An analysis method for tracking and positioning accuracy of an air target by a reconnaissance and early warning system

Abstract

The present application relates to the field of early warning detection, in particular to a kind of analysis method for reconnaissance early warning system air target tracking positioning precision.First, reconnaissance early warning system modeling is carried out, the operating rules of analysis reconnaissance early warning system component unit and each unit, information transmission relationship;Second, according to the given air target type, electromagnetic scattering characteristics, infrared radiation characteristics, motion characteristics and other parameters, analysis early warning system has early warning detection capability unit, respectively calculate each early warning unit air target detection range;Third, for the given air target, calculate whether each point in track point set is in early warning unit detection range, calculate the detection tracking position and tracking positioning precision of each early warning unit to air target track;Finally, according to sensor type, tracking positioning precision fusion is carried out respectively, and the tracking positioning precision of early warning system to this air target is obtained.The present application can more accurately determine the threat degree of early warning system to air target.

Description

Technical Field

[0001] This invention relates to the field of early warning detection, and more specifically to a method for analyzing the accuracy of tracking and locating aerial targets in a reconnaissance and early warning system. Background Technology

[0002] The primary operational mission of reconnaissance and early warning systems is to detect targets such as strategic ballistic missiles, cruise missiles, and medium-to-high-altitude, low-altitude penetrating, as well as stealth aircraft, providing air situation information for command and control systems and weapon systems. Data fusion from multi-sensor networking in early warning systems can improve the accuracy of aerial target location, providing combat units with more reliable target information and designations. Currently, research on the tracking and location accuracy of aerial targets in reconnaissance and early warning systems is limited, and analyses relying solely on the professional skills of staff officers are subjective. This study models the reconnaissance and early warning units and the early warning center within the system, analyzes the early warning units capable of detecting given aerial targets, and fuses the networked data from these units to obtain the tracking and location accuracy of the early warning system for aerial targets, providing support for combat operations. Summary of the Invention

[0003] In response to the problems and shortcomings mentioned in the background art, this invention proposes an automated analysis method for the tracking and positioning accuracy of aerial targets in a reconnaissance and early warning system.

[0004] The problem to be solved by this invention is achieved through the following technical solution:

[0005] A method for analyzing the tracking and positioning accuracy of aerial targets in a reconnaissance and early warning system includes the following steps:

[0006] (1) Modeling of the reconnaissance and early warning system: Analyze the constituent units of the reconnaissance and early warning system, including the reconnaissance and early warning unit and the early warning center, and establish the operating rules and information transmission relationships between the units of the reconnaissance and early warning system;

[0007] (2) Analysis of the detection range of the early warning unit: Based on the given parameters of the type of air target, electromagnetic scattering characteristics, infrared radiation characteristics and motion characteristics, the reconnaissance and early warning units that can detect air targets are obtained from the reconnaissance and early warning system, and the detection range of each reconnaissance and early warning unit for air targets is calculated respectively.

[0008] (3) Analysis of the detection and tracking position of the reconnaissance and early warning unit on the aerial target: For a given aerial target, calculate whether each point in the track point set is within the detection range of the reconnaissance and early warning unit, obtain the detection and tracking position of each reconnaissance and early warning unit on the aerial target track, and record the tracking and positioning accuracy of each position.

[0009] (4) Tracking and positioning accuracy fusion of the early warning system: For the units in the reconnaissance and early warning system that have the ability to detect and warn of a given air target, the tracking and positioning accuracy is fused according to the sensor type to obtain the tracking and positioning accuracy of the reconnaissance and early warning system for the air target.

[0010] Furthermore, in step (1), the reconnaissance and early warning unit includes a space-based infrared early warning satellite, a long-range early warning radar, an air surveillance and search radar, and an air and sea search radar; the operational rules of the reconnaissance and early warning system include the command and coordination relationships between the various units of the system; the information transmission relationship is that each reconnaissance and early warning unit generates early warning information and sends it to its respective early warning center, and the early warning centers interact with each other to achieve data sharing.

[0011] Furthermore, in step (2), the types of air targets include ballistic missiles, cruise missiles, and combat aircraft. Among them, the space-based infrared early warning satellite and the long-range early warning radar conduct early warning detection of ballistic missiles, while the long-range early warning radar, air surveillance and search radar, and air and sea search radar conduct early warning detection of cruise missiles and combat aircraft. The detection range of the space-based infrared early warning satellite is calculated based on the light-transmitting aperture, peak wavelength, corresponding detectivity, signal process factor, number of detector elements, instantaneous field of view parameters of a single detector element, and the infrared radiation characteristics of the ballistic missile's tail flame. The radar detection range is calculated based on the radar's transmit power, antenna gain, signal wavelength, minimum detectable signal power performance parameters, and the electromagnetic scattering characteristics of air targets.

[0012] Furthermore, step (3) specifically involves:

[0013] The determination of ballistic missiles includes using the exhaust plume detection range, telescope axis angle, and field of view to determine whether they are within the detection range of space-based infrared early warning satellites; using the radar detection range, elevation angle, and azimuth angle constrained by the Earth's curvature to determine whether they are within the detection range of long-range early warning radars; using the radar detection range, elevation angle, and azimuth angle constrained by the Earth's curvature to determine whether cruise missiles and combat aircraft are within the detection range of long-range early warning radars, air surveillance and search radars, and air and sea search radars; and determining the detection and tracking positions of each reconnaissance and early warning unit for a given aerial target and trajectory, and recording the tracking and positioning accuracy of each position.

[0014] Furthermore, the specific process of step (4) is as follows:

[0015] When multiple space-based infrared early warning satellites detect ballistic missiles simultaneously, the positioning accuracy of the satellite with the highest positioning accuracy is selected as the final positioning accuracy.

[0016] Long-range early warning radar, air surveillance and search radar, and air and sea search radar fuse their positioning accuracy against aerial targets, including ballistic missiles, cruise missiles, and combat aircraft.

[0017] (401) Based on the flight path, obtain the current position coordinates of the detected aerial target, extract all radars that can detect aerial targets, and select the information of the two radars with the highest measurement accuracy;

[0018] (402) Construct the K matrix according to the following formula:

[0019]

[0020] In the formula, These are the azimuth, elevation, and range measurement accuracy of the two radars, respectively.

[0021] (403) Transform the positions of the detected aerial target and the second radar from the ground-fixed system to a measurement system centered on the position of the first radar, and construct the P matrix according to the following formula:

[0022]

[0023] In the formula, the parameters in the matrix correspond to the calculated parameters of the detected aerial target relative to the two radars, and the calculation methods for each parameter are as follows:

[0024]

[0025]

[0026] Let i = 1, then we can calculate:

[0027]

[0028] a12 = 0

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] Let i = 2, then we can calculate:

[0037]

[0038] b12 = 0

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] In the formula, x1, y1, z1 are the coordinates of the first radar in the Cartesian coordinate system of the first radar site, i.e., 0, 0, 0; x2, y2, z2 are the coordinates of the second radar in the Cartesian coordinate system of the first radar site; x t ,y t ,z t The coordinates of the detected aerial target in the Cartesian coordinate system of the first radar station site;

[0047] (404) Calculate the position error covariance matrix C of the detected air target in the rectangular coordinate system of the first radar station after data fusion from the two radars, according to the following formula:

[0048] C = (P T K -1 P) -1 ;

[0049] (405) According to the following formula, the position error covariance matrix C is transformed into the Earth-Fixed System to obtain C′:

[0050] C'=FCF T

[0051] In the formula, F is the rotation matrix from the radar site measurement system to the ground-fixed system;

[0052] (406) Calculate the overall positioning accuracy σ of the radar for the detected aerial target according to the following formula:

[0053]

[0054] Compared with the prior art, the present invention has the following advantages:

[0055] 1. Systematic Approach: Compared with previous approaches that focused on early warning of individual early warning units for aerial targets, this approach considers multiple units with early warning capabilities for aerial targets, such as space-based infrared early warning satellites, long-range early warning radars, air surveillance and search radars, and air and sea search radars. Based on the basic capabilities of the early warning units and their mutual command and coordination relationships, a systematic analysis is conducted.

[0056] 2. Fusion: By fusing the tracking and positioning accuracy of the same type of sensors for the same aerial target, the threat level of the early warning system to the aerial target can be determined more accurately. Attached Figure Description

[0057] Figure 1 This is a flowchart of a method for analyzing the tracking and positioning accuracy of an aerial target in a reconnaissance and early warning system according to the present invention.

[0058] Figure 2 This is a schematic diagram of the DSP satellite scanning area for an analysis method of the tracking and positioning accuracy of an aerial target in a reconnaissance and early warning system according to the present invention.

[0059] Figure 3 This is a schematic diagram of the radar detection range of a reconnaissance and early warning system for analyzing the accuracy of tracking and locating aerial targets, as described in this invention. Detailed Implementation

[0060] As attached Figure 1 As shown, the reconnaissance and early warning system is first modeled to determine its constituent units and their operational rules and information transmission relationships. Secondly, parameters such as the type of aerial target, electromagnetic scattering characteristics, infrared radiation characteristics, and motion characteristics are acquired. Thirdly, based on the type of aerial target and the detection capabilities of each unit in the early warning system, the reconnaissance and early warning units within the system are traversed, and the tracking and positioning accuracy of each unit for aerial targets is recorded. Finally, the tracking and positioning accuracy of each reconnaissance and early warning unit is fused according to sensor type to obtain the tracking and positioning accuracy of the early warning system for a given aerial target.

[0061] The working principle diagram of this invention is as follows: Figure 1 As shown, the present invention provides a method for analyzing the tracking and positioning accuracy of an aerial target in a reconnaissance and early warning system, comprising the following steps:

[0062] (1) Modeling of reconnaissance and early warning system: Analyze the composition of the reconnaissance and early warning system, establish the operational rules and information transmission relationships of each unit of the reconnaissance and early warning system, and obtain the topology of the reconnaissance and early warning system;

[0063] In this embodiment, the reconnaissance and early warning system modeling is divided into three parts, based on specific business scenarios: acquiring the constituent units of the reconnaissance and early warning system, establishing the operational rules and relationships of the reconnaissance and early warning system, and establishing the information transmission relationships of the reconnaissance and early warning system. The reconnaissance and early warning system generally consists of reconnaissance and early warning units and an early warning center. The reconnaissance and early warning units typically perform early warning detection tasks. When a reconnaissance and early warning unit detects and identifies a target, it sends relevant alarm information and target detection data to the early warning center. The early warning center is responsible for fusing the received target detection data to obtain more accurate target location information, determining the nature of the target, and disseminating target information to command organizations and / or combat units at all levels. The operational rules and relationships of the reconnaissance and early warning system describe the relationships between the constituent units within the system. Common relationships include command relationships and coordination relationships. Command relationships generally refer to the relationship between the early warning center and its subordinate reconnaissance and early warning units. Typically, one early warning center has multiple subordinate reconnaissance and early warning units, such as a space-based strategic early warning center with multiple space-based infrared early warning satellites. Collaborative relationships generally exist between reconnaissance and early warning units under the same command structure, as they share the same or similar reconnaissance and early warning tasks. In information transmission relationships, data is generated by each reconnaissance and early warning unit and sent to its respective early warning center. Data exchanges occur between the early warning centers to achieve data sharing.

[0064] (2) Calculation of the detection range of the early warning unit: Based on the given parameters of the type of air target, electromagnetic scattering characteristics, infrared radiation characteristics and motion characteristics, obtain the reconnaissance and early warning units that can detect air targets from the reconnaissance and early warning system, and calculate the detection range of each reconnaissance and early warning unit for air targets.

[0065] In the embodiments, for the early warning detection of ballistic missiles, two types of early warning units are considered: space-based infrared early warning satellites and long-range early warning radars; for the early warning detection of cruise missiles and combat aircraft, three types of early warning units are considered: long-range early warning radars, air surveillance and search radars, and air and sea search radars.

[0066] 1) Infrared early warning satellite

[0067] Infrared early warning satellites are primarily used to identify missile launch events, provide early warnings of missile attacks, and conduct initial tracking of missile targets.

[0068] Infrared early warning satellites use scanning infrared detectors to scan the area under their responsibility. After scanning the same target (missile's active phase plume) multiple times, they identify the target type based on the acquired target position change information. Once the target type is confirmed to be a missile plume, an early warning message is issued. They also use staring detectors to perform coarse tracking of the target and send target tracking information.

[0069] a) Scope of action

[0070] The formula for calculating the effective range of space-based infrared detection is as follows:

[0071]

[0072] In the above formula,

[0073] SNR is the signal-to-noise ratio detected by the infrared detector.

[0074] I represents the spectral radiance of the target, in W / sr / cm⁻², taken as 1.0 × 10⁵ for the active phase plume and 75 for the midcourse warhead.

[0075] τ a This represents the atmospheric infrared spectral transmittance, with a default value of 0.6.

[0076] τ0 is the spectral transmittance of the optical system.

[0077] D0 is the diameter of the optical system's aperture, in meters (m).

[0078] N a The numerical aperture of the optical system is the diameter, in meters (m).

[0079] D * The detectivity is the value corresponding to the peak wavelength, expressed in cmHz¹ / ²W⁻¹.

[0080] δ is the signal process factor.

[0081] R is the distance from the target to the sensor, in meters (m).

[0082] n is the number of detector elements.

[0083] η sc For the efficiency of the optical system,

[0084] Ω represents the instantaneous field of view angle of a single probe element, in mrad.

[0085] F represents the detection frame rate.

[0086] b) Angle between the line of sight and the satellite's rotation axis

[0087] The DSP satellite employs spin stabilization, rotating at approximately six revolutions per minute around its Earth-facing main axis to maintain correct orientation. The telescope's axis forms a 7.5° angle with the satellite's main axis, creating a conical scanning area as the satellite spins. This area is used by the Schmidt telescope to collect infrared radiation for missile launch monitoring. An infrared scanning detector, mounted on the Earth-facing end, continuously scans to determine the location and direction of movement of infrared radiation sources. A schematic diagram of the DSP scanning area is shown below. Figure 2 As shown.

[0088] 2) Radar detection

[0089] The detection range of a single radar is typically described by its center pointing direction, the angular range it covers, the altitude range it covers, and its effective range, such as... Figure 3 As shown.

[0090] a) The impact of target RCS on effective range

[0091] According to the maximum effective range formula of the radar equation, we have

[0092]

[0093] In the above formula,

[0094] P t For radar transmission power,

[0095] σ is the radar cross section of the target.

[0096] A r The effective receiving area of ​​the radar receiving antenna.

[0097] λ is the radar wavelength.

[0098] S imin For the minimum detectable signal power,

[0099] G represents the radar antenna gain.

[0100] When calculating the RCS of different types of targets and the nominal range of a radar for a specific RCS target, the radar's transmit power, antenna gain, signal wavelength, minimum detectable signal power, and other performance parameters can be assumed to remain constant. By eliminating identical terms, a fast formula for calculating the radar's range is obtained as follows:

[0101]

[0102] In the above formula,

[0103] R std The nominal effective range of the radar is expressed in kilometers.

[0104] σ std The nominal target RCS is the radar's nominal effective range, in square meters.

[0105] σ represents the actual target's RCS (radius cross-section), in square meters.

[0106] R1 represents the radar's effective range against the actual target, in kilometers.

[0107] b) The effect of Earth's curvature on the effective distance

[0108] Due to the curvature of the Earth, radar detection effectiveness is constrained by the following formula:

[0109]

[0110] In the above formula,

[0111] H a The altitude of the antenna is in meters.

[0112] H t The altitude of the target, in meters;

[0113] R2 represents the radar's effective range, measured in kilometers.

[0114] Finally, the effective range R for a certain type of target is calculated using the following formula:

[0115] R = min{R1, R2}

[0116] (3) Analysis of the tracking and positioning accuracy of the early warning unit for aerial targets:

[0117] For a given aerial target, determine whether each position in its trajectory is within the detection range of the early warning unit, and obtain the detection and tracking position of the early warning unit on the target's trajectory. Calculate the detection and tracking position of each early warning unit for this aerial target, and record the tracking and positioning accuracy of each position.

[0118] In this embodiment, the detection and tracking positions of airborne targets by space-based infrared early warning satellites and radars are calculated according to the sensor type.

[0119] When the early warning unit is a space-based infrared early warning satellite, based on a given set of airborne target track points, the relative distance and relative angle from each point to the space-based infrared early warning satellite are calculated, starting from the starting point. If the relative distance is less than the detection range of the space-based infrared early warning satellite for the exhaust plume of the airborne target, and the relative angle is less than half of the field of view angle between the relative distance and the satellite telescope axis, it means that the missile can be detected by the satellite at that point.

[0120] When the early warning unit is a radar, the criteria for determining whether the radar has detected an aerial target at a certain trackpoint are: whether the distance between the trackpoint and the radar is within the radar's corrected detection range; whether the azimuth angle of the trackpoint relative to the radar is within the radar's azimuth coverage; and whether the elevation angle of the trackpoint relative to the radar is within the radar's elevation coverage. Therefore, it is necessary to convert the ground-to-fixed coordinates of the trackpoint to the station spherical coordinates of the radar position. The specific process is as follows: first, convert the ground-to-fixed coordinates of the trackpoint to the rectangular coordinate system for radar array position measurement.

[0121]

[0122] In the formula,

[0123] Measure the position of the track point in the rectangular coordinate system at the i-th radar array position;

[0124] The coordinates of the track point in the ground-fixed system;

[0125] Let i be the ground-fixed coordinates of the i-th radar array position;

[0126] F T This is the transpose of the transformation matrix from the station's rectangular coordinate system to the Earth-Fixed Coordinate System, where,

[0127] F = R z (90-L)*R x (-B)*R y (90+A)

[0128] In the formula,

[0129] L represents the longitude of the radar array position, in degrees;

[0130] B represents the radar array position latitude, in degrees;

[0131] A is the initial azimuth angle of the radar array position. Usually, the due north direction is taken as the 0-degree direction, that is, A = 0.

[0132] R z R x R y These are rotation matrices about the Z, X, and Y axes, respectively.

[0133] After obtaining the position of the track point relative to the radar array position measurement in rectangular coordinate system, it can be converted into radar array position spherical coordinate system coordinates according to the following formula, namely azimuth (A), elevation (E), and range (R).

[0134]

[0135] After obtaining the spherical coordinates of the track point relative to the radar array position, it can be compared with the radar's basic parameters to determine whether the aerial target at the track point is within the radar's detection range. Let the radar's detection range-related parameter be the detection distance R. tc Direction A zx Pitch pointing to E zx Aspect Coverage A fg Pitch Coverage E fg Therefore, the basis for the judgment is as follows:

[0136] 1) R≤R tc

[0137] 2) or or

[0138] 3) or

[0139] The reason why it's necessary to consider adding and subtracting 360 degrees when determining the azimuth is mainly because when the radar azimuth is close to true north, and the coverage area after adding or subtracting half the azimuth crosses true north, it will lead to... or

[0140] Determining the elevation angle requires analysis based on the radar's location. For land-based or sea-based radars, since the radar is looking "up," the elevation angle is determined using... The expression is used for judgment; for airborne radar, since the radar mainly looks "down", it is necessary to use... The expression continues to be evaluated.

[0141] (4) Fusion of tracking and positioning accuracy of early warning system: According to the sensor type, the tracking and positioning accuracy of each early warning unit in the system is fused to obtain the tracking and positioning accuracy of the reconnaissance and early warning system for a given air target.

[0142] 1. Fusion of positioning accuracy of space-based infrared early warning satellites

[0143] In this embodiment, since space-based infrared early warning satellites are generally only used for early warning of ballistic missiles and initial position tracking, their objective is to guide land-based long-range early warning radars to quickly detect and track targets, and more complex tracking data fusion is usually not required. Therefore, when multiple space-based infrared early warning satellites detect a target simultaneously, the positioning accuracy of the satellite with the highest positioning accuracy is selected as the final positioning accuracy.

[0144] 2. Fusion of the positioning accuracy of long-range early warning radar, air surveillance and search radar, and air and sea search radar for aerial targets (ballistic missiles, cruise missiles, and combat aircraft).

[0145] In this embodiment, it is assumed that each radar has the capability to locate the incoming target. The positioning accuracy of each radar for aerial targets (ballistic missiles, cruise missiles, and combat aircraft) is represented by distance measurement accuracy and angle measurement accuracy.

[0146] The radar's accuracy in locating aerial targets is calculated using a positional accuracy calculation model similar to that of the 2RAE external measurement system. The basic idea is as follows:

[0147] (a) Calculation of positioning accuracy of a single radar

[0148] When only a single radar can detect aerial targets, the process for calculating the positioning accuracy of aerial targets is as follows:

[0149] 1) Obtain the radar angle measurement accuracy σ jd and distance measurement accuracy σ jl =σr Assuming the azimuth / elevation angle measurement accuracy is consistent, i.e., σ a =σ e =σ jd And construct the K matrix according to the following formula;

[0150]

[0151] 2) Transform the target's position from the ground-based system to a measurement system centered on the radar position, and calculate the target's azimuth A, elevation E, and slant range r relative to the radar; and construct the P matrix according to the following formula;

[0152]

[0153] 3) Calculate the covariance matrix C of the positioning error according to the following formula;

[0154] C = PKP T

[0155] 4) According to the following formula, transform the positioning error covariance matrix to the Earth-Fixed system;

[0156] C'=FCF T

[0157] In the formula,

[0158] F is the rotation matrix from the radar site measurement system to the ground-fixed system.

[0159] 5) Calculate the overall positioning accuracy σ of the radar for the object at this location according to the following formula.

[0160]

[0161] (b) Calculation of positioning accuracy when multiple radars measure simultaneously

[0162] In this embodiment, it is assumed that all radars have the capability to measure the range and angle of the target. When multiple radars detect the target simultaneously, the two radars with the highest measurement accuracy can be selected. The specific determination method is as follows:

[0163]

[0164] In the formula,

[0165] Let be the square of the azimuth measurement error of the radar for the i-th detectable object;

[0166] Let be the square of the elevation angle measurement error of the radar for the i-th detectable object;

[0167] Let be the square of the range measurement error of the radar for the i-th detectable object;

[0168] The calculation is performed on the two radars with the smallest parameters among all radars capable of detecting objects.

[0169] The calculation process for the combined positional accuracy of dual radars measuring aerial targets is as follows:

[0170] 1) Based on the flight path, obtain the current position coordinates of the detected aerial target, extract all radars that can detect the aerial target, and select the information of the two radars with the highest measurement accuracy.

[0171] 2) Construct the K matrix according to the following formula;

[0172]

[0173] In the formula, These are the azimuth, elevation, and range measurement accuracy of the two radars, respectively.

[0174] 3) The positions of the detected aerial targets and the second radar are converted from the ground-fixed system to the measurement system centered on the position of the first radar, and the P matrix is ​​constructed according to the following formula;

[0175]

[0176] In the formula,

[0177] 'a' and 'b' correspond to the calculated parameters of the detected aerial target relative to the two radars, respectively. The calculation methods for parameters with corresponding numbers are consistent. For example, the calculation method for 'b11' is the same as that for 'a11'. The difference lies in the parameter used when calculating 'a11': the position of the detected aerial target relative to the first radar station in the Cartesian coordinate system; while the parameter used when calculating 'b11' is the position of the detected aerial target relative to the second radar in the Cartesian coordinate system. The calculation methods for each parameter are as follows:

[0178]

[0179]

[0180] Let i = 1, then we can calculate:

[0181]

[0182] a12 = 0

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189]

[0190] Let i = 2, then we can calculate:

[0191]

[0192] b12 = 0

[0193]

[0194]

[0195]

[0196]

[0197]

[0198]

[0199]

[0200] In the formula, x1, y1, z1 are the coordinates of the first radar in the rectangular coordinate system of the first radar site, i.e., 0, 0, 0; x2, y2, z2 are the coordinates of the second radar in the rectangular coordinate system of the first radar site; xx, y t ,z t The coordinates of the detected aerial target in the Cartesian coordinate system of the first radar station site;

[0201] 4) Calculate the position error covariance matrix C of the detected air target in the rectangular coordinate system of the first radar station site after the data of the two radars are fused according to the following formula;

[0202] C = (P T K -1 P) -1

[0203] 5) According to the following formula, the positioning error covariance matrix is ​​transformed to the Earth-Fixed system to obtain C';

[0204] C'=FCF T

[0205] In the formula, F is the rotation matrix from the radar site measurement system to the ground-fixed system;

[0206] 6) Calculate the overall positioning accuracy σ of the radar for the detected aerial target at this location according to the following formula.

[0207]

Claims

1. A method for analyzing the tracking and positioning accuracy of aerial targets in a reconnaissance and early warning system, characterized in that, Includes the following steps: (1) Modeling of the reconnaissance and early warning system: Analyze the constituent units of the reconnaissance and early warning system, including the reconnaissance and early warning unit and the early warning center, and establish the operating rules and information transmission relationships between the units of the reconnaissance and early warning system; (2) Calculation of the detection range of the early warning unit: Based on the given parameters of the type of air target, electromagnetic scattering characteristics, infrared radiation characteristics and motion characteristics, obtain the reconnaissance and early warning units that can perform early warning detection of air targets from the reconnaissance and early warning system, and calculate the detection range of each reconnaissance and early warning unit for air targets. (3) Analysis of the detection and tracking position of the reconnaissance and early warning unit on the aerial target: For a given aerial target, calculate whether each point in the track point set is within the detection range of the reconnaissance and early warning unit, obtain the detection and tracking position of each reconnaissance and early warning unit on the aerial target track, and record the tracking and positioning accuracy of each position; (4) Tracking and positioning accuracy fusion of the early warning system: For the units in the reconnaissance and early warning system that have the ability to detect and warn of a given air target, the tracking and positioning accuracy is fused according to the sensor type to obtain the tracking and positioning accuracy of the reconnaissance and early warning system for the air target; The specific process of step (4) is as follows: When multiple space-based infrared early warning satellites detect ballistic missiles simultaneously, the positioning accuracy of the satellite with the highest positioning accuracy is selected as the final positioning accuracy. Long-range early warning radar, air surveillance and search radar, and air and sea search radar fuse their positioning accuracy against aerial targets, including ballistic missiles, cruise missiles, and combat aircraft. (401) Based on the flight path, obtain the current position coordinates of the detected aerial target, extract all radars that can detect aerial targets, and select the information of the two radars with the highest measurement accuracy; (402) Construct according to the following formula. matrix: In the formula, , , , , , These are the azimuth, elevation, and range measurement accuracy of the two radars, respectively. (403) The positions of the detected aerial target and the second radar are converted from the ground-fixed system to a measurement system centered on the position of the first radar, and the following formula is used to construct... matrix: In the formula, the parameters in the matrix correspond to the calculated parameters of the detected aerial target relative to the two radars, and the calculation methods for each parameter are as follows: make =1, calculated to be: make =2, calculated to be: In the formula, Let be the coordinates of the first radar in the rectangular coordinate system of the first radar site, and ; The coordinates of the second radar in the Cartesian coordinate system of the first radar site; The coordinates of the detected aerial target in the Cartesian coordinate system of the first radar station site; (404) Calculate the position error covariance matrix of the detected air target in the rectangular coordinate system of the first radar site after data fusion from the two radars, according to the following formula. : ； (405) According to the following formula, the position error covariance matrix is... Transforming to the Earth-Firm System, we obtain : In the formula, This is the rotation matrix from the radar site measurement system to the Earth-fixed system; (406) Calculate the overall positioning accuracy of the radar for the detected aerial target according to the following formula. : 。 2. The method for analyzing the tracking and positioning accuracy of aerial targets in a reconnaissance and early warning system according to claim 1, characterized in that, In step (1), the reconnaissance and early warning unit includes a space-based infrared early warning satellite, a long-range early warning radar, an air surveillance and search radar, and an air and sea search radar; the operational rules of the reconnaissance and early warning system include the command and coordination relationships between the various units of the system; The information transmission relationship is that each reconnaissance and early warning unit generates early warning information and sends it to its respective early warning center. The early warning centers interact with each other to achieve data sharing.

3. The method for analyzing the tracking and positioning accuracy of aerial targets in a reconnaissance and early warning system according to claim 2, characterized in that, In step (2), the types of aerial targets include ballistic missiles, cruise missiles and combat aircraft. Among them, space-based infrared early warning satellites and long-range early warning radars conduct early warning detection of ballistic missiles, while long-range early warning radars, air surveillance and search radars and air and sea search radars conduct early warning detection of cruise missiles and combat aircraft. The detection range of space-based infrared early warning satellites is calculated based on the light-transmitting aperture, peak wavelength, detectivity, signal process factor, number of detector elements, instantaneous field of view parameters of a single detector element, and infrared radiation characteristics of ballistic missile tail flames. The detection range of radars is calculated based on the radar's transmit power, antenna gain, signal wavelength, minimum detectable signal power performance parameters, and electromagnetic scattering characteristics of airborne targets.

4. The method for analyzing the tracking and positioning accuracy of an aerial target in a reconnaissance and early warning system according to claim 3, characterized in that, Step (3) is as follows: The determination of ballistic missiles includes using the exhaust plume detection range, telescope axis angle, and field of view to determine whether they are within the detection range of space-based infrared early warning satellites; using the radar detection range, elevation angle, and azimuth angle constrained by the Earth's curvature to determine whether they are within the detection range of long-range early warning radars; using the radar detection range, elevation angle, and azimuth angle constrained by the Earth's curvature to determine whether cruise missiles and combat aircraft are within the detection range of long-range early warning radars, air surveillance and search radars, and air and sea search radars; and determining the detection and tracking positions of each reconnaissance and early warning unit for a given aerial target and trajectory, and recording the tracking and positioning accuracy of each position.

Images