Low altitude multipath radar elevation tracking method based on interactive multiple model particle filter

Abstract

This invention provides a low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering, comprising: performing range-Doppler two-dimensional processing on the complex signals of each target echo received by a multi-channel three-coordinate radar and constructing a complex monopulse ratio observation vector; constructing a dual-model state observation model based on the complex monopulse ratio observation vector; the dual-model state observation model includes a multipath observation model and a non-multipath observation model; calculating the dynamic multipath spatial gain factor based on the target elevation angle estimate and antenna pattern function of the previous measurement cycle, and reconstructing the model state transition probability matrix of the dual-model state observation model; performing interactive multi-model particle filtering based on the reconstructed model state transition probability matrix, fusing the obtained particle filter state estimates and model posterior probabilities of each model, and outputting the target elevation angle tracking result. This invention can improve the accuracy, stability, and environmental adaptability of target elevation angle tracking in low-altitude multipath environments.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering. Background Technology

[0002] With the rapid development of the low-altitude economy and the application of unmanned aerial vehicles (UAVs), the detection, identification, and tracking of low-altitude, slow-moving, and small targets have become crucial technical aspects of airspace security and key area defense. Three-coordinate radar can simultaneously acquire target range, azimuth, and elevation information, with elevation measurement directly affecting target altitude calculation and three-dimensional spatial positioning accuracy. Three-coordinate radars with a single transmitter and multiple receivers (SMRs) have wide application value in low-altitude target monitoring scenarios due to their relatively simple hardware structure, low cost, and convenient engineering deployment.

[0003] In low-altitude or ultra-low-altitude detection scenarios, the direct wave from the target and the mirror-reflected wave formed by ground reflection simultaneously enter the radar receiving antenna and undergo vector coherent superposition at the receiver. Influenced by ground reflection coefficient, surface roughness, antenna pattern, and target geometry, the amplitude and phase characteristics of the receiving channel exhibit strong nonlinear distortion, leading to significant oscillations in conventional amplitude comparison, phase comparison, and static amplitude and phase comparison angle measurement results. Related technologies such as beam control, antenna pattern correction, array super-resolution estimation, and methods like extended Kalman filtering, unscented Kalman filtering, and interactive multi-model filtering can mitigate multipath effects under certain conditions, but they often rely on environmental priors, array spatial degrees of freedom, accurate initial states, or fixed model transition probabilities.

[0004] Therefore, existing low-altitude multipath radar elevation tracking technology still has the following technical problems: low-altitude multipath coherent interferometry causes strong nonlinear distortion in complex single-pulse ratio measurements, making it difficult for conventional static angle measurement methods to stably output the target elevation angle; nonlinear filtering methods are sensitive to the initial state and are prone to filter divergence when the distortion of the first frame measurement is large; traditional interactive multi-model methods use fixed model state transition probabilities, making it difficult to adaptively switch as the ground reflected wave enters or leaves the antenna's high-gain region; and there is a lack of a joint estimation mechanism for unknown surface reflection characteristics, making it difficult to continuously compensate for multipath distortion in the absence of accurate site prior information. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering. The technical problem to be solved by this invention is achieved through the following technical solution: In a first aspect, the present invention provides a low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering, comprising: The complex echo signals of each target received by the multi-channel three-coordinate radar are acquired, and the range-Doppler two-dimensional processing is performed on each target echo complex signal to obtain the complex signal of each target element. Based on the complex signal of each target element, a complex single pulse ratio observation vector is constructed. A dual-model state observation model is constructed based on the complex single-pulse ratio observation vector; the dual-model state observation model includes a multipath observation model and a multipath-free observation model. The ground reflected wave incident angle is determined based on the target elevation angle estimate from the previous measurement cycle, and the dynamic multipath spatial gain factor is calculated based on the ground reflected wave incident angle and the antenna pattern function. The model state transition probability matrix of the dual-model state observation model is reconstructed based on the dynamic multipath spatial gain factor. Based on the reconstructed model state transition probability matrix, interactive multi-model particle filtering is performed on the multipath observation model and the non-multipath observation model to obtain the particle filter state estimate and model posterior probability of each model. State fusion is performed based on the particle filter state estimates and posterior probabilities of each model to output the target elevation angle tracking results.

[0006] In one embodiment of the present invention, the step of performing range-Doppler two-dimensional processing on the complex signals of each target echo to obtain complex signals of each target unit, and constructing a complex single-pulse ratio observation vector based on the complex signals of each target unit, includes: Coherent accumulation and range-Doppler two-dimensional processing are performed on the echo complex signals of each target to obtain the complex signal of each target unit; From the complex signals of each target unit, a reference channel complex signal and at least one channel complex signal to be compared are selected, and a complex ratio operation is performed between the channel complex signal to be compared and the reference channel complex signal to obtain a channel complex ratio value. The complex single-pulse ratio observation vector is generated based on the channel complex ratio value.

[0007] In one embodiment of the present invention, the step of constructing a dual-model state observation model based on the complex single-pulse ratio observation vector includes: Construct a first state vector for the multipath observation model, the first state vector including the target elevation angle, the rate of change of elevation angle, and environmental characteristic parameters; Based on the direct wave steering vector, the ground reflected wave steering vector, and the environmental characteristic parameters, a composite steering vector corresponding to the multipath observation model is constructed; based on the composite steering vector and the complex single-pulse ratio observation vector, the first measurement equation of the multipath observation model is constructed. The multipath observation model is constructed based on the first state vector and the first measurement equation. Construct a second state vector for the multipath-free observation model, the second state vector including the target elevation angle and the rate of change of elevation angle; Based on the direct waveguide vector and the complex single-pulse ratio observation vector, the second measurement equation of the multipath-free observation model is constructed. The multipath-free observation model is constructed based on the second state vector and the second measurement equation.

[0008] In one embodiment of the present invention, the step of determining the ground reflected wave incident angle based on the target elevation angle estimate of the previous measurement cycle, and calculating the dynamic multipath spatial gain factor based on the ground reflected wave incident angle and the antenna pattern function, includes: The ground reflection wave incident angle is determined based on the target elevation angle estimate and the radar low-altitude detection geometry. The ground reflected wave incident angle is input into the antenna pattern function to obtain the reflected wave pattern gain value; The dynamic multipath spatial gain factor is generated based on the reflected wave pattern gain value.

[0009] In one embodiment of the present invention, reconstructing the model state transition probability matrix of the dual-model state observation model based on the dynamic multipath spatial gain factor includes: The model preservation probability of the multipath observation model is determined based on the dynamic multipath spatial gain factor. The model preservation probability of the multipath-free observation model is determined based on the dynamic multipath spatial gain factor. The first model switching probability for transitioning from the multipath observation model to the non-multipath observation model is determined based on the model preservation probability of the multipath observation model. The second model switching probability from the multipath-free observation model to the multipath-observation model is determined based on the model preservation probability of the multipath-free observation model. The model state transition probability matrix is ​​generated based on the model preservation probability of the multipath observation model, the model preservation probability of the non-multipath observation model, the first model switching probability, and the second model switching probability.

[0010] In one embodiment of the present invention, the step of performing interactive multi-model particle filtering on the multipath observation model and the non-multipath observation model based on the reconstructed model state transition probability matrix to obtain the particle filter state estimate and model posterior probability of each model includes: The model mixture probability is calculated based on the model state transition probability matrix and the model posterior probability of the previous measurement period. The multipath observation model and the non-multipath observation model are inputted and interacted based on the model mixing probability to obtain the mixed input particle set of each model; State prediction is performed on the mixed input particle set of each model to obtain the predicted particle set of each model; Based on the complex single-pulse ratio observation vector and the measurement equations corresponding to each model, the likelihood weights of particles in the predicted particle set of each model are calculated. Based on the likelihood weights, the predicted particle sets of each model are resampled and weighted to obtain the particle filter state estimates of each model. The model likelihood value of each model is calculated based on the measurement residuals and residual covariance of each model, and the model probability is updated according to the model likelihood value to obtain the posterior probability of the model.

[0011] In one embodiment of the present invention, the step of performing input interaction on the multipath observation model and the non-multipath observation model according to the model mixing probability to obtain a mixed input particle set for each model includes: When the particles without the multipath observation model interact with the multipath observation model, the target elevation angle and elevation angle change rate in the particles without the multipath observation model are retained, and environmental feature parameters are injected into the particles without the multipath observation model to obtain the upgraded particles. When the particles of the multipath observation model interact with the particles of the non-multipath observation model, the target elevation angle and elevation angle change rate in the particles of the multipath observation model are retained, and the environmental feature parameters in the particles of the multipath observation model are removed to obtain the dimensionality-reduced particles. Based on the model mixing probability, the upgraded particles, the downgraded particles, and the particles interacting with the same model are weighted and mixed to obtain the mixed input particle set of each model.

[0012] Secondly, the present invention provides a low-altitude multipath radar elevation tracking device based on interactive multi-model particle filtering, comprising: The vector construction module is used to acquire the complex echo signals of each target received by the multi-channel three-coordinate radar, perform range-Doppler two-dimensional processing on each target echo complex signal to obtain the complex signal of each target element, and construct a complex single-pulse ratio observation vector based on each target element complex signal; The model building module is used to construct a dual-model state observation model based on the complex single-pulse ratio observation vector; the dual-model state observation model includes a multipath observation model and a non-multipath observation model; The gain calculation module is used to determine the ground reflected wave incident angle based on the target elevation angle estimate of the previous measurement cycle, and to calculate the dynamic multipath spatial gain factor based on the ground reflected wave incident angle and the antenna pattern function. The matrix reconstruction module is used to reconstruct the model state transition probability matrix of the dual-model state observation model based on the dynamic multipath spatial gain factor. The interactive filtering module is used to perform interactive multi-model particle filtering on the multipath observation model and the non-multipath observation model based on the reconstructed model state transition probability matrix, so as to obtain the particle filter state estimate and model posterior probability of each model. The state fusion module is used to perform state fusion based on the particle filter state estimates and posterior probabilities of each model, and output the target elevation angle tracking results.

[0013] Thirdly, the present invention provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; The memory is used to store computer programs; When the processor executes the computer program stored in the memory, it implements the steps of the low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering provided in the first aspect.

[0014] Fourthly, the present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, it implements the steps of the low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering provided in the first aspect.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: The low-altitude multipath radar elevation tracking method based on interactive multi-model particle filtering provided by this invention performs range-Doppler two-dimensional processing on the target echo complex signal received by a multi-channel three-coordinate radar and constructs a complex monopulse ratio observation vector, enabling amplitude and phase information to serve as a unified measurement input for subsequent nonlinear tracking. A dual-model state observation model is constructed, including both a multipath observation model and a non-multipath observation model, allowing the measurement process of direct wave and the measurement process of direct wave superimposed on ground reflected wave to be described within the same interactive framework. Based on the target elevation angle estimate and antenna pattern function of the previous measurement cycle, a dynamic multipath spatial gain factor is calculated, and the model state transition probability matrix is ​​reconstructed accordingly, allowing the model switching probability to adaptively adjust with the spatial gain of the ground reflected wave in the antenna pattern. Interactive multi-model particle filtering is used to estimate the target state and environmental characteristic parameters, enabling the particle swarm to perform global optimization in a strongly nonlinear measurement space and reducing dependence on the initial state. State fusion is performed based on the particle filter state estimation and model posterior probability of each model, enabling continuous output of multipath-suppressed target elevation tracking results. Therefore, this invention can improve the accuracy, stability, and environmental adaptability of target elevation angle tracking in low-altitude multipath environments.

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a schematic diagram illustrating the implementation process of a low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering, provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of an interactive multi-model structure provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of a receiver antenna provided in an embodiment of the present invention; Figure 4 This is a schematic diagram comparing the elevation angle measurement performance of the method of the present invention and the amplitude and phase comparison angle measurement method provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the evolution curves of the preservation probability of each model provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of an environmental characteristic parameter estimation curve provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of the performance comparison of elevation angle measurement and the evolution curves of the probability of each model and the estimation curves of environmental characteristic parameters provided by an embodiment of the present invention; Figure 8 This is a schematic diagram of the structure of a low-altitude multipath radar elevation angle tracking device based on interactive multi-model particle filtering provided in an embodiment of the present invention; Figure 9 This is a schematic diagram of the hardware entity of an electronic device to which embodiments of the present invention are applied. Detailed Implementation

[0018] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0019] Please see Figure 1 , Figure 1 This is a schematic diagram illustrating the implementation process of a low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering, provided in an embodiment of the present invention. Figure 1 As shown in the embodiments of the present invention, the low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering may include the following steps: Step S101: Obtain the complex echo signals of each target received by the multi-channel three-coordinate radar, perform range-Doppler two-dimensional processing on the complex echo signals of each target to obtain the complex signal of each target element, and construct the complex single pulse ratio observation vector based on the complex signal of each target element.

[0020] In one possible implementation, coherent accumulation and range-Doppler two-dimensional processing can be performed on the complex signals of each target echo to obtain the complex signals of each target unit; a reference channel complex signal and at least one channel complex signal to be compared are selected from the complex signals of each target unit, and the complex ratio of the channel complex signal to be compared and the reference channel complex signal is calculated to obtain the channel complex ratio; a complex single-pulse ratio observation vector is generated based on the channel complex ratio.

[0021] The multi-channel three-coordinate radar can adopt a one-transmit-multiple-receiver system, with two or more receiving channels. For example, one receiving channel can be set as the reference channel, and the remaining receiving channels can be set as the comparison channels. A complex monopulse ratio observation vector containing amplitude ratio and phase difference information can be constructed through complex ratio values.

[0022] Taking a dual-channel three-coordinate radar as an example, it is possible to acquire the target echo complex signal received by the dual-channel three-coordinate radar, and perform range-Doppler two-dimensional processing on the target echo complex signal to extract the complex single-pulse ratio observation vector of the two channels.

[0023] Step S102: Construct a dual-model state observation model based on the complex single-pulse ratio observation vector; the dual-model state observation model includes a multipath observation model and a non-multipath observation model.

[0024] In one possible implementation, a first state vector of the multipath observation model can be constructed, which includes the target elevation angle, the rate of change of elevation angle, and environmental characteristic parameters. Based on the direct wave steering vector, the ground reflected wave steering vector, and the environmental characteristic parameters, a composite steering vector corresponding to the multipath observation model is constructed. Based on the composite steering vector and the complex single-pulse ratio observation vector, a first measurement equation of the multipath observation model is constructed. The multipath observation model is constructed according to the first state vector and the first measurement equation. A second state vector of the multipath-free observation model is constructed, which includes the target elevation angle and the rate of change of elevation angle. Based on the direct wave steering vector and the complex single-pulse ratio observation vector, a second measurement equation of the multipath-free observation model is constructed. The multipath-free observation model is constructed according to the second state vector and the second measurement equation.

[0025] In the multipath observation model, the radar received signal is formed by the superposition of the direct wave and the ground reflected wave vector. Environmental characteristic parameters can include the Fresnel reflection coefficient and surface roughness parameters of the reflecting surface. The composite steering vector can be obtained by superimposing the direct wave steering vector and the ground reflected wave steering vector carrying the amplitude and phase changes of the reflection. The measurement equation constructed from the composite steering vector can describe the nonlinear relationship between the complex single-pulse ratio observation vector and the target elevation angle in a low-altitude multipath environment.

[0026] In the multipath-free observation model, the radar receives signals primarily from direct waves. The second state vector of the multipath-free observation model preserves the target elevation angle and the rate of change of elevation angle. A second measurement equation can be constructed using the direct wave steering vector to describe the complex single-pulse ratio measurement relationship when there is no significant multipath influence.

[0027] For example, there are multipath observation models in The first state vector at time t can be determined by the following formula: ; in, Let be the first state vector. and They are respectively The target elevation angle and rate of change of elevation angle at any given time. denoted as Fresnel reflection coefficient (horizontal polarization) of the reflecting surface. This is the surface roughness parameter of the reflecting surface, which is the root mean square value of the surface height variation near the reflecting surface.

[0028] Assuming the target moves at a constant velocity for a short period of time, the Fresnel reflection coefficient of the reflecting surface... and surface roughness parameters If it follows a stochastic model, then the state evolution equation is: ; in, Let be the first state vector. This is the first state vector of the previous measurement cycle. Here is the state transition matrix. The noise is the process noise, with a mean of 0 and a variance of . The normal distribution This represents the radar sampling interval. The state transition matrix can be represented as: ; according to The ratio of the complex single pulse received by the two channels at time t is equal to the observation vector. The observation vector is formed by the first state vector. for: ; in, For observing noise, the observation function It is a nonlinear function for superimposing multipath reflection signals.

[0029] In low-altitude target tracking scenarios with multipath observation models, the echo signal received by the radar is a vector superposition of the direct wave and the multipath reflected wave. Since the radar altitude is much lower than the target altitude, the reflected wave can be considered to come from a mirror target and can be approximately simplified as follows: Set the upper channel as the reference channel for the incident angle. Direct waveguide vector It can be represented as: ; in, The pattern gain of the first antenna. For the pattern gain and phase term of the second antenna The path difference and phase lag between the lower antenna and the upper antenna.

[0030] The reflected wave experiences additional path delay due to reflection from the ground. And amplitude attenuation. Complex reflection coefficient It can be represented as: ; in, The Fresnel reflection coefficient is given by horizontal polarization. The roughness attenuation factor can be expressed as: ; in, This represents the root mean square value of the surface height variation near the reflecting surface. for The target elevation angle at any given moment.

[0031] Reflected wave from The direction of incidence, and carrying the reflection lag phase, therefore the ground reflected wave steering vector It can be represented as: ; in, for The target elevation angle at any moment The complex reflection coefficient, It is a reflected wave. To use the reflected wave as the pattern gain of the first antenna, The reflected wave is used as the pattern gain of the second antenna.

[0032] Will The composite steering vector, referred to as the direct wave superimposed with multipath, ,make Then the composite guiding vector It can be represented as: ; in, The complex reflection coefficient, The pattern gain of the first antenna. The pattern gain of the second antenna. To use the reflected wave as the pattern gain of the first antenna, To use the reflected wave as the pattern gain of the second antenna, For direct waves, It is a multipath.

[0033] The first measurement equation is derived from the composite guiding vector. The first measurement equation is determined. It can be represented as: ; in, The first of the composite guide vectors One portion, It can be 1 or 2.

[0034] For example, the multipath-free observation model in The second state vector at time t can be represented as: ; in, This is the second state vector. and They are respectively The target elevation angle and the rate of change of elevation angle at any given time.

[0035] Since the received signal comes only from the direct wave, the second state vector only contains the target elevation angle and the rate of change of elevation angle. Assuming the target moves at a constant velocity for a short time, the state evolution equation is: ; in, This is the second state vector. This is the second state vector from the previous measurement cycle. Here is the state transition matrix. For process noise, the state transition matrix for: ; in, This refers to the radar sampling interval.

[0036] Constructing the observation vector Direct wave steering vector containing only direct waves It can be represented as: ; in, The pattern gain of the first antenna. The pattern gain of the second antenna. It is a direct wave.

[0037] Similarly, the second measurement equation of the multipath-free observation model It can be represented as: ; in, The first direct waveguide vector represents the... One portion, It can be 1 or 2.

[0038] Step S103: Determine the ground reflected wave incident angle based on the target elevation angle estimate of the previous measurement cycle, and calculate the dynamic multipath spatial gain factor based on the ground reflected wave incident angle and the antenna pattern function.

[0039] In one possible implementation, the ground reflection wave incident angle can be determined based on the target elevation angle estimate and the radar low-altitude detection geometry; the ground reflection wave incident angle is input into the antenna pattern function to obtain the reflection wave pattern gain value; and a dynamic multipath spatial gain factor is generated based on the reflection wave pattern gain value.

[0040] For example, the target elevation angle estimate can be obtained based on the estimation results of the previous measurement cycle. At this point, the angle of incidence of the ground reflected wave reaching the receiving antenna (i.e., the angle of incidence of the ground reflected wave) can be approximated as: The antenna pattern function of the antenna is defined as follows: , Time-based dynamic multipath spatial gain factor for: ; in, for The dynamic multipath spatial gain factor at time step. The incident angle of the ground reflected wave. This represents the gain value of the reflected wave pattern.

[0041] Understandably, in low-altitude detection scenarios, ground-reflected waves can be approximated as originating from the direction of the mirror target. When the target elevation angle is low, the ground-reflected wave may fall into the main lobe or high-gain region of the receiving antenna, enhancing multipath effects. As the target elevation angle gradually increases, the direction of the ground-reflected wave may deviate from the main lobe and fall into the side lobe region, weakening multipath effects. Therefore, the dynamic multipath spatial gain factor can reflect the trend of multipath intensity changes in the current measurement period based on the antenna pattern.

[0042] Step S104: Reconstruct the model state transition probability matrix of the dual-model state observation model based on the dynamic multipath spatial gain factor.

[0043] In one possible implementation, the model retention probability of a multipath-observed model can be determined based on the dynamic multipath spatial gain factor; the model retention probability of a non-multipath-observed model can be determined based on the dynamic multipath spatial gain factor; a first model switching probability from a multipath-observed model to a non-multipath-observed model can be determined based on the model retention probability of the multipath-observed model; a second model switching probability from a non-multipath-observed model to a multipath-observed model can be determined based on the model retention probability of the non-multipath-observed model; and a model state transition probability matrix can be generated based on the model retention probability of the multipath-observed model, the model retention probability of the non-multipath-observed model, the first model switching probability, and the second model switching probability.

[0044] For example, set in From the model at all times To model The model state transition probability is The state transition probability matrix for a scenario with two modes can be expressed as: ; in, for The model state transition probability matrix at time step [time]. for From the model at all times Transfer to model The state transition probability, or When the value is 1, the model or model This indicates a multipath observation model. or When the value is 2, the model or model This indicates a model without multipath observations. For example, in... =1 and When it is 2, For the first model switching probability, in 2 and When it is 1, This represents the switching probability of the first model.

[0045] For example, within the Interacting Multiple Model (IMM) framework, the extracted dynamic gain factor can be used to adjust the model state transition probability matrix. Adaptive reconstruction is performed. For multipath observation models, when the system has extremely high spatial gain in the reflected wave direction, multipath interference dominates, and the system should maintain multipath filtering mode with a very high probability. A model preservation probability for multipath observation models can be constructed. for: ; in, To maintain a lower probability bound for the model, To maintain an upper probability limit for the model, This is the dynamic multipath spatial gain factor.

[0046] Similarly, the physical logic of the multipath-free observation model is exactly the opposite of that of the multipath-free observation model. When the reflected wave falls into the antenna sidelobe, causing the dynamic gain factor to decrease, the probability of the system maintaining the multipath-free filtering mode should decrease. Therefore, the model-keeping probability of the multipath-free observation model is... It can be represented as: ; in, To maintain a lower probability bound for the model, To maintain an upper probability limit for the model, This is the dynamic multipath spatial gain factor.

[0047] Based on the model preservation probability of a multipath observation model and the model preservation probability of a multipath-free observation model, the final model state transition probability matrix is ​​constructed. It can be represented as: ; in, To preserve the model probability for multipath observation models, For models without multipath observations, the model preservation probability is... To maintain a lower probability bound for the model, To maintain an upper probability limit for the model, This is the dynamic multipath spatial gain factor.

[0048] Step S105: Based on the reconstructed model state transition probability matrix, perform interactive multi-model particle filtering on the multipath observation model and the non-multipath observation model to obtain the particle filter state estimate and model posterior probability of each model.

[0049] In one possible implementation, the model mixture probability can be calculated based on the model state transition probability matrix and the model posterior probability of the previous measurement period; the model mixture probability is used to input the multipath observation model and the non-multipath observation model to obtain the mixed input particle set of each model; the mixed input particle set of each model is used to predict the state to obtain the predicted particle set of each model; the likelihood weight of the particles in the predicted particle set of each model is calculated based on the complex single-pulse ratio observation vector and the measurement equation corresponding to each model; the predicted particle set of each model is resampled and weighted according to the likelihood weight to obtain the particle filter state estimate of each model; the model likelihood value of each model is calculated based on the measurement residual and residual covariance of each model, and the model probability is updated according to the model likelihood value to obtain the model posterior probability.

[0050] In one possible implementation, input interactions are performed between a multipath observation model and a non-multipath observation model based on model mixing probabilities to obtain a mixed input particle set for each model. This includes: when particles from the non-multipath observation model interact with particles from the multipath observation model, retaining the target elevation angle and elevation angle change rate in the particles from the non-multipath observation model, and injecting environmental feature parameters into the particles from the non-multipath observation model to obtain up-dimensional particles; when particles from the multipath observation model interact with particles from the non-multipath observation model, retaining the target elevation angle and elevation angle change rate in the particles from the multipath observation model, and removing the environmental feature parameters from the particles from the multipath observation model to obtain down-dimensional particles; based on model mixing probabilities, the up-dimensional particles, down-dimensional particles, and particles interacting with the same model are weighted and mixed to obtain a mixed input particle set for each model.

[0051] For example, it is possible to At time 1, initialize the number of particles. and from the initial prior distribution Extraction Sampled particles The process of extracting particles from the selected importance density function is expressed as follows: ; in, for The first state vector or the second state vector at time 1 One particle. When it is 1, Let be the first state vector in the multipath observation model. When it is 2, This is the second state vector in the multipath-free observation model. Let be the set of mixed input particles up to time k.

[0052] Calculate the weight of each particle obtained from importance sampling: ; in, for Time of the first The weight of each particle, for Time of the first The weight of each particle, for The first state vector or the second state vector at time 1 One particle.

[0053] It should be noted that for Sequential Importance Resampling (SIR) filters, the particle weights can be simplified to... .

[0054] The weights of each particle can then be normalized using the following formula: ; in, For normalized Time-based particle weights.

[0055] according to Calculate the number of effective particles Determine the degree of degradation of the current particle set, if If the high-weight particles are copied and the low-weight particles are discarded, the updated particle set is resampled; otherwise, the particle set is obtained directly by weighting each particle. The state estimate at time step [time]. The resampled and updated particle set can be represented as [formula]. .in, The state estimate at time t can be expressed as: ; in, for State estimate at time 1.

[0056] Next, we can make New particles are then extracted from the selected importance density function.

[0057] For example, in each radar measurement cycle, the posterior probability of each model can be updated using the residual covariance and likelihood function of each model, and the states of the two particle filter (PF) matched filters can be mixed, interacted and weighted to continuously and stably output the high-precision target elevation angle after multipath suppression.

[0058] The Interacting Multiple Model-Particle Filter (IMM-PF) algorithm is a target tracking algorithm that combines particle filtering and interactive multiple model algorithms. It uses IMM as the target's multiple model and PF as the matched filter for the model. The algorithm assumes the target's multiple model state transition equations and measurement equations are as follows: ; in, For the first The model is in The state transition matrix at time t, For the first The model is in The observation matrix at time, For the first The model is in Time-based process noise, For the first The model is in Regarding the observation noise at any given time, it should be noted that... A value of 1 indicates a multipath observation model. A value of 2 indicates that there is no multipath observation model.

[0059] Define model set , Represents the model's state transitions. and process noise matrix and observation matrix All with the model Related; the state transition matrix between models is an adaptive state transition matrix. Each motion model is matched with a particle filter to estimate the state variables under the current model. The two filters work simultaneously in parallel, and the input to each filter is a mixture of the outputs of the previous filters. The IMM-PF algorithm mainly includes four steps: input interaction, model matching filtering, model probability update, and state fusion estimation. Its structure is as follows: Figure 2 As shown, Figure 2 middle, express Time model Target state estimation, express Time model covariance, for The observed value at time, For the goal Time model The probability, for Time model The likelihood function.

[0060] The system contains 2 models. Time-transition probability matrix and the probability matrices of each model ,in, For the number of particles, Representation Model To model The transition probability, express Moment Particle In the model The probability of.

[0061] Model Mixture Probability It can be represented as: ; in, for From the model at all times Transfer to model The state transition probability, for Time model The posterior probability, normalization factor .

[0062] In addition, the model needs to be unified before calculating mixed input states. Relative to the model The dimension increases when the model without multipath observations interacts with the model without multipath observations. State expansion is used to maintain the kinematic components of the particles in the model without multipath observations, and environmental feature parameters are injected into the model with multipath observations based on the prior distribution of the environment or the mean of the previous time step. When the model with multipath observations interacts with the model without multipath observations, the dimension decreases. Projective truncation is used to retain only the elevation angle and angular velocity components of the particles in the model with multipath observations, discarding the environmental feature parameters, resulting in the mixed input state of the model. The model after interaction... exist The mixed input state at time t is: ; ; in, express Time model Neutron Mixed input states, express Time model Transform to model The probability, express Time model State estimation, express Time model Neutron The covariance. In and When they are equal, Represents particles interacting with the same model; in For 1, When it is 2, As a reduced-dimensional particle; in For 2, When it is 1, This refers to particles that have increased in dimensionality.

[0063] Can The first in the input particle filter Each model is resampled to obtain... Time of the first In the model, the first State estimate of each particle Covariance Particle weights At this point, the particle filter state estimation of the model... It can be represented as: ; in, express Time model Neutron State estimation.

[0064] Estimating covariance Represented as: ; in, express Time model Neutron State estimation.

[0065] The state estimates of each model can be mapped to the complex single-pulse ratio observation space, and the predicted observation mean is: ; in, For the model Neutron The observation vector.

[0066] Residual Covariance Represented as: ; in, To observe the noise covariance, For the model Neutron The observation vector, To predict the observed mean.

[0067] Measurement residuals for: ; in, for The actual complex single-pulse ratio of the observed vector at time t is 1. For the model Neutron The observation vector.

[0068] The model likelihood values ​​for each model are calculated based on the residual covariance and measurement residuals: ; in, For the model The model likelihood value, To measure the residual, For residual covariance.

[0069] The model probability can be updated based on the model likelihood value to obtain the model posterior probability: ; in, for Time model The posterior probability, For the model The posterior probability, .

[0070] In the above implementation, during the interactive multi-model particle filtering process for both multipath observation models and non-multipath observation models, particles from each model are predicted in their corresponding state spaces. The predicted particles are mapped to the complex single-pulse ratio observation space using measurement equations, and likelihood weights are calculated based on the residuals between the predicted measurements and the actual complex single-pulse ratio observation vectors. Resampling is used to retain high-likelihood particles and suppress low-likelihood particles, gradually converging the target state and environmental characteristic parameters towards the region consistent with the observation data.

[0071] Step S106: Perform state fusion based on the particle filter state estimation and model posterior probability of each model, and output the target elevation angle tracking result.

[0072] For example, the particle filter state estimate from a multipath observation model and the particle filter state estimate from a model without multipath observation can be weighted and fused according to the model's posterior probability to obtain a global state estimate. The target elevation angle component can then be extracted from the global state estimate as the target elevation angle tracking result. Repeating the above steps within a continuous measurement period yields a dynamic tracking curve of the target elevation angle in a low-altitude multipath environment. The global state estimate... It can be represented as: ; in, for Time model Neutron State estimation, for Time model The posterior probability.

[0073] In one possible implementation, taking a 1T2R dual-channel three-coordinate radar as an example, the two receiver antennas are designed as follows: Figure 3 The two receiving antennas are spaced a certain distance apart. This causes a phase difference in the target echo, allowing for phase comparison angle measurement. Simultaneously, the two receiving antennas are tilted x° to the sides to perform amplitude and phase comparison angle measurement. The results of amplitude and phase comparison angle measurement can resolve the angular ambiguity caused by the phase comparison method to a certain extent, thus serving as the amplitude and phase comparison angle measurement method.

[0074] Under conditions without multipath propagation, the amplitude-phase ratio angle measurement result is close to the actual elevation angle. However, under conditions with multipath propagation, the coherent interference of low-altitude multipath signals will disrupt the stability of the target echo signal, causing not only oscillations in the echo amplitude but also severe fluctuations in the phase difference information of the two channels, rendering the conventional static amplitude-phase ratio angle measurement method completely ineffective in the low elevation angle region.

[0075] The low-altitude multipath radar elevation tracking system based on interactive multi-model particle filtering provided by the present invention is compared with the static amplitude and phase ratio angle measurement method to illustrate the optimization of the elevation tracking performance of the method in a multipath environment.

[0076] In one possible implementation, taking a target at a fixed altitude of 50m far from the flight scenario as an example, in order to closely approximate the real low-elevation radar environment and verify the effectiveness of the adaptive IMMPF algorithm, a flight detection simulation scenario of the target in a low-altitude multipath environment was constructed. The system and environmental characteristic parameters were set as follows: the radar system beam adopted the measured antenna pattern data, the baseline length between antennas was set to 12 times the wavelength, the two antennas were tilted to both sides by 5°, the antenna installation height was 2m, and the receiver signal-to-noise ratio was kept constant at 20dB.

[0077] The target maintains a constant altitude of 50m and flies at a uniform speed within a horizontal distance ranging from 500m to 4000m, with the entire flight path discretized into 2000 sampling points. The reflecting surface is set as a smooth physical ground surface, with its actual surface roughness root mean square value... Set to 0.005m, Fresnel reflectance coefficient Set as .

[0078] Regarding the parameter configuration of the filtering algorithm, the system adopts an IMMPF framework containing 2000 particles to evolve the nonlinear state space of the target, and the single-pulse ratio observation noise variance is... The process noise of the target state is Initially, the particle swarm is randomly scattered across a wide range of elevation angles from 0° to 10°, and the particle sizes are at Fresnel reflection coefficients. arrive The model transition probability is randomly initialized within the range of 0.005m to 0.01m, and within the range of surface roughness. The upper and lower boundaries of the confidence level of the model transition probability are constrained to 0.95 and 0.05, respectively. Under these initial constraints, the IMM-PF algorithm drives the likelihood evaluation and continuous angle tracking of the composite measurement equation.

[0079] Simulation results of target tracking at a fixed altitude of 50m away from the target, including elevation angle tracking, model hold-up probabilities, and environmental characteristic parameter estimation. Figure 4 , Figure 5 and Figure 6 As shown.

[0080] like Figure 4 As shown, in low-altitude multipath environments, the amplitude-phase comparison angle measurement method is affected by the interference of ground-reflected waves, causing distortion of the measured amplitude and phase characteristics, resulting in severe oscillations in the angle measurement results, with a root mean square error of 13.2°. In contrast, the adaptive IMM-PF algorithm of this invention can overcome multipath interference, closely follow the real trajectory to achieve high-precision continuous tracking, and has a root mean square error of 0.281°, reducing the error by approximately 97.87%. Figure 5 As shown, the model adaptive interaction mechanism based on the radiation pattern characteristics ensures that the ground specular reflection wave always falls into the main lobe and high-gain region of the radar antenna within the ultra-low altitude flight range. This mechanism keeps the holding probability of the multipath model stable at around 0.9, which conforms to the spatial radiation law and effectively avoids the problem of mismatch and divergence of the fixed model under complex trajectories.

[0081] Furthermore, the underlying mechanism by which the algorithm maintains high accuracy in multipath environments lies in its joint estimation of characteristic parameters of unknown environments, such as... Figure 6As shown, for unknown surface environments, the algorithm expands the Fresnel reflection coefficient and surface roughness into the target state vector in Model 1 (corresponding to the multipath observation model in the above implementation), and endows the particle swarm with random walk optimization capabilities in the state space. Driven by the likelihood evaluation and resampling mechanism of the composite measurement equation, even in the absence of accurate prior environmental information, the estimated values ​​of reflection coefficient and roughness can be rapidly approximated to the true physical values. and The algorithm converges and remains stable. This virtuous cycle of optimizing environmental characteristic parameters and dynamically tracking the target state fundamentally eliminates nonlinear measurement errors caused by multipath interference, verifying the effectiveness of the algorithm.

[0082] In one possible implementation, taking a target approaching at a constant altitude of 300m as an example, the simulation demonstrates the process of a target approaching at a constant altitude of 300m, with the horizontal distance decreasing from 4000m to 700m. The target's true elevation angle will continuously increase from approximately 4.3° to approximately 23.2°, and the ground-reflected wave generated by the target undergoes a gradual transition from the high-gain region of the antenna's main lobe to the side lobe. The simulation results are as follows... Figure 7 As shown.

[0083] In this cross-regional proximity scenario, according to Figure 7 Figure (a) shows that the simulation results further highlight the tracking capability of the adaptive IMM-PF algorithm of this invention. The root mean square error of amplitude-phase angle measurement is 8.59°, and the root mean square error of angle measurement for IMM-PF elevation tracking is 0.32°, representing a reduction in error of approximately 96.27%. When the target distance is relatively far, due to the low elevation angle, the multipath reflected wave falls within the main lobe, and the model holding probability of Model 1 (corresponding to the multipath observation model in the above implementation) dominates. However, as the target approaches and the elevation angle increases, the multipath energy attenuates rapidly in the antenna spatial pattern, and the system adaptively weakens the weight of Model 1. At the same time, the model holding probability of Model 2 (corresponding to the non-multipath observation model in the above implementation) steadily increases, such as... Figure 7 As shown in Figure (b).

[0084] See Figure 7 Figure (c) in the middle and Figure 7 The environmental characteristic parameter estimation curves shown in Figure (d) represent, in the current implementation, estimates of the Fresnel reflectance coefficient and surface roughness compared to... Figure 6The results showed more pronounced oscillations, but overall remained within the range of true physical values ​​without diverging. Due to the high flight altitude of 300m, the rate of change of the spatial path difference between the direct wave and the ground-reflected wave with horizontal distance increased. This resulted in faster alternation of multipath interference received by the radar. The high-frequency fluctuations in the measured single-pulse ratio forced the particle swarm to undergo intensive dynamic adjustments during the optimization process, manifesting as rapid oscillations. In the latter half of the target approach, as the true elevation angle continuously increased, the ground-reflected wave gradually moved out of the antenna main lobe and into the sidelobe region, causing multipath energy attenuation. At this point, the prior information about the surface environment carried in the observation data decreased, weakening the constraint of the likelihood equation on the reflection coefficient and roughness. Driven by process noise, the parameters in Model 1 exhibited more pronounced random walks and wide-amplitude oscillations.

[0085] The low-altitude multipath radar elevation tracking method based on interactive multi-model particle filtering provided by this invention performs range-Doppler two-dimensional processing on the target echo complex signal received by a multi-channel three-coordinate radar and constructs a complex monopulse ratio observation vector, enabling amplitude and phase information to serve as a unified measurement input for subsequent nonlinear tracking. A dual-model state observation model is constructed, including both a multipath observation model and a non-multipath observation model, allowing the measurement process of direct wave and the measurement process of direct wave superimposed on ground reflected wave to be described within the same interactive framework. Based on the target elevation angle estimate and antenna pattern function of the previous measurement cycle, a dynamic multipath spatial gain factor is calculated, and the model state transition probability matrix is ​​reconstructed accordingly, allowing the model switching probability to adaptively adjust with the spatial gain of the ground reflected wave in the antenna pattern. Interactive multi-model particle filtering is used to estimate the target state and environmental characteristic parameters, enabling the particle swarm to perform global optimization in a strongly nonlinear measurement space and reducing dependence on the initial state. State fusion is performed based on the particle filter state estimation and model posterior probability of each model, enabling continuous output of multipath-suppressed target elevation tracking results. Therefore, this invention can improve the accuracy, stability, and environmental adaptability of target elevation angle tracking in low-altitude multipath environments.

[0086] Please see Figure 8 , Figure 8 This is a schematic diagram of a low-altitude multipath radar elevation angle tracking device based on interactive multi-model particle filtering, provided by an embodiment of the present invention. The low-altitude multipath radar elevation angle tracking device based on interactive multi-model particle filtering provided by the present invention includes a vector construction module 801, a model construction module 802, a gain calculation module 803, a matrix reconstruction module 804, an interactive filtering module 805, and a state fusion module 806.

[0087] Among them, the vector construction module 801 is used to acquire the complex echo signals of each target received by the multi-channel three-coordinate radar, perform range-Doppler two-dimensional processing on each target echo complex signal to obtain the complex signal of each target element, and construct a complex single pulse ratio observation vector based on the complex signal of each target element. Model building module 802 is used to construct a dual-model state observation model based on the complex single-pulse ratio observation vector; the dual-model state observation model includes a multipath observation model and a non-multipath observation model. The gain calculation module 803 is used to determine the ground reflected wave incident angle based on the target elevation angle estimate of the previous measurement cycle, and to calculate the dynamic multipath spatial gain factor based on the ground reflected wave incident angle and the antenna pattern function. The matrix reconstruction module 804 is used to reconstruct the model state transition probability matrix of the dual-model state observation model based on the dynamic multipath spatial gain factor. The interactive filtering module 805 is used to perform interactive multi-model particle filtering on multipath observation models and non-multipath observation models based on the reconstructed model state transition probability matrix, so as to obtain the particle filter state estimate and model posterior probability of each model. The state fusion module 806 is used to perform state fusion based on the particle filter state estimates and model posterior probabilities of each model, and output the target elevation angle tracking results.

[0088] Please see Figure 9 , Figure 9 This is a schematic diagram of the hardware entity of an electronic device to which an embodiment of the present invention applies. The electronic device provided in this embodiment includes a processor 901, a communication interface 902, a memory 903, and a communication bus 904, wherein the processor 901, the communication interface 902, and the memory 903 communicate with each other via the communication bus 904. Memory 903 is used to store computer programs; When the processor 901 executes the program stored in the memory 903, it implements the steps in the above method embodiments.

[0089] The communication bus 904 mentioned in the above electronic device can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus 904 can be divided into address bus, data bus, control bus, etc. For ease of illustration, it is represented by only one thick line in the figure, but this does not indicate that there is only one bus or one type of bus.

[0090] The communication interface 902 is used for communication between the above-mentioned electronic device and other devices.

[0091] The memory 903 may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory 903 may also be at least one storage device located remotely from the aforementioned processor.

[0092] The processor 901 mentioned above can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0093] The method provided in this invention can be applied to electronic devices. Specifically, the electronic device can be a desktop computer, a portable computer, a smart mobile terminal, a server, etc. No limitation is made herein; any electronic device that can implement this invention falls within the protection scope of this invention.

[0094] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps provided in the above-described method embodiments.

[0095] For the embodiments of the device / electronic device / storage medium, since they are basically similar to the method embodiments, the description is relatively simple. For specific details and beneficial effects, please refer to the description of the method embodiments.

[0096] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0097] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0098] Those skilled in the art will understand that embodiments of this application can be provided as methods, apparatus (devices), or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects, all of which are collectively referred to herein as "modules" or "systems." Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The computer program may be stored / distributed in a suitable medium, provided with or as part of other hardware, or may take other distribution forms, such as via the Internet or other wired or wireless telecommunications systems.

[0099] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (devices), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0100] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0101] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0102] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering, characterized in that, include: The complex echo signals of each target received by the multi-channel three-coordinate radar are acquired, and the range-Doppler two-dimensional processing is performed on each target echo complex signal to obtain the complex signal of each target element. Based on the complex signal of each target element, a complex single pulse ratio observation vector is constructed. A dual-model state observation model is constructed based on the complex single-pulse ratio observation vector; the dual-model state observation model includes a multipath observation model and a multipath-free observation model. The ground reflected wave incident angle is determined based on the target elevation angle estimate from the previous measurement cycle, and the dynamic multipath spatial gain factor is calculated based on the ground reflected wave incident angle and the antenna pattern function. The model state transition probability matrix of the dual-model state observation model is reconstructed based on the dynamic multipath spatial gain factor. Based on the reconstructed model state transition probability matrix, interactive multi-model particle filtering is performed on the multipath observation model and the non-multipath observation model to obtain the particle filter state estimate and model posterior probability of each model. State fusion is performed based on the particle filter state estimates and posterior probabilities of each model to output the target elevation angle tracking results.

2. The method according to claim 1, characterized in that, The step of performing range-Doppler two-dimensional processing on the complex echo signals of each target to obtain the complex signal of each target unit, and constructing a complex single-pulse ratio observation vector based on the complex signal of each target unit, includes: Coherent accumulation and range-Doppler two-dimensional processing are performed on the echo complex signals of each target to obtain the complex signal of each target unit; From the complex signals of each target unit, a reference channel complex signal and at least one channel complex signal to be compared are selected, and a complex ratio operation is performed between the channel complex signal to be compared and the reference channel complex signal to obtain a channel complex ratio value. The complex single-pulse ratio observation vector is generated based on the channel complex ratio value.

3. The method according to claim 1, characterized in that, The construction of the dual-model state observation model based on the complex single-pulse ratio observation vector includes: Construct a first state vector for the multipath observation model, the first state vector including the target elevation angle, the rate of change of elevation angle, and environmental characteristic parameters; Based on the direct wave steering vector, the ground reflected wave steering vector, and the environmental characteristic parameters, a composite steering vector corresponding to the multipath observation model is constructed; based on the composite steering vector and the complex single-pulse ratio observation vector, the first measurement equation of the multipath observation model is constructed. The multipath observation model is constructed based on the first state vector and the first measurement equation. Construct a second state vector for the multipath-free observation model, the second state vector including the target elevation angle and the rate of change of elevation angle; Based on the direct waveguide vector and the complex single-pulse ratio observation vector, the second measurement equation of the multipath-free observation model is constructed. The multipath-free observation model is constructed based on the second state vector and the second measurement equation.

4. The method according to claim 1, characterized in that, The step of determining the ground reflected wave incident angle based on the target elevation angle estimate from the previous measurement cycle, and calculating the dynamic multipath spatial gain factor based on the ground reflected wave incident angle and the antenna pattern function, includes: The ground reflection wave incident angle is determined based on the target elevation angle estimate and the radar low-altitude detection geometry. The ground reflected wave incident angle is input into the antenna pattern function to obtain the reflected wave pattern gain value; The dynamic multipath spatial gain factor is generated based on the reflected wave pattern gain value.

5. The method according to claim 1, characterized in that, The step of reconstructing the model state transition probability matrix of the dual-model state observation model based on the dynamic multipath spatial gain factor includes: The model preservation probability of the multipath observation model is determined based on the dynamic multipath spatial gain factor. The model preservation probability of the multipath-free observation model is determined based on the dynamic multipath spatial gain factor. The first model switching probability for transitioning from the multipath observation model to the non-multipath observation model is determined based on the model preservation probability of the multipath observation model. The second model switching probability from the multipath-free observation model to the multipath-observation model is determined based on the model preservation probability of the multipath-free observation model. The model state transition probability matrix is ​​generated based on the model preservation probability of the multipath observation model, the model preservation probability of the non-multipath observation model, the first model switching probability, and the second model switching probability.

6. The method according to claim 1, characterized in that, Based on the reconstructed model state transition probability matrix, interactive multi-model particle filtering is performed on the multipath observation model and the non-multipath observation model to obtain the particle filter state estimate and model posterior probability for each model, including: The model mixture probability is calculated based on the model state transition probability matrix and the model posterior probability of the previous measurement period. The multipath observation model and the non-multipath observation model are inputted and interacted based on the model mixing probability to obtain the mixed input particle set of each model; State prediction is performed on the mixed input particle set of each model to obtain the predicted particle set of each model; Based on the complex single-pulse ratio observation vector and the measurement equations corresponding to each model, the likelihood weights of particles in the predicted particle set of each model are calculated. Based on the likelihood weights, the predicted particle sets of each model are resampled and weighted to obtain the particle filter state estimates of each model. The model likelihood value of each model is calculated based on the measurement residuals and residual covariance of each model, and the model probability is updated according to the model likelihood value to obtain the posterior probability of the model.

7. The method according to claim 6, characterized in that, The step involves inputting the multipath observation model and the non-multipath observation model into the model based on the model mixing probability to obtain a set of mixed input particles for each model, including: When the particles without the multipath observation model interact with the multipath observation model, the target elevation angle and elevation angle change rate in the particles without the multipath observation model are retained, and environmental feature parameters are injected into the particles without the multipath observation model to obtain the upgraded particles. When the particles of the multipath observation model interact with the particles of the non-multipath observation model, the target elevation angle and elevation angle change rate in the particles of the multipath observation model are retained, and the environmental feature parameters in the particles of the multipath observation model are removed to obtain the dimensionality-reduced particles. Based on the model mixing probability, the upgraded particles, the downgraded particles, and the particles interacting with the same model are weighted and mixed to obtain the mixed input particle set of each model.

8. A low-altitude multipath radar elevation tracking device based on interactive multi-model particle filtering, characterized in that, include: The vector construction module is used to acquire the complex echo signals of each target received by the multi-channel three-coordinate radar, perform range-Doppler two-dimensional processing on each target echo complex signal to obtain the complex signal of each target element, and construct a complex single-pulse ratio observation vector based on each target element complex signal; The model building module is used to construct a dual-model state observation model based on the complex single-pulse ratio observation vector; the dual-model state observation model includes a multipath observation model and a non-multipath observation model; The gain calculation module is used to determine the ground reflected wave incident angle based on the target elevation angle estimate of the previous measurement cycle, and to calculate the dynamic multipath spatial gain factor based on the ground reflected wave incident angle and the antenna pattern function. The matrix reconstruction module is used to reconstruct the model state transition probability matrix of the dual-model state observation model based on the dynamic multipath spatial gain factor. The interactive filtering module is used to perform interactive multi-model particle filtering on the multipath observation model and the non-multipath observation model based on the reconstructed model state transition probability matrix, so as to obtain the particle filter state estimate and model posterior probability of each model. The state fusion module is used to perform state fusion based on the particle filter state estimates and posterior probabilities of each model, and output the target elevation angle tracking results.

9. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; The memory is used to store computer programs; When the processor executes the computer program stored in the memory, it implements the steps of the low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the low-altitude multipath radar elevation angle tracking method based on interactive multi-model particle filtering as described in any one of claims 1-7.

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