Estimating the 3D alignment of migratory insects is essential for understanding their 3D directional behavior. The existing approach reconstructs 3D alignment using azimuthal angle measurements from dual-view entomological radars. However, the measurement errors often propagate into the reconstructed 3D alignment, causing significant inaccuracies, especially under low signal-to-noise ratio conditions. To overcome this problem, this letter proposes a new method based on a multi-view, multi-frequency, and full-polarization entomological radar system. The method directly estimates insect 3D alignment by integrating polarization scattering matrices (SMs) from multiple views and frequencies, leveraging the assumption of scattering symmetry in insect bodies. For symmetric targets, the off-diagonal SM elements vanish when the polarization direction aligns with the symmetry plane. Based on this theory, an optimization problem is formulated to estimate 3D alignment by minimizing the sum of the powers of off-diagonal elements across multi-view and multi-frequency SMs. Both simulations and field experiments demonstrate that the proposed method achieves substantially higher accuracy than the traditional method.

For vertical-looking radars (VLRs), it is typically assumed that insects maintain a steady and approximately horizontal flight attitude as they pass through the radar beam, allowing for the estimation of insect morphological parameters by measuring the Radar Cross Section (RCS) for a ventral aspect. However, for tracking radars, which dynamically track and monitor insects, the attitude of the insect relative to the radar beam constantly changes. This dynamic change in attitude renders traditional insect morphological parameter estimation methods based on the ventral-aspect RCS ineffective. This paper proposes a novel method for estimating the morphological parameters of insects in non-horizontal flight attitudes. By determining the azimuth and pitch angles of the insect’s body axis relative to the radar antenna reference coordinate system and reconstructing the scattering matrix (SM) of the insect from non-horizontal attitudes to a horizontal attitude, we achieve the estimation of morphological parameters for insects in non-horizontal attitudes. The effectiveness of the proposed method is validated using a fully-polarimetric multi-angle observation dataset of 33 insects from 6 species measured in a microwave anechoic chamber. The mean relative errors in estimating the mass and length of the insects across 20 different observation angles are 20.06% and 12.85%. Compared to estimates obtained without making the correction, the accuracy of mass and body length estimation is improved by 19.80% and 13.79%, respectively.

Entomological radar utilizes full-polarization data to estimate insect orientation, which is essential for understanding the orientation mechanisms of migrating insects and predicting their trajectories. Traditional orientation estimation methods rely on the empirical assumption that maximum echo intensity occurs when the polarization direction aligns with the insect’s body axis. Orientation is then extracted by identifying the polarization direction corresponding to the maximum echo intensity, based on the polarization pattern or the scattering matrix (SM) measured by single-frequency radars. However, the accuracy of the estimated orientation is affected by noise and polarization errors. To further improve orientation accuracy, based on a new generation of multifrequency and full-polarization entomological radar, this article proposes a novel method. The approach integrates multifrequency SMs of an insect under the assumption of insect body symmetry. First, a parametric SM model, characterized by four independent parameters, including insect orientation, was developed based on the polarization theory that when the symmetry axis of a symmetric target aligns with the horizontal or vertical polarization direction, the cross-polarization elements in the SM are zero. Using this principle, a cost function was constructed by summing the cross-polarization powers across multifrequency SMs. By minimizing the cost function, the analytical formula for insect orientation estimation was derived. Simulations using data from 159 insects measured in an anechoic chamber, along with field measurements, demonstrated that the proposed method provides superior accuracy and robustness against noise and polarization errors compared to traditional single-frequency approaches.

Insects are categorized into two classes, “parallel (PA)” and “perpendicular (PE),” based on the relationship between radar cross section (RCS) values when the polarization direction is PA and PE to the insect body axis. Distinguishing between these classes is essential for accurately measuring insect orientation and morphological parameters. The current classification method relies on the relative phase sign of two eigenvalues from the insect’s polarization scattering matrix (SM). However, this method is susceptible to phase unwrapping errors and noise in practical applications. To enhance classification accuracy, the multifrequency characteristics of the relative amplitudes of SM eigenvalues, the polarization pattern shape, and insect class were analyzed using multifrequency SM data from both electromagnetic simulations and microwave anechoic chamber measurements. The analysis revealed that insect class can be distinguished based on the relative amplitude and phase of SM eigenvalues at two subfrequencies in the X-band. Building on this, a classification model for PA and PE insects was developed using the random forest (RF) algorithm, with the relative eigenvalues at 9.5 and 11.5 GHz as key features. Simulations demonstrated that the proposed method outperforms the traditional approach, particularly at low signal-to-noise ratios (SNRs). The model was then applied to a multifrequency, fully-polarimetric entomological radar, achieving 99.4% accuracy in distinguishing PA and PE insect classes based on body-axis alignment in the field. Finally, the reliability of the method was further validated through observations of freely flying migratory insects.

Insect morphological parameters, including mass and length, are crucial for species identification. Entomological radar can estimate morphological parameters by establishing mappings from insect radar cross section (RCS) estimators to them. Current high-accuracy methods relying on absolute RCS estimators are sensitive to echo intensity. When applied to radars without angle measurement capability, these methods may underestimate morphological parameters. This underestimation arises from the inability of such radars to compensate for reduced echo intensity caused by insects deviating from the beam center. A method using single-frequency echo intensity-independent estimators (EIIEs) was attempted; however, it could only estimate the mass of insects below 200 mg with limited accuracy. This article explores the use of multifrequency EIIEs (MFEIIEs) to enhance the estimation of insect mass and length. Based on the multifrequency scattering dataset for 159 insects measured in an anechoic chamber, the insect multifrequency scattering matrix (SM) was studied. The study revealed that four EIIEs, including the amplitude ratio and phase difference of SM eigenvalues, and two relative RCS features related to the shape of the insect polarization pattern, were correlated with insect mass and length with varied correlations with frequency. Subsequently, morphological parameter estimation was achieved by establishing the mappings from MFEIIEs to mass and length using a random forest algorithm. The presented dataset demonstrated that this method was suitable for insects below 1000 mg. Finally, the method’s effectiveness and robustness were demonstrated through field measurements on 160 insects, which yielded mean relative estimation errors of 21.82% for mass and 13.18% for length.

The accurate identification of migratory insect species is pivotal for effective pest forecasting and control strategies. Radar entomology continues to face challenges in insect identification, prompting the exploration of innovative solutions. The precision of conventional insect identification methodologies relying on morphological parameters or radar cross section (RCS) shape was inherently constrained. This study employed ensemble learning algorithms, utilizing multiple electromagnetic scattering parameters of insects as features for species classification, thereby enhancing radar’s capability to identify insects. Experiments of measuring insects using two unmanned aerial vehicles (UAVs) were carried out, aiming to establish an electromagnetic scattering database. Data were collected using a multifrequency fully polarimetric entomological radar, capturing echoes from nine major migratory pests in mainland China. Extracting the insect scattering matrix (SM) yielded a total of 22 electromagnetic scattering features categorized into four classes. Three ensemble learning algorithms were employed for classification: random forest (RF), extreme gradient boosting (XGBoost), and stacked generalization (SG). The results demonstrated that the model trained with the XGBoost algorithm consistently exhibited outstanding performance across various frequencies. In the X-band (9.5 GHz, typical operating frequency of entomological radar), the proposed XGBoost algorithm achieved an average identification accuracy of 87.50% for the nine pest species, which is approximately 13% higher than the traditional identification methods based on body size parameters. This study validated the feasibility of insect species identification based on electromagnetic scattering parameters, offering promising prospects for radar entomology to overcome challenges in insect identification.

Insect mass could be estimated by estimators calculated by the radar cross-section (RCS) measured by entomological radar, which is essential for the statistics of migratory biomass and classification of insects. In order to obtain the insect mass through radar, the RCS of various insects are measured in the Microwave Anechoic Chamber by a specially designed system containing dual-polarization antennas, which point at insects in the measurement process, and the mapping between RCS and the insect mass are constructed and applied to entomological radar. However, insects might deviate from beam center in practice, and the echo intensity will decrease. The decrease cannot be compensated for radar without angle measurement capability. Through the study of insect scattering matrix (SM), it is found that co-polarization estimators, such as co-polarization ratio and co-polarization phase, are echo intensity independent and correlated with insect mass. Therefore, a co-polarization estimators calculation method driven by model and data is elaborately designed, and an estimation method for insect mass is given on basis of the co-polarization estimators. Analyses present that the method is suitable for insects below 200mg, and the mean relative mass estimation error is lower than 30% in X band and 20% in Ku band. The effectiveness and robustness of this method is verified by measuring 39 individual insects with a Ku band fully polarimetric radar in field. The proposed methods provide a way to estimate insect mass for entomological radar without angle measurement capability.

The ability of insect orientation measurement of entomological radars supported the study of insect heading behaviors. However, the current entomological radars can only measure the two-dimension (2D) orientation that is the projection of the three-dimension (3D) orientation on the horizontal plane. The ability to measure the 3D orientation of insect will promote the study of the vertical and 3D heading behaviors of insect. In this study, an insect 3D orientation estimation method based on cooperative observation from two views of entomological radars is proposed. The expression of 3D orientation is deduced based on 2D orientation, azimuth and elevation measured with two radars at different stations through vector operation. The simulations are conducted to verify the effectiveness of the proposed method. The result shows that the estimation error of 3D orientation depends on that of the 2D orientation and the included angle between two lines of sight of two radars. A multi-aspect fully polarimetric rig is designed to measure insect echo signals from two aspects in a microwave anechoic chamber. The experiment data is used to further validate the effectiveness of the proposed method.

Polarization information can greatly improve the ability of detection, parameter retrieval and classification for entomological radar. In recent, the instantaneous fully polarimetric measurement technique is used in entomological radar, so as to relax restriction of invariant orientation during observation compared to the typical vertical-looking radar with linear-polarized rotation configuration. However, the fully polarimetric measurement is based on a multi-channels radar system, and the imbalance and cross-talk between channels, namely polarimetric errors, will severely affect the measurement of the polarimetric scattering matrix (PSM). So, polarimetric calibration is essential to obtain the accurate polarization information of targets. In contrast to inefficient and manual calibration methods, a data-driven polarimetric calibration method is proposed based on the assumption of reciprocity and bilateral symmetry of insects in this paper. The polarimetric errors are elaborately decomposed into two components which could be estimated by reciprocity and bilateral symmetry, respectively. In addition, because the proposed method is data-driven, the calibration process could be automatically executed to compensate the temporal-variant polarimetric errors induced by temperature change, and thus suitable for long-term operation of entomological radar. Simulations and experiments are carried out to evaluate the performance of the proposed calibration method. Results show that it could achieve high accuracy when the number of insects used as calibrators is large enough. The proposed method has been applied in Ku-band high-resolution fully polarimetric entomological radars for cross-border migratory insect observation in Yunnan province, China.

For insect radar observations, exploiting radar echoes from insects to accurately estimate size parameters such as body mass, length, and width of insects can help to identify insect species. At present, the commonly used method for estimating insect body size parameters in insect radar is to use the monotonic mapping relationship between insect RCS parameters of a single frequency (mainly 9.4 GHz) and body size, and obtain the empirical formula for body size estimation by polynomial fitting. However, the useful information used by the traditional methods is limited (1 to 2 features), and these retrieval methods are simple and with limited estimation accuracy. This paper proposed a feature-selection-based machine learning method for insect body size estimation, which could effectively improve the body size parameter estimation accuracy of insect radars. First of all, based on the published insect scattering dataset (9.4GHz, 366 specimens of 76 species), stepwise regression was used to select the optimal feature combinations for body size estimation, then three machine learning methods, Random Forest Regression (RFR), Support Vector Regression (SVR) and Multilayer Perceptron (MLP), were adopted to achieve estimation of insect body size. Among them, RFR has the best performance (mass 18.83%, length 11.37%, width 16.87%). Subsequently, based on the measured dataset of migratory insects (5532 specimens of 23 species), the influence of the estimation error of insect body size on the identification accuracy of migratory insect species was analyzed. When incorporating the estimation error of the feature-selection-based RFR method, the insect identification rate of 83.68% was reached.

Vertical-looking radar (VLR) is a significant milestone in the development of insect radars with the capability of detecting the behavior of migratory insects and their biological parameters. In current VLRs, high-speed continuous sampling and long-time integration can barely be performed simultaneously, leading to a low detection probability for tiny insects (weight < 10 mg). Based on the large amount of data acquired by our developed high-range resolution insect radar, the insect echo signals and vertical motion characteristics are initially analyzed and demonstrate that the linear-motion mode is dominant in insect migration; also, the echo signal power of most insects follows the gamma distribution. Based on these characteristics, a long-time integration and detection method for detecting migratory insects, especially tiny targets from echo signals that often dip below the noise level, is proposed. The radial target velocity is also measured as one of the output parameters. The theoretical derivation and optimal choice of detection thresholds are also presented. Simulation and experimental results demonstrate that the proposed method exhibits better insect detection performance and effectively increases the detection range compared with conventional methods. In addition, the measured target velocity can be directly applied to current continuous-sampling VLRs for the ascent and descent rate analysis. Many typical insect migration phenomena have been detected effectively utilizing our developed VLR, and the measured ascent and descent rates of insects agree well with typical take-off, cruising, and landing behaviors. This is the first reported successful VLR application on take-off and landing behaviors of migratory tiny and dense insects.

Current vertical-beam entomological radars record the polarization direction corresponding to the maximal ventral-aspect radar cross section (RCS) as the insect's orientation. For so-called “parallel” insects, this direction is indeed their orientation; but for “perpendicular” insects, it is at right angles to the orientation. Current entomological radars cannot discriminate the parallel and perpendicular cases. This article shows here that discrimination is possible using the relative phase of the scattering matrix (SM) eigenvalues. Multifrequency fully polarimetric ventral aspect SM measurements of 80 insect specimens of 12 species have been made in a microwave anechoic chamber. The relationship of the polarization direction corresponding to the maximal RCS and the radar frequency has been analyzed, and from these results a method of discriminating parallel and perpendicular insects, based on the relative phase of the SM eigenvalues, is proposed. The method is applicable to X- and Ku-band observations, with a high correct-identification rate, and can be used with both fully polarimetric entomological radars and coherent rotating-polarization units, but not with the noncoherent rotating-polarization configuration used in traditional vertical-looking radars (VLRs). Finally, the performance of the method is discussed, and it is found that it has better performance for middle and large insects at X-band and small and middle insects at Ku-band.

For radar observations, invariant target parameters extracted from the scattering matrix (SM) provide information about the target's geometry and composition. By studying the invariant target parameters of a small sample of insects, it is shown that the two eigenvalues and the determinant of the Graves power matrix are strongly correlated with insect body length and mass. Therefore, two methods are proposed to estimate the body length and mass from the eigenvalues or the determinant. The two eigenvalues identify the maximum of the insect polarization pattern and the perpendicular to the maximum direction, while the determinant is the product of these two values. A sample of 207 insect specimens measured at X-band in the laboratory rigs is used to determine the relationships between SM parameters and body lengths and masses. The results show that the length and mass can be estimated with a good performance and without an initial classification stage. In addition, the use of the determinant of the Graves power matrix is shown to provide an improved, SM-based, method of determining insect orientation and to solve the 90° orientation-extraction error problem that arises at X-band with very large insects.

A novel insect orientation extraction method is proposed based on the target polarization scattering matrix (PSM) estimation, which is applicable for traditional vertical-looking insect radar with noncoherent reception as well as the coherent radar. The insect echo signal at different polarization directions on the radar polarization plane is usually acquired by means of rotating linearly polarized antenna. In this letter, the insect echo signal is first used to accurately estimate insect PSM by an iterative algorithm based on the second-order polynomial approximation. Meanwhile, the Cramer-Rao lower bound is also analyzed to test the estimation performance. Next, based on the assumption that the target orientation is consistent with the dominant eigenvector, the insect orientation is extracted from the estimated PSM. Finally, both theoretical simulations and real experimental data are used to validate the effectiveness and feasibility of our proposed method, which can achieve good orientation estimation accuracy at low signal-to-noise ratio.