameters

[0181] 1) Target parameters: The target flies towards the radar from the initial position (30km, 10km) with an initial velocity of (-6000m / s, -150m / s, 10m / s). The simulation lasts for 15s. The target moves in a straight line at a uniform speed for the first third of the time, and turns in a turning motion in the middle third of the time, where the turning rate ω=π / 360. The target moves in a straight line again in the last third of the time, and first rises and then dives. The process noise of the target motion is [σ x , σ y , σ z ]=[1m / s 2 , 1m / s 2 , 0.1m / s 2 ].

[0182] 2) Single pulse radar parameters: The radar height is 100m, and the radar transmission frequency is 4GHz. The antenna boresight pitch angle θ0 is 0, the angle of the offset antenna from the antenna boresight is 0.55°, the sampling period is 0.02s, and the radial distance, single pulse ratio, and azimuth angle measurement standard deviation are

[0183] 3) Environmental parameters: The sea surface is selected as the reflective surface. In this scenario, the relative dielectric constant of the sea surface is ∈ / ∈0=65, the conductivity is σ=4, and the root mean square of the wave height is 1m.

[0184] B. Simulation Results

[0185] The spatial distribution of the single pulse ratio is as follows: Figure 6 As shown in the figure, one of the targets is flying horizontally at a constant speed at a height of 90m, and its single pulse ratio changes as follows Figure 7 shown.

[0186] The three-dimensional tracking results of a single tracking with a target height of 60m and a frequency of 4GHz are as follows: Figure 8 The corresponding height tracking results are shown in Fig. 9 shown.

[0187] Fig.10 To correctly initialize the weights of the two filters, when the weights of the two filters rise to around 0.5, Fig. 9 The height tracking accuracy of the mid-estimation pre-tracking method is greatly improved. The sum of the weights of the two sub-filters approaches 1. The two correctly tracked filters basically occupy all the weights. The estimated results of the filter will be consistent with the tracking results of these two filters. Fig.11 Height tracking results for these two correctly initialized sub-filters.

[0188] It should be noted that, in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "comprise a ..." do not exclude the presence of other identical factors in the process, method, article or device including the elements.

[0189] A person of ordinary skill in the art can understand that all or part of the steps of implementing the above method embodiments can be completed by hardware related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps of the above method embodiments; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk, etc., various media that can store program codes.

[0190] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A three-dimensional pre-estimation tracking method for low-altitude maneuvering targets under multipath conditions, characterized in that: include: Establishing a system model of a maneuvering target to be tracked in a three-dimensional coordinate system; wherein the observation equation of the system model is a function of the measurement data with respect to the three-dimensional Cartesian coordinate state of the target, and the measurement data includes radial distance, real single pulse ratio and azimuth; According to the monotonicity of the single pulse ratio in altitude, the altitude is divided into multiple monotonic intervals, and the possible initial state of the target is searched in each monotonic interval; In each monotonic interval, a filter corresponding to the number of possible motion modes of the target is established, and the filtering results of each filter in the interval are dynamically fused using a dynamic multi-model framework to obtain the state estimation in the monotonic interval; The state estimation is re-used as a model in the static multi-model, and the state estimation results of all segmented intervals are statically fused to obtain the target state estimation, thereby realizing the three-dimensional tracking of low-altitude maneuvering targets.

2. The method according to claim 1, characterized in that The observation equation is established by the following formula: In the formula, z k is the observation vector; k 、Re{r k }and are the radial distance, real single pulse ratio and azimuth of the maneuvering target to be tracked observed at time k; h r is the radar altitude; w k is the noise vector; x k is the state vector; x k ,y k and z k are the x, y and z Position component of direction; h ratio (·) is a function that characterizes the relationship between the real single pulse ratio measurement and the state vector.

3. The method according to claim 1, characterized in that The step of dividing the altitude into a plurality of monotonic intervals according to the monotonicity of the single pulse ratio in altitude comprises: According to the pitch angle value θ within the predetermined search range i and the direct path length ρ, the reflection path length l with a path difference equal to an integer multiple of half the wavelength is calculated i for: Where i = 1, 2, ..., m, m is the number of monotonic intervals; According to the reflection path length l i The path difference Δρ from the direct path length ρ i , the number of monotonic intervals m is calculated as: Among them, λ is the wavelength of electromagnetic wave, and m is a positive integer; The height value of the single pulse ratio is divided according to the number of monotonic intervals m, and the height value z of the boundary of each monotonic interval is obtained. i : Among them, h r is the radar altitude.

4. The method according to claim 3, characterized in that The searching in each monotonic interval to obtain a possible initial state of the target includes: Calculate the difference between each single pulse ratio and the single pulse ratio measurement in the monotonic interval, and use the height value corresponding to the single pulse ratio whose first difference meets the single pulse ratio error range as the initial height value of the filter in the monotonic interval; The initial state of the maneuvering target to be tracked at the initial moment in each monotonic interval is calculated based on the radial distance, the azimuth angle and all the initial height values.

5. The method according to claim 1, characterized in that The filtering results of each filter in the interval are dynamically fused using a dynamic multi-model framework to obtain a state estimate in the monotonic interval, including: Apply the dynamic multi-model to interact the state vector and covariance of the previous moment, and obtain the first state estimate of each mode after the interaction process of the previous moment; Apply filters corresponding to different motion models to filter each first state estimate obtained, and obtain the state update of each motion model at the current moment in turn; The state update of each motion model in the monotonic interval is dynamically fused using the dynamic multi-model after probability update to obtain the fused state estimate of the monotonic interval.

6. The method according to claim 5, characterized in that The step of applying the dynamic multi-model to interact the state vector and covariance at the previous moment to obtain the first state estimation of each mode after the interaction process at the previous moment includes: According to the predetermined mode transition probability p ab , the total probability that the maneuvering target to be tracked is in motion mode b after the interaction at the last moment is calculated as: in, is the probability of motion mode a at the previous moment, r = 1, 2, …, m; According to the total probability and the probability of motion mode a at the previous moment, the conditional probability of the maneuvering target to be tracked changing from any of the two modes to the determined mode during the interaction process at the previous moment is calculated. for: According to the conditional probability and the state vector and covariance of the previous moment, the first state estimation vector of each mode after the interaction process at the previous moment is calculated. and the first estimated covariance They are: in, and They are the state vector and covariance of the previous moment respectively.

7. The method according to claim 6, characterized in that The dynamic fusion includes: According to the updated dynamic multi-model probability The state update vector corresponding to each motion model Fusion is performed and the fusion state vector is calculated in, is the likelihood function of the dynamic multi-model; According to the updated dynamic multi-model probability The updated covariance corresponding to each motion model Fusion is performed and the fusion covariance is calculated for:

8. The method according to claim 7, characterized in that The static fusion of the state estimation results of all segmented intervals to obtain the target state estimation includes: According to the updated dynamic multi-model probability, the static multi-model probability is updated; The static multi-model after probability update is used to statically fuse the fusion states of all monotonic intervals respectively, and the target state vector and target covariance of the maneuvering target to be tracked are obtained in turn.

9. The method according to claim 8, characterized in that Updated static multi-model probability for: in, is the likelihood function of the rth sub-model of the static multi-model.

10. The method according to claim 9, characterized in that The static fusion includes: According to the updated static multi-model probability The fused state vectors corresponding to all monotonic intervals are fused to calculate the target state vector for: According to the updated static multi-model probability The fusion covariances corresponding to all monotonic intervals are fused to calculate the target covariance P k|k for:

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