Method for multi-target equivalent zero bias compensation and effectiveness evaluation based on double active sensors

Abstract

The application provides a multi-target equivalent zero offset compensation and effectiveness evaluation method based on double active sensors, which comprises the following steps: firstly, determining the coordinates of the sensors in the geocentric coordinate system and the conversion matrix, and equivalently converting the distance and angle measurement of the sensors to the reference target into the coordinates of the target in the geocentric coordinate system; then, calculating a theoretical approximate formula of the equivalent zero offset difference; calculating the equivalent zero offset and performing compensation; finally, calculating an equivalent zero offset effectiveness index and evaluating the effectiveness of the equivalent zero offset. The application provides a theoretical approximate formula of the equivalent zero offset difference of similar targets, explicitly describes the change behavior of the equivalent zero offset, provides a practical tool and a theoretical fulcrum for the effectiveness analysis of the equivalent zero offset, the multi-target equivalent zero offset compensation method is easy to implement, and a specific quantitative index T i is provided for evaluating the effectiveness of the equivalent zero offset, and the index has practical significance, that is, T i reflects the proportional relationship between the length of the equivalent zero offset difference of similar targets and the distance between the targets.

Description

Technical Field

[0001] This invention relates to a method for equivalent bias compensation and effectiveness evaluation of target measurements using active sensors. The method provides a quantitative theoretical analysis of the difference in equivalent bias between similar targets and offers a reasonable scheme for equivalent bias compensation and effectiveness evaluation of multiple targets. Background Technology

[0002] When two active sensors measure multiple nearby targets, two problems arise. First, due to inherent errors such as zero bias in sensor measurements, even for the same target, there is a significant discrepancy between the positions of the measurements from the two sensors when transformed into the geocentric coordinate system. This discrepancy is often referred to as equivalent zero bias. Second, when multiple targets are close together, it cannot be guaranteed that the elements within the measurement data sets from the two sensors will correspond one-to-one. This makes matching and information fusion between the measurements from the two sensors difficult. To overcome this problem, equivalent zero bias compensation is needed for the sensor measurements, so that measurements from the same target or equivalent measurements are as close as possible. For multiple targets, direct multi-target matching is often difficult when the equivalent zero bias is unknown, but it is easier to first determine that a pair of measurement data from the two sensors comes from the same target.

[0003] There is currently no universally applicable method for this zero-bias compensation scenario. If zero-bias compensation is not performed, or if traditional methods are used, the following limitations exist:

[0004] 1. Without zero-bias compensation, the measurements of all targets by the same active sensor will cluster together, and the distance between the measurement points of two active sensors will be dominated by zero bias, making it difficult to perform target matching or information fusion.

[0005] 2. Traditional methods cannot explain the extent to which the data after compensation for equivalent zero bias is effective or reliable for subsequent matching or information fusion processing.

[0006] 3. Traditional tracking-based methods have high requirements for the acquired data, high computational complexity, and cannot process single-frame data, making them unsuitable for this scenario.

[0007] To address the aforementioned issues, this invention establishes a theoretical approximate formula for the difference in equivalent zero bias between similar targets, addressing the questions of how to perform zero bias compensation for multiple targets measured by dual active sensors and whether this compensation method is effective. Furthermore, it proposes an equivalent zero bias compensation and effectiveness evaluation method, thereby achieving equivalent zero bias compensation and effectiveness evaluation for multiple targets. Summary of the Invention

[0008] The technical problem solved by this invention is: how to perform zero-bias compensation for multiple targets measured by dual active sensors and whether this compensation method is effective. A theoretical approximate formula for the difference of equivalent zero bias between similar targets is established, and then an equivalent zero-bias compensation and effectiveness evaluation method is proposed, realizing the equivalent zero-bias compensation and effectiveness evaluation for multiple targets.

[0009] The solution of this invention is as follows: determine the coordinates of the sensor in the geocentric coordinate system and the transformation matrix, and convert the distance and angle measurements of the sensor to the reference target into the coordinates of the target in the geocentric coordinate system; then calculate the theoretical approximate formula of the equivalent zero bias difference; calculate the equivalent zero bias and compensate for it; finally calculate the effectiveness index of the equivalent zero bias and evaluate the effectiveness of the equivalent zero bias.

[0010] The specific steps proposed in this invention are explained below in response to the problem. Let the coordinates of the position vector of the target i's center of mass relative to the Earth's center in the Earth system be r. i =[x i y i z i ] T , where x i ,y i ,z i r i The components of the coordinates in the three directions of the Earth coordinate system. The coordinates of the position vectors of the center of mass of sensors u and v relative to the Earth's center in the Earth system are r and r, respectively. u =[x u y u z u ] T and r v =[x v y v z v ] T , where x u ,y u ,z u r u The components of the coordinates in the three directions of the Earth coordinate system, x v ,y v ,z v r v The components of the coordinates in the three directions of the Earth coordinate system. and These are the transformation matrices from the geocentric coordinate system to the sensor u and sensor v coordinate systems, respectively.

[0011] The following coordinate transformation uses sensor u and target i as examples; the same applies to sensor v and other targets. The transformation is based on the geographical latitude λ of sensor u. u Longitude L uThe transformation matrix from the geocentric coordinate system to the sensor u-coordinate system is:

[0012]

[0013] Sensor u Geographic latitude λ u Longitude L u and the height H above the ground surface u To the coordinates r in the geocentric coordinate system u The conversion relationship is as follows:

[0014]

[0015] in For the first eccentricity, a0=6378137m, b0=6356752m.

[0016] The coordinates of the relative position vector between sensor u and target i in the sensor u coordinate system are:

[0017]

[0018] Coordinates of the relative position vector from sensor u to target i in polar coordinates of sensor u for:

[0019]

[0020] Measurement of target i by sensor u for:

[0021]

[0022] in Let represent the distance, azimuth, and elevation angle of target i in the polar coordinate system of sensor u, respectively. This represents the corresponding measurement error, including systematic error and random error. Assume... Compared to Compared to Compared to All were in small quantities.

[0023] The coordinates of sensor u measuring target i in the Earth system for:

[0024]

[0025] The coordinates of the measurement error vector in the geocentric coordinate system are:

[0026]

[0027] in These represent the differences between the measured position of sensor u relative to target i and the actual position of target i in the three coordinate axes of the Earth coordinate system.

[0028] Then the equivalent zero bias of sensors u and v at target i is:

[0029]

[0030] This equivalent zero bias B i This indicates that even for the same target, measurements taken from different sensors may result in significantly different position coordinates when converted to the geocentric coordinate system. To facilitate subsequent target matching or information fusion, it is necessary to compensate for measurement bias to achieve an equivalent zero bias.

[0031] In practical applications, it is often impossible to obtain the equivalent zero bias for every target. Therefore, for similar targets, compensating with a unified equivalent zero bias is a common method. For a given equivalent zero bias... The equivalent zero-bias compensation method is as follows:

[0032]

[0033] Consider another target j that is close to target i, whose true coordinates in the geocentric coordinate system are r. i =[x i y i z i ] T and r j =[x j y j z j ] T ,remember Their equivalent zero bias difference is B j -B i , recorded as If B is used i If the measurement of target j is compensated, then

[0034]

[0035] The equivalent zero bias calculation and compensation model of equations (8)-(10) shows that if the measurement of target j is compensated according to the equivalent zero bias of target i, then the position of target j after compensation will be... Rather than converting the sensor v measurement to the position in the geocentric coordinate system The coordinates of the difference vector in the geocentric coordinate system are δ(B) ij To ensure the smooth progress of subsequent work, such as target matching or information fusion, it is desirable to transform the measurements of the same target from sensor u and sensor v to the geocentric coordinate system and compensate for the distance ||δ(B) of the position coordinates after equivalent zero offset. ji )‖2 The distance should be as small as possible to the distance δ(r) between different targets. ji ).

[0036] Therefore, on the one hand, the measurement of multiple targets by dual active sensors needs to compensate for equivalent zero bias; on the other hand, the effectiveness of unified zero bias compensation for multiple targets needs to be measured and evaluated. Based on the measurement model and the equivalent zero bias calculation and compensation model (5)-(10), the specific steps of the dual active sensor multi-target equivalent zero bias compensation and effectiveness evaluation method are as follows:

[0037] Step 1: Determine the sensor's coordinates in the geocentric coordinate system and the transformation matrix, converting the sensor's distance and angle measurements of the target into the target's coordinates in the geocentric coordinate system.

[0038] Taking sensor u as an example, the geographical latitude λ of the location of sensor u is known. u Longitude L u The transformation matrix from the geocentric coordinate system to the sensor u-coordinate system is:

[0039]

[0040] Given the sensor u's geographical latitude λ u Longitude L u and the height H above the ground surface u To the coordinates r in the geocentric coordinate system u The conversion relationship is as follows:

[0041]

[0042] in For the first eccentricity, a0 = 6378137m, b0 = 6356752m

[0043] Taking sensor u and target i as an example, the measurement of target i by sensor u with error is known to be:

[0044]

[0045] The coordinates of sensor u measuring target i in the Earth system for:

[0046]

[0047] Step 2: Calculate the approximate formula for equivalent zero bias.

[0048] Assume the coordinates of target i in the sensor u coordinate system are: The coordinates of sensor u in the polar coordinate system are: remember:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] Assumption Let be the measurement deviation of sensor u for the distance, azimuth, and elevation angles of target i. Assume... Compared to Compared to Compared to All are small quantities. Following the chain rule and ignoring second-order and higher errors in measurement, we have:

[0055]

[0056] in The difference between the actual positions of the similar target j and target i.

[0057] This is the difference in their measurement errors.

[0058] Calculations show that Therefore, equation (20) can be simplified to:

[0059]

[0060] In equation (21), Each element in the expression is a continuous function of the position coordinates of sensor u, and the position coordinates of sensor v are close to those of sensor u. Ignoring smaller quantities of higher order, we have:

[0061]

[0062] Equation (22) reflects the variation law of equivalent zero bias with the target position. Equation (22) is the theoretical approximate formula for the difference of equivalent zero bias between similar targets.

[0063] Step 3: Calculate the equivalent zero bias based on the baseline target measurement data and compensate for multiple targets.

[0064] Assuming target i is known as the baseline target, it is possible to determine which pair of measurements from sensors u and v originates from the same target. Based on the first step, it is known... and The equivalent zero bias is:

[0065]

[0066] As defined by equivalent zero bias, it is known that only the measurement of sensor u needs to be compensated for this equivalent zero bias. For any measurement of sensor u... The position coordinates after this measurement compensation equivalent to zero bias are:

[0067]

[0068] Step 4: Evaluate the effectiveness of equivalent zero-bias compensation

[0069] Furthermore, we quantitatively demonstrate the effectiveness of such a compensation method. According to the matrix norm inequality, we have:

[0070]

[0071] According to the analysis, the left side of Equation (25) is a measure of the effectiveness of the equivalent zero bias, which is controlled by the right side of Equation (25).

[0072] In practical applications, while the measurement data of target i with errors may be known, it may be impossible to obtain the specific measurement errors of sensors u and v for target i. Consider the following:

[0073]

[0074] The upper and lower bounds of the ranging error rate of sensor u are known, denoted as . Upper and lower bounds of azimuth and elevation angle measurement errors Δ(b u ) , D(e u ) The upper and lower bounds of the ranging error rate of sensor v are denoted as... Upper and lower bounds of azimuth and elevation angle measurement errors Δ(b v ) , D(e v ) .

[0075] Calculate separately:

[0076]

[0077]

[0078] Then, the equivalent zero-biased effectiveness evaluation index for objective i is calculated:

[0079]

[0080] This equivalent zero-biased effectiveness index T i satisfy:

[0081]

[0082] Equivalent zero-biased effectiveness index Ti The smaller the value, the better the relative distance between the measured values ​​of any target j under the two sensors after conversion to the geocentric coordinate system and compensation for the equivalent zero bias of target i. Compared to the distance between target i and target j, the smaller the value, the better the equivalent zero bias compensation effect and subsequent matching performance may be.

[0083] If the calculated equivalent zero-biased effectiveness assessment index meets the requirements, i.e., T i If the ratio is less than the given ratio index T0, then the measurement of this target is considered to be equivalent to zero bias calculated according to equation (8), and is valid for all points near this target.

[0084] The advantages of this invention compared to existing technologies are as follows: First, it provides a theoretical approximate formula for the difference in equivalent zero bias between similar targets. This formula explicitly explains the relationship between the difference in equivalent zero bias between similar targets and the difference in coordinates between similar targets, and decouples the errors of the three components measured by the sensor, explicitly explaining the changing behavior of the equivalent zero bias, thus providing a practical tool and theoretical support for the effectiveness analysis of the equivalent zero bias. Second, the proposed multi-target equivalent zero bias compensation method is easy to implement. Third, it proposes a specific quantitative index T for evaluating the effectiveness of the equivalent zero bias. i And this indicator has practical significance, namely T. i It reflects the proportional relationship between the modulus of the equivalent zero bias difference between similar targets and the distance between the targets. Attached image description:

[0085] Figure 1 This is a flowchart of the equivalent zero-bias validity assessment method.

[0086] Figure 2 It is a frequency distribution diagram of the percentage error between the theoretical approximation and the actual equivalent zero bias difference.

[0087] Figure 3 This is a scatter plot of measurement data from 10 targets randomly selected by active sensor 1 and active sensor 2 in simulation 1.

[0088] Figure 4 This is a scatter plot of measurement data from 10 randomly selected targets from the simulation of active sensor 2 and active sensor 1 after zero bias compensation.

[0089] Figure 5 This is a scatter plot of measurement data from 10 randomly selected targets, obtained from simulation 2 (active sensor 2) and active sensor 1 (active sensor 1) after zero bias compensation using conventional methods.

[0090] Symbol explanation:

[0091] [L u λ u H u ] TThe sensor's longitude, latitude, and altitude above the Earth's surface;

[0092] The transformation matrix from the geocentric coordinate system to the sensor u-coordinate system;

[0093] r u The coordinates of the position vector of the sensor's center of mass relative to the Earth's center in the geocentric coordinate system;

[0094] r i : The coordinates of the position vector of the center of mass of target i relative to the center of the Earth in the Earth system;

[0095] The coordinates of the relative position vector between sensor u and target i in the sensor u coordinate system;

[0096] The coordinates of the relative position vector between sensor u and target i in polar coordinates of sensor u;

[0097] The measurement of target i by sensor u;

[0098] The coordinates of the target i measured by sensor u in the Earth system;

[0099] B i : Target i is equivalent to zero bias;

[0100] T i : The equivalent zero-biased effectiveness index for objective i;

[0101] T0: Proportional indicator. Detailed Implementation

[0102] The following simulation example illustrates the specific implementation of the method for multi-target equivalent zero-bias compensation and effectiveness evaluation based on dual active sensors. This simulation is designated Simulation 1. In this simulation, the latitude, longitude, and altitude of sensor u are [0 0 0]. T The latitude, longitude, and altitude of sensor v are [0.0001 0.0001 0]. T The measurement of the reference target i at sensor u is [2025043.70322.3762 1.5102]. T The sensor value v is measured as [1984881.3138 2.3362 1.4908]. T .

[0103] The target measurement model and the equivalent zero bias calculation and compensation model are (5)-(10). The sensor u measurement error is fixed as [Δ(ρ u ) / ρ u Δ(b u ) Δ(e u)] T =[0.01 0.02 0.01] T The sensor v measurement error is fixed at [Δ(ρ)]. v ) / ρ v Δ(b v ) Δ(e v )] T = [-0.01 -0.02 -0.01] T 1000 points are randomly selected within a sphere with a radius of 100 centered on the baseline target.

[0104] The algorithm first calculates the coordinates of sensor u and sensor v in the geocentric coordinate system and the transformation matrix from the geocentric coordinate system to the sensor coordinate system. and Then, the reference target i is measured in polar coordinates of sensor u and sensor v. and Convert to geocentric coordinates and Then, the theoretical approximation formula for the difference between the equivalent zero biases is calculated. Then, the equivalent zero bias B is calculated. i And compensate for multi-target measurements. Then, based on the measurements of the reference target i in polar coordinates of sensor u and sensor v. and And the upper and lower bounds of the measurement errors of sensors u and v are calculated. Calculate the equivalent zero-biased effectiveness index T i Finally, the equivalent zero-biased effectiveness index T is used. i Compare it with the actual required ratio indicator T0. If T i If <T0, then the equivalent zero bias calculated according to Equation (8) is considered valid for all targets in the sense of validity proposed in this invention.

[0105] According to the simulation scenario of the present invention, for 1000 randomly generated targets, the frequency distribution curve of the error percentage of the magnitude of the equivalent zero bias difference between the target and the reference target, calculated according to equation (25), is shown below. Figure 2 As shown, the approximate formula for the equivalent zero bias theory of similar targets proposed in this invention has a very small error on the vast majority of targets, indicating that the theoretical approximation formula for the difference of equivalent zero bias proposed in this invention has a very good approximate accuracy for the actual difference of equivalent zero bias. Figure 3 This is a scatter plot of measurement data from active sensor 1 and active sensor 2 for 10 randomly selected targets. Figure 4The image shows a scatter plot of the measurement data from active sensor 1 and active sensor 2 after zero-bias compensation for these 10 targets. Measurements from the same target from both active sensors are connected by lines. It can be seen that without zero-bias compensation, the measurement data points from the two active sensors are far apart and clustered together, making matching difficult. However, after zero-bias compensation using the method of this patent, the measurements from the same target from the two active sensors are very similar, easily distinguishable, and facilitate subsequent target matching.

[0106] The equivalent zero-biased effectiveness index T is calculated from the simulation scenario data. i =0.2810. If the proportional index T0 = 0.3, then since T < T0, according to the method proposed by this invention, the equivalent zero bias calculated by the benchmark target according to equation (8) is considered to be effective in compensating all targets in the neighborhood of the benchmark target. Among 1000 randomly generated targets, the maximum value of the ratio of the magnitude of the difference of equivalent zero bias to its distance from the benchmark target is 0.2703, indicating that the effectiveness assessment of the equivalent zero bias proposed by this invention is correct, and the equivalent zero bias compensation method proposed by this invention is effective in the proposed sense.

[0107] For comparison, the measurement of the baseline target j at sensor u is [22221125.3181 2.0342 1.5707]. T The sensor value v is measured as [21781094.6876 1.9881 1.5509]. T For example, the simulation scenario settings are the same as the previous simulation. This simulation is denoted as Simulation 2. According to the method of this invention, the equivalent zero-biased efficiency index T is calculated. j = 5.7390, this validity index is obviously too high, and T j >T0. According to the method of the present invention, compensation for uniform equivalent zero bias is ineffective in this scenario. Taking the conventional method of using the difference between the geometric center points of the measurement data from two active sensors as an estimate of the equivalent zero bias and performing compensation without effectiveness evaluation as an example, the measurement data from active sensor 1 and active sensor 2 of 10 targets are randomly selected. Figure 5 The scatter plots show the measurement data of active sensor 1 and active sensor 2 after zero bias compensation using the conventional method for these 10 targets. It can be seen that without an effectiveness assessment, estimating and compensating for equivalent zero bias using the conventional method still makes it difficult to distinguish measurements from different targets, failing to guarantee successful subsequent matching. This demonstrates that the equivalent zero bias effectiveness assessment proposed in this invention has guiding significance for subsequent equivalent zero bias compensation.

[0108] In summary, this invention addresses the issues of how to perform equivalent zero-bias compensation for multiple targets using dual active sensors and how to evaluate its effectiveness. It provides a theoretical approximation of the difference in equivalent zero-bias between similar targets, proposes an evaluation index for the effectiveness of equivalent zero-bias, and offers a reasonable scheme for equivalent zero-bias compensation and effectiveness evaluation for multiple targets.

Claims

1. A method for equivalent zero-bias compensation and effectiveness evaluation of multiple targets based on dual active sensors, assuming the target... The coordinates of the position vector of the center of mass relative to the center of the Earth in the Earth system are: ,in They are respectively Components of coordinates in the three directions of the Earth coordinate system; sensor and sensors The coordinates of the position vector of the center of mass relative to the center of the Earth in the Earth system are as follows: and ,in They are respectively The components of coordinates in the three directions of the Earth coordinate system. They are respectively The components of the coordinates in the three directions of the Earth coordinate system; and From the geocentric coordinate system to the sensor and sensors The transformation matrix of the coordinate system; characterized in that, Includes the following steps: Step 1: Determine the sensor's coordinates in the geocentric coordinate system and the transformation matrix, converting the sensor's distance and angle measurements of the target into the target's coordinates in the geocentric coordinate system; Step 2: Calculate the approximate formula for equivalent zero bias; Step 3: Calculate the equivalent zero bias based on the baseline target measurement data and compensate for multiple targets; Step 4: Evaluate the effectiveness of equivalent zero-bias compensation; In step two, the target is set. In the sensor The coordinates under the coordinate system are In the sensor The coordinates in the polar coordinate system are ,remember: (15) (16) (17) (18) (19) set up For sensors For the target Measurement deviations of distance, azimuth, and elevation angles; assuming Compared to , Compared to , Compared to All are small quantities; according to the chain rule and ignoring second-order and higher errors in measurement, we have: (20) in For similar goals With the goal The difference in actual location; The difference in their measurement errors; in, Equation (20) simplifies to: (21) In equation (21), Each element in the middle is a sensor. The position coordinates are a continuous function, while the sensor With sensors Since the position coordinates are close, ignoring smaller quantities of higher order, we have: (22) Equation (22) reflects the variation law of equivalent zero bias with the target position; Equation (22) is the theoretical approximate formula for the difference of equivalent zero bias between similar targets; In step three, the target is set. As a benchmark target, determine the sensor and sensors Which pair of measurements comes from the same target; according to and Then the equivalent zero bias is: (23)； This is derived from the definition of equivalent zero bias, which only requires the sensor The measurement compensates for this equivalent zero bias; for the sensor Any measurement The position coordinates after this measurement compensation equivalent to zero bias are: (24)； In step four, according to the matrix norm inequality, we have: (25) The left side of equation (25) is a measure of the effectiveness of the equivalent zero bias, which is controlled by the right side of equation (25); Among them, due to the fact that in practical applications, the target Measurement data with errors, but may not be available from the sensor. and sensors For the target For specific measurement errors, consider: (26) sensor The upper and lower bounds of the ranging error rate are denoted as . Upper and lower bounds of azimuth and elevation angle measurement errors ,sensor The upper and lower bounds of the ranging error rate are denoted as . Upper and lower bounds of azimuth and elevation angle measurement errors ; Calculate separately: (27) (28) (29) Then calculate the target Equivalent zero-biased effectiveness evaluation index: (30)。 2. The method for multi-target equivalent zero-bias compensation and effectiveness evaluation based on dual active sensors according to claim 1, characterized in that: In step one, the sensor The geographical latitude of the location ,longitude From the geocentric coordinate system to the sensor The transformation matrix of the coordinate system is: (11) sensor Geographical latitude ,longitude and height above the ground surface coordinates in the geocentric coordinate system The conversion relationship is as follows: (12) in, For the first eccentricity, , .

3. The method for multi-target equivalent zero-bias compensation and effectiveness evaluation based on dual active sensors according to claim 1 or 2, characterized in that: sensor For the target The measurement with error is as follows: (13) sensor For the target The measurement in the Earth system coordinates for: (14)。 4. The method for multi-target equivalent zero-bias compensation and effectiveness evaluation based on dual active sensors according to claim 1, characterized in that: This equivalent zero-biased effectiveness index satisfy: (31) Equivalent zero-biased effectiveness index The smaller the value, the better for any target. Measurements from both sensors were converted to the geocentric coordinate system and the target was compensated. The relative distance from the position after equivalent zero offset, compared to the target. With the goal The smaller the distance between them, the better the equivalent zero-bias compensation effect and the subsequent matching performance.

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