A charged small target detection and positioning method based on double-sphere differential array

Abstract

A charged small target detection and positioning method based on double-sphere differential array, when the flying small target carries electric charge due to friction, contact separation, air action or environmental electric field induction during movement, different induced charge changes are generated on the detection electrode and reference electrode of each double-sphere differential electrostatic sensor when passing through the detection area, after current-voltage conversion, differential amplification, filtering and synchronous acquisition, multi-channel differential electrostatic response signals are obtained. Based on the calibration correction mirror model, combined with multiple sensor observations, a variable-width sliding window electrostatic distortion weighted nonlinear target detection algorithm is used to solve the target position and charged quantity, and through sliding window trajectory fitting, the target velocity, incident direction and motion trajectory are obtained, realizing the non-contact passive detection and positioning of the charged small target. The sensor array can use a system composed of a double-sphere differential electrostatic sensor array, a front-end signal conditioning unit, a synchronous acquisition unit, a data transmission unit and a parameter solving unit.

Description

Technical Field

[0001] This invention relates to a method for passively detecting, estimating the position, solving for the charge, and obtaining the velocity parameters of high-speed charged flying small targets using a dual-sphere differential electrostatic sensor array. It can be used in scenarios such as high-speed impact tests, debris monitoring, projectile simulation testing, industrial debris detection, and low-altitude UAV motion parameter measurement. Background Technology

[0002] In scenarios such as high-speed impact testing, material protection performance testing, debris monitoring, industrial safety protection, and measurement of motion parameters of small targets like low-altitude drones, it is necessary to obtain parameters such as the position, velocity, incident direction, and trajectory of flying charged small targets. Flying charged small targets are typically characterized by their small size, wide velocity range, short transit time, and difficulty in capturing their trajectories, posing significant challenges to non-contact detection and parameter measurement.

[0003] Existing methods for detecting and measuring the velocity of small flying targets mainly include light curtain targets, high-speed photography, radar velocity measurement, contact targets, piezoelectric sensing, and acoustic detection. Light curtain targets and high-speed photography are sensitive to optical path layout, ambient lighting, and field of view obstruction; radar velocity measurement equipment is complex and costly, and has requirements for the echo characteristics of small targets; contact targets and piezoelectric sensing usually require the target to hit or penetrate before a significant response is generated, making it difficult to achieve non-contact sensing during the target's approach or passage; acoustic methods are easily affected by environmental noise and reflection interference.

[0004] During their movement, small flying targets may acquire electrical charges or act as equivalent charged bodies due to launch, friction, contact separation, aerodynamic effects, material charging, or induction by the environmental electric field. When a charged small target passes through a detection area, it causes a rapid change in the electrostatic field of the surrounding space. Utilizing electrostatic sensors to non-contactly sense this change can provide a new technical approach for the passive detection and motion parameter acquisition of small flying targets.

[0005] However, existing electrostatic detection methods suffer from insufficient reliability and anti-interference capabilities in detecting small flying targets. Relying solely on a single electrostatic sensor makes it difficult to simultaneously obtain parameters such as target position, charge, and velocity. Furthermore, single-electrode electrostatic sensors are susceptible to environmental common-mode electrostatic disturbances, resulting in insufficient stability in target signal recognition. Therefore, it is necessary to propose a passive detection and localization method that uses a dual-sphere differential array to obtain the position, charge, velocity, and direction of motion of a small flying target. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and propose a method for detecting and locating charged small targets based on a dual-sphere differential array, which realizes non-contact, passive electrostatic sensing, differential detection, position estimation and motion parameter acquisition of flying small targets.

[0007] The basic principle of this invention is as follows: A small flying target carries or is equivalent to carrying a charge during its motion. When it passes near a dual-sphere differential electrostatic sensor array, it causes a rapid change in the spatial electrostatic field, resulting in different induced charge changes on the upper detection sphere electrode and the lower reference sphere electrode in each dual-sphere differential electrostatic sensor. The upper detection sphere electrode is used to pick up near-field electrostatic disturbances of the target; the lower reference sphere electrode faces away from the target's passage area and is used to pick up environmental common-mode disturbances; a grounded shield plate is placed between the two sphere electrodes to weaken the direct electric field coupling between them; and environmental common-mode interference is suppressed by differentially analyzing the induced signals from the detection and reference sphere electrodes. Target calculation is based on a single-sphere mirror method, combined with sensor calibration parameters to establish a calibration correction mirror model between the induced charge, target distance, and target charge. The differential induced charge of multiple dual-sphere differential electrostatic sensors in the array is used as an observation, and a robust width sliding window electrostatic distortion weighted nonlinear target detection algorithm is employed to solve for the position coordinates and target charge of the charged flying small target. Furthermore, based on the target position estimation results at multiple consecutive time points, a robust sliding window trajectory fitting method is used to obtain the target velocity, incident direction, and trajectory parameters.

[0008] This method is implemented through the following technical solution:

[0009] 1. A system consisting of a dual-sphere differential electrostatic sensor array, a front-end signal conditioning unit, a synchronous acquisition unit, a data transmission unit, and a parameter calculation unit can be used. The dual-sphere differential electrostatic sensor array consists of four dual-sphere differential electrostatic sensors, each arranged in a square around the detection area to form multi-point electrostatic observation. Each dual-sphere differential electrostatic sensor consists of an upper sphere detection electrode, a middle grounding shield, a lower sphere reference electrode, an insulating isolator, and a support. The upper sphere detection electrode and the lower sphere reference electrode are both conductive metal spheres or surface conductive spheres, arranged coaxially in the vertical direction. The middle grounding shield is located between the upper sphere detection electrode and the lower sphere reference electrode and is connected to the system ground to limit the direct electric field coupling between the upper and lower sphere electrodes and enhance the difference in electrostatic response between the upper and lower spaces. The insulating isolator, located between the upper sphere detection electrode, the middle grounding shield, and the lower sphere reference electrode, can be made of polytetrafluoroethylene (PTFE) high-insulation material to ensure the insulation performance between the electrodes and between the electrodes and the grounding shield. The front-end signal conditioning unit consists of an I / V conversion channel, a differential amplifier circuit, and a filter circuit. The upper ball current-voltage conversion channel receives the weak induced current output by the upper ball detection electrode and converts it into an upper ball voltage signal. The lower ball current-voltage conversion channel receives the weak induced current output by the lower ball reference electrode and converts it into a lower ball voltage signal. The differential amplifier circuit differentially amplifies the two voltage signals to obtain a differential electrostatic response signal. The synchronous acquisition unit synchronously acquires the differential electrostatic response signals output by each dual-ball differential electrostatic sensor, and the data transmission unit transmits the synchronous acquisition results to the parameter calculation unit.

[0010] The two-parameter calculation unit employs a differential induced charge modeling method based on a calibration-corrected mirror model. During target parameter calculation, the equivalent gain coefficient, probe electrode coupling correction coefficient, reference electrode coupling correction coefficient, and background bias term for each dual-sphere differential electrostatic sensor are first obtained through calibration experiments and finite element simulation, or a combination of both. Let the target position coordinates be (x, y, z), and the center coordinates of the i-th dual-sphere differential electrostatic sensor be (x, y, z). i y i , z i If the distance between the centers of the detection ball electrode and the reference ball electrode is h, then the theoretical differential induced charge of the i-th sensor is:

[0011]

[0012] in, Let K be the theoretical differential induced charge of the i-th sensor. i λ is the equivalent gain coefficient of the i-th sensor, Q is the target charge, and λ is the effective gain coefficient of the i-th sensor. ui and λ di b are the coupling correction coefficients for the probe ball electrode and the reference ball electrode, respectively. iThe background bias term is used. The equivalent gain coefficient, coupling correction coefficient, and background bias term are obtained through calibration experiments, finite element simulation, or a combination of both.

[0013] The three-parameter calculation unit converts the differential induced current acquired by each dual-sphere differential electrostatic sensor into a differential induced charge observation. For the i-th dual-sphere differential electrostatic sensor, let the upper sphere detection electrode current I... ui (t), the reference ball electrode current of the lower ball is I. di If (t), then the differential induced current of the sensor is:

[0014] I Δi (t)=I ui (t)-I di (t)

[0015] A variable-width sliding window electrostatic distortion-weighted nonlinear target detection algorithm is proposed, wherein the variable-width sliding window is an effective response time window [t] that can be adjusted by the sensor. a , t b The differential induced current is integrated within the time window. When the target speed is high and the response duration is short, the time window width automatically decreases; when the target speed is low or the response waveform is wide, the time window width automatically increases. Therefore, this variable-width sliding window can adaptively adjust the integration range according to the target's transient electrostatic distortion response; the electrostatic distortion weight is the weighting coefficient ω of the i-th sensor. i The threshold value can be determined based on channel noise, signal-to-noise ratio, calibration error, or effective response strength of the sensor. To reduce the impact of abnormal observation channels on the solution results, δ is defined as the electrostatic distortion threshold. When the error is small, it is treated as a squared error. When the error is too large, it is treated as a way to reduce the impact of abnormal residuals on the solution results of target position and charge.

[0016] The equations for the variable-width sliding window electrostatic distortion weighted nonlinear target detection algorithm are as follows, which can obtain the target position coordinates and target charge:

[0017]

[0018] in, The estimated coordinates of the target location. Here, N represents the estimated charge level of the target object, and N is the number of dual-sphere differential electrostatic sensors. Let be the background differential current of the i-th dual-sphere differential electrostatic sensor.

[0019] 4. Then, based on the target position coordinate estimation results at consecutive time points, the target velocity, direction of motion, and trajectory are obtained. To reduce the impact of single-time-time positioning errors on velocity calculation, the parameter calculation unit uses the aforementioned sliding window and trajectory fitting method for velocity calculation. Specifically, the parameter calculation unit selects the target position estimation results from the most recent M sampling times, i.e. And linear fitting was performed on the position changes over time in the x, y, and z directions respectively:

[0020]

[0021] Among them, a x a y a z For the fitting intercept, v x v y v z These represent the velocity components of the target in the x, y, and z directions, respectively. To further reduce the impact of outlier locations on the velocity calculation, the parameter calculation unit introduces location point weights in the trajectory fitting. For the x, y, and z directions, the robust weighted fitting relationship is as follows:

[0022]

[0023] Where M is the number of sampling points within the sliding window, ω m The fitting weights for the m-th location estimation point can be determined based on the positioning residual, signal amplitude, signal-to-noise ratio, or location estimation reliability at that moment. Location points with smaller positioning residuals and higher signal quality have larger weights; location points with larger positioning residuals or suspected anomalies have smaller weights.

[0024] After fitting, the parameter calculation unit calculates the target velocity magnitude based on the velocity components in three directions:

[0025]

[0026] The target's motion direction is calculated based on the velocity components. Compared with position difference velocity measurement between adjacent time points, sliding window trajectory fitting uses position estimation results from multiple consecutive time points to jointly determine the velocity, which can reduce the impact of single-frame positioning errors and transient noise on the velocity calculation results and improve the stability of velocity and trajectory estimation for charged small targets.

[0027] Compared with the prior art, the positive effects of the present invention are:

[0028] 1. This invention proposes a method for detecting and locating charged small targets based on a dual-sphere differential array. Using the mirror method as its physical basis, it introduces an equivalent gain coefficient, a coupling correction coefficient, and a background bias term to establish a calibration correction mirror model suitable for dual-sphere differential electrostatic sensor arrays. Furthermore, it employs a variable-width sliding window electrostatic distortion weighted nonlinear target detection algorithm and robust sliding window trajectory fitting to calculate the position, charge, velocity, and trajectory parameters of charged flying small targets, thereby improving the stability and anti-interference capability of the calculation.

[0029] 2. This invention enables passive, non-contact detection of small, charged flying targets without the need for the target to actively transmit signals or come into contact with the detection device.

[0030] 3. This invention uses an array of multiple dual-sphere differential electrostatic sensors to obtain multi-point differential electrostatic response information when a charged flying small target passes through the detection area, thus solving the problem that a single electrostatic sensor is difficult to obtain the target's spatial position and direction of motion. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a schematic diagram illustrating the principle of a method for detecting and locating small charged targets based on a dual-sphere differential array.

[0033] Figure 2 This is a flowchart of the objective parameter calculation process.

[0034] Figure 3 This is a schematic diagram of a dual-sphere differential electrostatic sensor.

[0035] Figure 4 This is a block diagram of the signal conditioning structure of a dual-sphere differential electrostatic sensor. Detailed Implementation

[0036] Embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. While some embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the invention. It should be understood that the accompanying drawings and embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the invention.

[0037] The technical solution of the present invention will be described in detail below with reference to specific embodiments. The specific embodiments below can be combined with each other, and for the same or similar concepts or processes, they will not be described again in some embodiments.

[0038] Example 1:

[0039] This disclosure provides a method for detecting and locating small charged targets based on a dual-sphere differential array, including:

[0040] See 1 Figure 1 When a charged small target passes above or near a dual-sphere differential electrostatic sensor array, the charge it carries or is equivalent to causes a change in the electrostatic field of the surrounding space. The distance between the dual-sphere differential electrostatic sensors and the small target varies at different locations, resulting in different differential induced charge responses from each sensor. The parameter calculation unit can determine the position and charge of the small target based on these differences. A system consisting of a dual-sphere differential electrostatic sensor array, a front-end signal conditioning unit, a synchronous acquisition unit, a data transmission unit, and a parameter calculation unit can be used. The dual-sphere differential electrostatic sensor array senses the change in the spatial electrostatic field caused by the charged small target; the front-end signal conditioning unit converts the weak induced current into an acquireable voltage signal; the synchronous acquisition unit synchronously acquires multi-channel differential electrostatic response signals; the data transmission unit transmits the acquired data to the parameter calculation unit; and the parameter calculation unit calculates the target's position, charge, and velocity parameters.

[0041] 2 See Figure 2 The target parameter calculation process first converts the differential electrostatic response signals of each channel into differential induced charge quantities. If the acquired quantity is differential induced current, the differential induced charge quantity can be obtained by integration:

[0042]

[0043] Where, q Δi (t) represents the differential induced charge of the i-th dual-sphere differential electrostatic sensor at time t, i Δi (τ) represents the differential induced current of the i-th dual-sphere differential electrostatic sensor, and t0 represents the integration start time.

[0044] 3. When calculating the target parameters, the flying small target is treated as a point charge, and the image method is used to establish the relationship between the induced charge of the spherical electrode and the target distance and target charge. For a single spherical electrode, when the target charge is Q, the radius of the spherical electrode is R, and the distance from the target to the center of the sphere is r, the induced charge of the spherical electrode can be expressed as:

[0045]

[0046] 4. For the i-th dual-sphere differential electrostatic sensor, the induced charges corresponding to the upper sphere detection electrode and the lower sphere reference electrode are respectively expressed as:

[0047]

[0048] Where, q ui Let q be the induced charge on the sphere detection electrode of the i-th dual-sphere differential electrostatic sensor. di Let r be the induced charge on the lower sphere reference electrode of the i-th dual-sphere differential electrostatic sensor. ui Let r be the distance from the target to the center of the sphere on the sensor. di The distance from the target to the center of the ball under the sensor.

[0049] 5. The differential induced charge of the i-th dual-sphere differential electrostatic sensor can be expressed as:

[0050]

[0051] 6. In the array coordinate system, let the position coordinates of the charged flying target at a certain moment be (x, y, z). Let the position of the center of the upper sphere of the i-th dual-sphere differential electrostatic sensor be (x, y, z). i y i , z i The detection ball electrode and the reference ball electrode are arranged vertically or towards the target channel, and the distance between the centers of the two balls is h. Then the coordinates of the center of the detection ball electrode of the i-th dual-sphere differential electrostatic sensor are:

[0052]

[0053]

[0054] 7. When calculating the target parameters, the single-sphere mirror method is used to establish the basic relationship between the induced charge of the spherical electrode and the target distance and target charge. Based on this, an equivalent gain coefficient, coupling correction coefficient, and background bias term are introduced to establish a calibration correction mirror model suitable for the actual dual-sphere differential electrostatic sensor structure. For the i-th dual-sphere differential electrostatic sensor, its theoretical differential induced charge can be expressed as:

[0055]

[0056] The theoretical differential induced charge is determined by the target position coordinates, the target charge, the sensor spatial coordinates, and calibration parameters. Let K be the theoretical differential induced charge of the i-th sensor. i λ is the equivalent gain coefficient of the i-th sensor, Q is the target charge, and λ is the effective gain coefficient of the i-th sensor. ui and λ di b are the coupling correction coefficients for the probe ball electrode and the reference ball electrode, respectively.i This is the background bias term. The equivalent gain coefficient, coupling correction coefficient, and background bias term mentioned above can be obtained through standard charged body calibration tests, finite element simulation, or a combination of both.

[0057] The 8-parameter calculation unit converts the differential induced current acquired by each dual-sphere differential electrostatic sensor into a differential induced charge observation. For the i-th dual-sphere differential electrostatic sensor, let the upper sphere detection electrode current I... ui (t), the reference ball electrode current of the lower ball is I. di If (t), then the differential induced current of the sensor is:

[0058] I Δi (t)=I ui (t)-I di (t)

[0059] A variable-width sliding window electrostatic distortion-weighted nonlinear target detection algorithm is proposed, wherein the variable-width sliding window is an effective response time window [t] that can be adjusted by the sensor. a , t b The differential induced current is integrated within the time window. When the target speed is high and the response duration is short, the time window width automatically decreases; when the target speed is slow or the response waveform is wide, the time window width automatically increases. This variable-width sliding window can adaptively adjust the integration range according to the target's transient electrostatic distortion response; the electrostatic distortion weight is the weighting coefficient ω of the i-th sensor. i The threshold value can be determined based on channel noise, signal-to-noise ratio, calibration error, or effective response strength of the sensor. To reduce the impact of abnormal observation channels on the solution results, δ is defined as the electrostatic distortion threshold. When the error is small, it is treated as a squared error. When the error is too large, it is treated as a way to reduce the impact of abnormal residuals on the solution results of target position and charge.

[0060] The equations for the variable-width sliding window electrostatic distortion weighted nonlinear target detection algorithm are as follows, which can obtain the target position coordinates and target charge:

[0061]

[0062] in, The estimated coordinates of the target location. Here, N represents the estimated charge level of the target object, and N is the number of dual-sphere differential electrostatic sensors. Let be the background differential current of the i-th dual-sphere differential electrostatic sensor.

[0063] 9. During continuous detection, the parameter calculation unit obtains the target velocity and trajectory based on the target position coordinate estimation results at multiple consecutive time points. To reduce the impact of single-time-time positioning errors on velocity calculation, the parameter calculation unit employs a robust sliding window trajectory fitting method for velocity calculation. Specifically, the parameter calculation unit selects the target position estimation results from the most recent M sampling times and performs linear fitting on the relationship between the position and time changes in the x, y, and z directions respectively:

[0064]

[0065] Among them, a x a y a z For the fitting intercept, v x v y v z These are the velocity components of the target in the x, y, and z directions, respectively.

[0066] To further reduce the impact of outlier locations on velocity calculation, the parameter calculation unit introduces location point weights in the sliding window trajectory fitting. For the x, y, and z directions, the robust weighted fitting relationship is as follows:

[0067]

[0068] Where M is the number of sampling points within the sliding window, ω m The fitting weights for the m-th location estimation point can be determined based on the positioning residual, signal amplitude, signal-to-noise ratio, or location estimation reliability at that moment. Location points with smaller positioning residuals and higher signal quality have larger weights; location points with larger positioning residuals or suspected anomalies have smaller weights.

[0069] After fitting, the parameter calculation unit calculates the target velocity magnitude based on the velocity components in three directions:

[0070]

[0071] The target's motion direction and trajectory are obtained based on the velocity components. Compared with position difference velocity measurement between two adjacent time points, robust sliding window trajectory fitting uses position estimation results from multiple consecutive time points to jointly determine the target velocity, which can reduce the impact of single-frame positioning error, transient noise, and abnormal position points on the velocity calculation results, and improve the stability of velocity and trajectory estimation for charged small targets.

[0072] See 10 Figure 3A dual-sphere differential electrostatic sensor can be used, each consisting of an upper sphere detection electrode, a middle grounding shield, a lower sphere reference electrode, an insulating isolator, and a support. Both the upper and lower sphere detection electrodes are made of conductive metal spheres or surface-conductive spheres, and are coaxially arranged vertically. The middle grounding shield is positioned between the upper and lower sphere detection electrodes and connected to the system ground. The upper sphere detection electrode is primarily used to sense near-field electrostatic disturbances caused by small flying targets, while the lower sphere reference electrode is primarily used to sense environmental background disturbances similar to those of the upper sphere detection electrode. By differentially dividing the output signals of the upper and lower sphere reference electrodes, the influence of common-mode environmental disturbances on the detection results can be reduced, and the spatial non-uniform electrostatic response caused by the target can be highlighted. The middle grounding shield is a conductive plate, preferably a circular metal plate. The middle grounding shield is connected to the system ground to limit direct electric field coupling between the upper and lower sphere detection electrodes, allowing them to form relatively independent sensing regions. An insulating component, made of polytetrafluoroethylene (PTFE), is positioned between the upper sphere detection electrode, the intermediate grounding shield, and the lower sphere reference electrode. A support component is used to fix the relative positions of the upper sphere detection electrode, the intermediate grounding shield, and the lower sphere reference electrode, and to maintain insulation between the dual-sphere differential electrostatic sensor and the external mounting bracket.

[0073] 11 See Figure 4 The front-end signal conditioning unit consists of an upper sphere I / V conversion channel, a lower sphere I / V conversion channel, a differential amplifier circuit, and a filter circuit. The upper sphere current-voltage conversion channel receives the weak induced current output from the upper sphere detection electrode and converts it into an upper sphere voltage signal; the lower sphere current-voltage conversion channel receives the weak induced current output from the lower sphere reference electrode and converts it into a lower sphere voltage signal; the differential amplifier circuit subtracts and amplifies the upper and lower sphere voltage signals to obtain a differential electrostatic response signal; the filter circuit suppresses low-frequency drift and high-frequency noise; the synchronous acquisition unit synchronously samples the differential electrostatic response signals output by each dual-sphere differential electrostatic sensor, ensuring that different sensor channels have a synchronous sampling frequency and a unified time reference. The data transmission unit can use wired or wireless transmission to transmit the synchronous acquisition results to the parameter calculation unit.

[0074] The number of dual-sphere differential electrostatic sensors, array spacing, sphere electrode radius, upper and lower sphere spacing, intermediate grounding shield size, and front-end signal conditioning circuit parameters in this method can be adjusted according to the actual detection distance, detection area size, and sensitivity requirements. Increasing the number of dual-sphere differential electrostatic sensors in the array can improve observation redundancy and parameter calculation stability; increasing the array deployment range can accommodate a larger detection area.

[0075] 13 This method can be used to acquire multi-channel transient differential electrostatic response signals caused by the target when a charged flying small target passes through the detection area. After processing by the front-end signal conditioning unit, synchronous acquisition unit and parameter calculation unit, parameters such as target position, target charge, velocity, incident direction and motion trajectory are obtained, thereby realizing non-contact, passive detection and positioning of charged flying small targets.

Claims

1. A method for detecting and locating charged small targets based on a dual-sphere differential array, characterized in that, The basic principle is that a small flying target carries an electric charge or an equivalent charge during its motion. When it passes near a dual-sphere differential electrostatic sensor array, it causes a rapid change in the spatial electrostatic field, resulting in different induced charge changes on the upper detection electrode and the lower reference electrode in each dual-sphere differential electrostatic sensor. The upper detection electrode mainly picks up the near-field electrostatic response caused by the target, while the lower reference electrode mainly picks up common-mode disturbances in the environment near the upper detection electrode. The intermediate grounding shield is used to weaken the direct electric field coupling between the upper and lower electrodes and provide a grounding reference. The parameter calculation unit calculates the induced charge q of the upper detection electrode. u and the induced charge q of the lower spherical reference electrode d By performing a differential equation and using the mirror method, the relationship between the induced charge, the target distance, and the target charge is established. The relationship is as follows: Where, q u For the induced charge on the upper sphere, q d For the induced charge on the lower sphere, q Δ R is the differential induced charge, R is the radius of the spherical electrode, and r is the differential induced charge. u r is the distance from the center of the ball to the target. d Let Q be the distance from the center of the ball to the target, and let Q be the charge on the target.

2. A method for detecting and locating charged small targets based on a dual-sphere differential array, characterized in that, The dual-sphere differential electrostatic sensor array can be arranged in a square, rectangular, ring, or polygonal structure around the detection area. The parameter calculation unit integrates the differential electrostatic response signal to obtain the differential induced charge corresponding to each dual-sphere differential electrostatic sensor. The target is equivalent to a point charge. Let the target position coordinates be (x, y, z), and the center coordinates of the i-th dual-sphere differential electrostatic sensor be (x, y, z). i y i , z i If the distance between the centers of the upper detection electrode and the lower reference electrode is h, then the theoretical differential induced charge of the i-th sensor is: in, Let K be the theoretical differential induced charge of the i-th sensor. i λ is the equivalent gain coefficient of the i-th sensor, Q is the target charge, and λ is the effective gain coefficient of the i-th sensor. ui and λ di b represents the coupling correction coefficients for the upper probe sphere electrode and the lower reference sphere electrode, respectively. i The background bias term is obtained through calibration experiments, finite element simulation, or a combination of both.

3. A method for detecting and locating small charged targets based on a dual-sphere differential array, characterized in that, The parameter calculation unit number converts the differential induced current collected by each dual-sphere differential electrostatic sensor into a differential induced charge observation. For the i-th dual-sphere differential electrostatic sensor, let the upper sphere detection electrode current I... ui (t), the reference ball electrode current of the lower ball is I. di If (t), then the differential induced current of the sensor is: I Δi (t)=I ui (t)-I di (t) A variable-width sliding window electrostatic distortion weighted nonlinear target detection algorithm is proposed, wherein the variable-width sliding window is an effective response time window [t] that can be adjusted by the sensor. a , t b The differential induced current is integrated within the time window. When the target speed is high and the response duration is short, the time window width automatically decreases; when the target speed is low or the response waveform is wide, the time window width automatically increases. This variable-width sliding window can adaptively adjust the integration range according to the target's transient electrostatic distortion response. The electrostatic distortion weight is the weighting coefficient ω of the i-th sensor. i The value can be determined based on channel noise, signal-to-noise ratio, calibration error, or effective response strength of the sensor. To reduce the impact of abnormal observation channels on the solution results, δ is defined as the electrostatic distortion threshold. When the error is small, it is treated as a square error. When the error is too large, it is treated as a way to reduce the impact of abnormal residuals on the solution results of target position and charge. The equations for the variable-width sliding window electrostatic distortion weighted nonlinear target detection algorithm are as follows, which can obtain the target position coordinates and target charge: in, The estimated coordinates of the target location. Here, N represents the estimated charge level of the target object, and N is the number of dual-sphere differential electrostatic sensors. Let be the background differential current of the i-th dual-sphere differential electrostatic sensor.

4. A method for detecting and locating charged small targets based on a dual-sphere differential array, characterized in that, The parameter calculation unit uses the aforementioned sliding window and trajectory fitting method to calculate velocity; specifically, the parameter calculation unit selects the target position estimation results from the most recent M sampling times and performs linear fitting on the position changes over time in the x, y, and z directions respectively: Among them, a x a y a z For the fitting intercept, v x v y v z These represent the velocity components of the target in the x, y, and z directions, respectively. To further reduce the impact of outlier locations on the velocity calculation, the parameter calculation unit introduces location point weights in the sliding window trajectory fitting. For the x, y, and z directions, the robust weighted fitting relationship is as follows: Where M is the number of sampling points within the sliding window, ω m The fitting weights for the m-th location estimation point can be determined based on the positioning residual, signal amplitude, signal-to-noise ratio, or location estimation reliability at that moment. Location points with smaller positioning residuals and higher signal quality have larger weights; location points with larger positioning residuals or suspected anomalies have smaller weights. After fitting, the parameter calculation unit calculates the target velocity magnitude based on the velocity components in three directions: It can also calculate the target's direction of motion based on the velocity components.

5. A method for detecting and locating small charged targets based on a dual-sphere differential array, characterized in that, It consists of a dual-sphere differential electrostatic sensor array, a front-end signal conditioning unit, a synchronous acquisition unit, a data transmission unit, and a parameter calculation unit. The dual-sphere differential electrostatic sensor array comprises at least four dual-sphere differential electrostatic sensors. Each dual-sphere differential electrostatic sensor consists of a detection sphere electrode, an intermediate grounding shield, a reference sphere electrode, an insulating isolator, and a support. The upper detection electrode and the lower reference electrode are both conductive metal spheres or surface conductive spheres, and they are coaxially arranged vertically. The intermediate grounding shield is a conductive plate disposed between the upper detection electrode and the lower reference electrode, connected to the system ground, and used to limit the electrical current in the vertical space. Field coupling is achieved by placing an insulating isolator between the upper spherical detection electrode, the intermediate grounding shield, and the lower spherical reference electrode. The insulating isolator is made of polytetrafluoroethylene (PTFE). The support is used to fix the relative positions of the detection spherical electrode, the intermediate grounding shield, and the reference spherical electrode. The front-end signal conditioning unit and the power supply unit are located inside the circuit box. The detection spherical electrode is positioned facing the area where the charged flying small target passes, and the reference spherical electrode is positioned on the side facing away from the target passage area. The detection spherical electrode and the reference spherical electrode are respectively connected to the front-end signal conditioning unit, and after current-voltage conversion and differential processing, a transient differential electrostatic response signal is formed. The synchronous acquisition unit synchronously acquires the transient differential electrostatic response signals of each channel, and the data transmission unit sends the acquisition results to the parameter calculation unit. The parameter calculation unit obtains the position, charge, velocity, and direction of motion parameters of the charged flying small target based on the differential electrostatic response signals of each channel.

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