CN112285701B - Error correction method for three-dimensional networking radar system - Google Patents
Error correction method for three-dimensional networking radar system Download PDFInfo
- Publication number
- CN112285701B CN112285701B CN202011135492.7A CN202011135492A CN112285701B CN 112285701 B CN112285701 B CN 112285701B CN 202011135492 A CN202011135492 A CN 202011135492A CN 112285701 B CN112285701 B CN 112285701B
- Authority
- CN
- China
- Prior art keywords
- sensor
- model
- formula
- coordinate system
- matrix
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 45
- 238000012937 correction Methods 0.000 title claims abstract description 19
- 230000006855 networking Effects 0.000 title claims abstract description 13
- 238000006243 chemical reaction Methods 0.000 claims abstract description 17
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 12
- 238000005457 optimization Methods 0.000 claims abstract description 8
- 239000011159 matrix material Substances 0.000 claims description 31
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 6
- 230000008569 process Effects 0.000 claims description 6
- 101100001674 Emericella variicolor andI gene Proteins 0.000 claims description 3
- 230000003190 augmentative effect Effects 0.000 claims description 3
- 238000013178 mathematical model Methods 0.000 claims description 3
- 230000009897 systematic effect Effects 0.000 description 7
- 230000000694 effects Effects 0.000 description 5
- 238000005259 measurement Methods 0.000 description 4
- 230000001360 synchronised effect Effects 0.000 description 4
- 230000004927 fusion Effects 0.000 description 3
- 238000013459 approach Methods 0.000 description 2
- 238000004364 calculation method Methods 0.000 description 2
- 230000008859 change Effects 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 230000007547 defect Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000001914 filtration Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 239000002245 particle Substances 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 230000003595 spectral effect Effects 0.000 description 1
- 238000013179 statistical model Methods 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/87—Combinations of radar systems, e.g. primary radar and secondary radar
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/40—Means for monitoring or calibrating
Landscapes
- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention belongs to the technical field of radars, and particularly relates to a three-dimensional networking radar system error correction method. A three-dimensional networking radar system error correction method comprises the following steps: s1, setting a conversion relation model of a target between a local coordinate system and a global coordinate system of a sensor; s2, setting a sensor local observation model; s3, setting a global observation model of the sensor; s4, setting a target motion model; s5, establishing a sensor system deviation estimation model according to the non-deflection relation between the observed data and the target position; s6, establishing a system error estimation model; and S7, solving the optimization model established in the step 6 by using a coordinate round descent algorithm. According to the invention, the sensor system error estimation model is built by building the conversion relation model between the sensor local coordinate system and the global coordinate system, the sensor global observation model and the local observation model, and the model is optimized and solved, so that the error of the sensor system is effectively compensated.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a three-dimensional networking radar system error correction method.
Background
In the application of the radar sensor network, the positioning accuracy and the detection performance of the target can be obviously improved by fusing the observation data of each radar. However, for the radar networking sensor network, due to external uncontrollable factors such as orientation errors of array antennas, signal processing delay system errors and the like, the system errors of the radar stations exist in different degrees. The existence of the system error seriously affects the subsequent multi-sensor information fusion performance. Therefore, correcting the systematic errors of the radar sensors is a necessary precondition for successful information fusion of the whole sensor network. Since radar sensor system errors change slowly over time, the sensor system errors are treated as unknown constants contained in the metrology data over a relatively long period of time.
According to the working model of the multi-sensor network, the methods can be divided into asynchronous sensor network error system error correction and synchronous sensor network system error correction. Most research has focused on systematic error correction of synchronous sensor networks, whereas in practice multi-sensor networks tend to work in an asynchronous manner. Therefore, how to estimate the sensor system error by each sensor asynchronously observing data is a real problem to be solved. The problem of multi-sensor system error estimation in asynchronous modes of operation is generally underdetermined (i.e., the number of observations is less than the number of unknown parameters). To overcome this difficulty, it is often necessary to use a priori statistical models of the target motion, such as approximately uniform motion models, which, while effectively utilizing the asynchronous observed quantity of the sensor, do not handle well the nonlinear components contained in the model. Based on PHD theory, the PHD particle filter is used for jointly estimating the target state and the sensor system error, however, the calculated amount required by the method increases exponentially with the increase of the number of sensors, and is difficult to be used in scenes with a large number of sensors.
In summary, most of the current work for error correction of the multi-sensor system is concentrated on the assumption of synchronous working mode, which is not consistent with the multi-sensor network model of actual asynchronous working. On the other hand, the research work of system error correction in an asynchronous working mode often processes nonlinear parts in the problem of multi-sensor system error correction by means of linear approximation or large calculation amount, which can bring problems of model mismatch or limitation to calculation amount and the like, so that estimation performance is not ideal. Therefore, for asynchronous operation modes, how to build an effective estimation model and design an efficient algorithm to solve (estimate) the sensor system error is a task to be further studied.
Disclosure of Invention
The invention aims to provide a three-dimensional networking radar system error correction method aiming at overcoming the defects of the prior art, so as to perfect a system error model and effectively solve the error of an actual observation model. Based on the purpose, the technical scheme adopted by the invention is as follows:
the error correction method of the three-dimensional networking radar system is characterized by comprising the following steps of:
s1, setting a conversion relation model of a target between a local coordinate system and a global coordinate system of a sensor, wherein the conversion relation model is as follows:
where ζ k denotes the position of the object in the global coordinate system at time k, ζ' k is the position of the object in the sensor local coordinate system at time k, When the sensor is a rotation sensor in k, R (& gt) is a rotation matrix, and the rotation matrix is expressed by the formula of/>Representing the position of the sensor s k in the global coordinate system;
s2, setting a sensor local observation model according to the conversion relation model set in the step S1,
Where z 'k denotes the position of the sensor in the local coordinate system at k, ρ' k、φ′k,Respectively representing the distance, azimuth and pitch angle, x' k、y′k、z′k represents the position of the target in the local sensor, h (·) represents the cartesian-polar transformation function as defined by equation (3);
S3, setting a global sensor observation model according to the conversion relation model set in the step S1 and the local sensor observation model set in the step S2,
Where the symbol z k denotes the position of the sensor in the global coordinate system at k, R T denotes the three-dimensional coordinate rotation matrix transpose, h is defined as in equation (3),Is an additional deviation of the distance, azimuth and elevation of the sensor s k, Δζ s represents an additional deviation of the coordinate rotation, where w k is zero-mean gaussian noise,/>
S4, setting a target motion model,
In the formula, xi k＝[xk,yk,zk andIs the position and speed of the target at time k, T k. Gtoreq.0 is the time interval between time k and time k+1, n k and/>The process noise of the position and the speed at time k respectively obeys Gaussian distribution;
s5, setting the following observation data z k and xi k without deflection change according to the observation model set in the step 1-4, wherein z k represents the observation data of the sensor at the moment k, setting the observation data from the sensor S k,ξk to represent the spatial position of the target in the global coordinate system,
Further a sensor system error estimation model is established,
Step S6, based on step S5, establishing a systematic deviation estimation model, defined in step S4And/>Systematic deviations, each sensor contains the same type of systematic error (deviation).
Q in the formula (10) represents a positive definite symmetric matrix, and the physical meaning of the positive symmetric matrix is a covariance matrix of noise;
Step S7, solving the optimization model established in the step 6, solving by using a coordinate round descent algorithm,
Where Δρ= [ Δρ 1,Δρ2,...,ΔρM ] (similar to other types of deviations) andThe objective function in equation (10) can be expressed as f (v, Δρ, Δη, Δα, Δβ, Δγ).
Further, in the step S1,
Wherein alpha is the rotation angle of the x-axis of the radar self rectangular coordinate system when the three-dimensional coordinates rotate, beta is the rotation angle of the y-axis of the radar self rectangular coordinate system when the three-dimensional coordinates rotate, and gamma is the rotation angle of the z-axis of the radar self rectangular coordinate system when the three-dimensional coordinates rotate.
Further, in the step S7, according to the formula (10) in the step S5, in the formula (12 a),
Wherein H v is a coefficient matrix, c v is a constant vector, Q is a positive definite matrix, and the closed-form solution of formula (12 a) is:
Further, in the step S7, in the formula (12 b), Δρ has a closed form, and the formula (12 b) may be expressed as
Wherein H ρ is a coefficient matrix, c ρ is a constant vector, and the closed-form solution of formula (12) b is:
further, in the step S7, the optimized formulas (12 c) - (12 f) have the same mathematical model structure,
In the method, in the process of the invention,Is a coefficient matrix,/>The constant vector is a constant vector.
Further, in the formula (17),
Further, the optimization method in the formula (17) adopts the following algorithm to carry out iterative solution,
Wherein,
Further, in the formula (19), D x is a diagonal matrix defined as
Representing Kronecker product, based on the "projection" property, introducing an auxiliary variable x=z, splitting the formula (17), allowing all sub-formulas in the ADMM to iterate allowing a closed form solution,
Where iota C (z) is an indicator function of set C, as follows:
The augmented lagrangian function of equation (20) is:
where ρ > 0 is a penalty parameter and λ is the Lagrangian multiplier of the equation constraint x=z.
Compared with the prior art, the method and the device have the advantages that the sensor system error estimation model is built by building the conversion relation model between the local coordinate system and the global coordinate system of the sensor, the global observation model and the local observation model of the sensor, and the model is optimized and solved, so that the error of the sensor system is effectively compensated.
Drawings
FIG. 1 is a flow chart of the present invention;
figure 2 is a schematic diagram of various types of error effects,
In the figure, range bias represents distance bias, azimuth bias represents Azimuth bias, elevation bias, roll bias, yaw bias, pitch bias represent rotational angle bias of X, Y, Z coordinate axes, respectively.
Figure 3 is a schematic illustration of a simulated scene,
In the figure, sensor represents a sensor, target represents a target, and coordinate represents coordinates;
Figures 4a to 4e are graphs showing the effect of various types of systematic error estimates RMSE as performance metrics,
In the figure, RMSE is root mean square error, ASKF denotes an enhancement state kalman filter method, linearized LS denotes a linear least squares method, SKF-GN denotes a sensor bias estimation method estimated by a smoothed kalman filter, BCD-NLS denotes a proposed method (Q is an identity matrix), BCD-PML denotes a proposed method (Q is a corresponding noise covariance matrix), and RHCRLB denotes a theoretical lower bound of system error estimation performance.
Detailed Description
As shown in fig. 1, the error correction method of the three-dimensional networking radar system comprises the following steps:
s1, setting a conversion relation model of a target between a local coordinate system and a global coordinate system of a sensor, wherein the conversion relation model is as follows:
Where ζ k denotes the position of the object in the global coordinate system at time k, ζ' k is the position of the object in the sensor local coordinate system at time k, The average angle deviation of the rotation sensor when k is the value, R is the deflection angle of the rotation sensor,/>, andRepresenting the position of the sensor s k in the global coordinate system;
Wherein,
Wherein alpha is the rotation angle of the x-axis of the radar self rectangular coordinate system when the three-dimensional coordinates rotate, beta is the rotation angle of the y-axis of the radar self rectangular coordinate system when the three-dimensional coordinates rotate, and gamma is the rotation angle of the z-axis of the radar self rectangular coordinate system when the three-dimensional coordinates rotate;
Consider a three-dimensional multi-sensor system comprising M (M > 1) sensors of different known locations Assuming that a moving object (speed is not known) is used as a reference point in space, the asynchronous mode of sensor measurement of the relative position at different times associated, i.e. the object position, is actually measured by different sensors at different times. Briefly, the measurements of all sensors are classified and mapped onto a time axis, indexed by time instance k=1, 2, …, K. Without loss of generality, it is assumed that only one sensor observes a target at time instance k, with the corresponding sensor indexed by s k e {1, 2. Let xi k＝[xk,yk,zk and/>The target is located at a position at time k in the global cartesian coordinate system and the local coordinate system of the sensor s k, respectively.
Note that in practice, the relationship is as follows: cannot be precisely known, but rather, only the hypothetical/> Can measure andWherein/>Is the angular deviation of the rotation sensor s k.
S2, setting a sensor local observation model according to the conversion relation model set in the step S1, and modeling the xi k in the sensor S k local polar coordinate system as
Where z 'k denotes the position of the sensor in the local coordinate system at k, ρ' k,φ′k,Respectively representing the distance, azimuth angle and pitch angle, x' k、y′k、z′k represents the coordinates of the sensor in the xyz three directions, and h represents the Cartesian-polar coordinate transfer function defined as formula (3);
S3, setting a global sensor observation model according to the conversion relation model set in the step S1 and the local sensor observation model set in the step S2,
Where the symbol z k denotes the position of the sensor in the global coordinate system at k, R T denotes the three-dimensional coordinate rotation matrix, h is defined as in equation (3),Is an additional deviation of the distance, azimuth and elevation of the sensor s k, w k is zero-mean Gaussian noise,/>The measurement specification model (4) is shown in fig. 2 and can be found to be an inherent ambiguity between sensor bias.
S4, setting a target motion model,
In the formula, xi k＝[xk,yk,zk andIs the position and speed of the target at time k, T k. Gtoreq.0 is the time interval between time k and time k+1, n k and/>The process noise of the position and the speed at time k respectively obeys Gaussian distribution;
Wherein q' is the sum of the values of the noise power spectral density The gaussian distribution with mean μ and covariance Σ is shown.
S5, setting the following non-deflection conversion relation between the observation z and\xi according to the observation model set in the step 1-4
Further a sensor system error estimation model is established,
Wherein,And e k＝εk+1-εk-nk is also a zero mean random noise.
Step S6, based on step S5, a system deviation estimation model is built, and each sensor contains the same type of system error
In formula (10), Q represents a positive definite symmetric matrix whose physical meaning is the covariance matrix of noise, i.eStep S7, solving the optimization model established in the step 6, solving by using a coordinate round descent algorithm,
Where Δρ= [ Δρ 1,Δρ2,...,ΔρM ] (similar to other types of deviations) andThe objective function in equation (10) can be expressed as f (v, Δρ, Δη, Δα, Δβ, Δγ).
According to the formula (10) in step S5, in the formula (12 a),
Wherein H v is a coefficient matrix, c v is a constant vector, Q is a positive definite matrix, and the closed-form solution of formula (12 a) is:
in equation (12 b), Δρ has a closed form, and equation (12 b) may also be expressed as
Wherein H ρ is a coefficient matrix, c ρ is a constant vector, and the closed-form solution of formula (12 b) is:
in the step S7, the optimized formulas (12 c) - (12 f) have the same mathematical model structure,
In the method, in the process of the invention,Is a coefficient matrix,/>Is a constant vector.
In the above-mentioned formula (17),
The optimization method in the formula (17) adopts the following algorithm to carry out iterative solution,
Wherein,
Further, in the formula (19), D x is a diagonal matrix defined as
Representing Kronecker product, based on the "simple" - "projection" property, introducing an auxiliary variable x=z, splitting the formula (17), allowing all sub-formulas in the ADMM to iterate allowing a closed form solution,
Where iota c (z) is the indicator function of set C, as follows:
The augmented lagrangian function of equation (20) is:
where ρ > 0 is a penalty parameter and λ is the Lagrangian multiplier of the equation constraint x=z.
The above model was tested, and the test scenario and results were as follows:
Simulation results are provided to illustrate the performance of solving the proposed equation (10) using the proposed BCD algorithm (i.e., algorithm 2) with two different choices of Q k: one is Q k =i, which corresponds to classical nonlinear LS estimation (called BCD-NLS), the other is Can be considered as a pseudo-ML estimate (referred to as BCD-PML). We select three representative approaches in the literature and extend them to 3-dimensional situations where all sensors are offset and asynchronous. The first method is an enhancement state Kalman filtering (ASKF) method that treats the sensor bias as an enhancement state and uses the Kalman filter to jointly estimate the sensor bias and the target state. The second method is the LS method, which uses a first order approximation (called linearization LS) to solve the NLS formula set forth in (10). The third method is the ML method, originally proposed for the scenario of a synchronous multisensor system or one unbiased sensor. To extend this to the 3-dimensional case with stable numerical behavior, we first estimate the target state by a Smoothed Kalman Filter (SKF) and then the sensor bias by gaussian-newton method. For simplicity, we refer to this method as SKF-GN.
Experimental scenario:
Consider a scenario with four sensors and one target in 3-dimensional space, as shown in fig. 3. The position and offset of each sensor are listed in table I. The target being at an almost constant speed And (5) moving. /(I)The initial position is [ -30; -5;8 km. For all m=1; it is assumed that the rotation angle m is fixed to (0 ° ). The 1,2,3,4 sensors operate in an asynchronous mode, with four sensors measuring target positions at different start times (i.e., 2.5s,5s,7.5s,10s, respectively) every 10 seconds. In addition, each sensor sends 20 stamped measurements to the fusion center for sensor registration and total observation for the last 210 s.
Experimental effect comparison:
RMSE is used as a performance metric with various types of systematic error estimates, the effect of which is shown in fig. 4 a-e.
(BCD-NLS and BCDPML are the methods proposed in this patent, RHCRHB is the theoretical limit) fig. 4c shows RMSE of distance offset for different sensors, and fig. 4d shows RMSE of different angle offset. It can be observed that the two proposed methods (i.e. BCD-NLS and BCDPML) can achieve a great effect. RMSE is smaller compared to the other three methods. The main reason for this is that all three other approaches use first order approximations to deal with nonlinearities and such approximations typically result in model mismatch, which reduces the estimation performance. Note that the only difference between linearization LS and BCD-NLS is the algorithm used to solve problem (10) and q=i. More specifically, the linearized LS utilizes a first order approximation that allows the bias to be estimated using a closed-form solution, while the BCD-NLS uses the proposed BCD algorithm to handle nonlinearities. Obviously, BCD-NLS achieves a smaller RMSE. Furthermore, by combining the second order statistics, the RMSE of BCD-PML implementation is smaller than BCD-NLS, which demonstrates the effectiveness of Qk selection proposed in (11).
Finally, it should be noted that: the above embodiments are only for illustrating the present invention and not for limiting the technical solution described in the present invention; thus, while the invention has been described in detail with reference to the various embodiments described above, it will be understood by those skilled in the art that the invention may be modified or equivalents; all technical solutions and modifications thereof that do not depart from the spirit and scope of the present invention are intended to be included in the scope of the appended claims.
Claims (7)
1. The error correction method of the three-dimensional networking radar system is characterized by comprising the following steps of:
s1, setting a conversion relation model of a target between a local coordinate system and a global coordinate system of a sensor, wherein the conversion relation model is as follows:
where ζ k denotes the position of the object in the global coordinate system at time k, ζ' k is the position of the object in the sensor local coordinate system at time k, For the rotation angle of the sensor at k, R (& gt) is a rotation matrix,/>Representing the position of the sensor s k in the global coordinate system;
s2, setting a sensor local observation model according to the conversion relation model set in the step S1,
Wherein Z 'k represents the position of the sensor in the local coordinate system at k, ρ' k、φ′k,Respectively representing the distance, azimuth angle and pitch angle, wherein x' k、y′k、z′k represents the coordinates of the sensor xyz in three directions, and h (·) represents a Cartesian-polar coordinate conversion function defined as formula (3);
S3, setting a global sensor observation model according to the conversion relation model set in the step S1 and the local sensor observation model set in the step S2,
Where the symbol z k denotes the position of the sensor in the global coordinate system at k, R T denotes the rotation matrix transpose, h is defined as in equation (3),Is an additional deviation of the distance, azimuth and elevation of the sensor s k,/>Representing an additional deviation of the coordinate rotation, w k is zero-mean gaussian noise,
S4, setting a target motion model,
In the formula, xi k＝[xk,yk,zk andIs the position and speed of the target at time k, T k. Gtoreq.0 is the time interval between time k and time k+1, n k and/>The process noise of the position and the speed at time k respectively obeys Gaussian distribution;
S5, setting the following observation data z k and xi k without deflection exchange relation according to the observation model set in the step 1-4, wherein z k represents the observation data of the sensor at the moment k, and the set observation data come from the sensor S k,ξk to represent the spatial position of the target in the global coordinate system;
Further a sensor system error estimation model is established,
Step S6, based on the step S5, a system error estimation model is established;
Q in the formula (10) represents a positive definite symmetric matrix, and the physical meaning of the positive symmetric matrix is a covariance matrix of noise;
Step S7, solving the optimization model established in the step 6, solving by using a coordinate round descent algorithm,
According to the formula (10) in step S6, in the formula (12 a),
Wherein H v is a coefficient matrix, c v is a constant vector, Q is a positive definite matrix, and the closed-form solution of formula (12 a) is:
Wherein Δρ= [ Δρ 1,Δρ2,...,ΔρM ] and The objective function in equation (10) can be expressed as f (v, Δρ, Δη, Δα, Δβ, Δγ).
2. The method for correcting errors in a three-dimensional networking radar system according to claim 1, wherein in the step S1,
Wherein alpha is the rotation angle of the x-axis of the radar self rectangular coordinate system when the three-dimensional coordinates rotate, beta is the rotation angle of the y-axis of the radar self rectangular coordinate system when the three-dimensional coordinates rotate, and gamma is the rotation angle of the z-axis of the radar self rectangular coordinate system when the three-dimensional coordinates rotate.
3. The error correction method of three-dimensional networking radar system according to claim 2, wherein in the step S7, Δρ has a closed form in the formula (12 b), and the formula (12 b) may be expressed as
Wherein H ρ is a coefficient matrix, c ρ is a constant vector, and the closed-form solution of formula (12 b) is:
4. The error correction method for three-dimensional networked radar system according to claim 1, wherein in the step S7, the optimization formulas (12 c) - (12 f) have the same mathematical model structure,
Where H θ is a coefficient matrix and c θ is a constant vector.
5. The method for error correction of a three-dimensional networked radar system according to claim 4, wherein, in the formula (17),
6. The error correction method for three-dimensional networking radar system according to claim 5, wherein the optimization method in the formula (17) is iteratively solved by adopting the following algorithm,
Wherein,
7. The method of claim 6, wherein in the formula (19), D x is a diagonal matrix defined as
Representing Kronecker product, based on the "simple" - "projection" property, introducing an auxiliary variable x=z, splitting the formula (17), allowing all sub-formulas in the ADMM to iterate allowing a closed form solution,
Where iota c (z) is the indicator function of set C, as follows:
The augmented lagrangian function of equation (20) is:
where ρ > 0 is a penalty parameter and λ is the Lagrangian multiplier of the equation constraint x=z.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011135492.7A CN112285701B (en) | 2020-10-22 | 2020-10-22 | Error correction method for three-dimensional networking radar system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011135492.7A CN112285701B (en) | 2020-10-22 | 2020-10-22 | Error correction method for three-dimensional networking radar system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112285701A CN112285701A (en) | 2021-01-29 |
| CN112285701B true CN112285701B (en) | 2024-05-10 |
Family
ID=74423508
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202011135492.7A Active CN112285701B (en) | 2020-10-22 | 2020-10-22 | Error correction method for three-dimensional networking radar system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112285701B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116156445A (en) * | 2023-01-04 | 2023-05-23 | 西安电子科技大学 | Error correction method for multi-sensor network system under general sense integrated background |
Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103344946A (en) * | 2013-07-08 | 2013-10-09 | 杭州电子科技大学 | Foundation radar and aerial mobile platform radar real-time error registering method |
| CN103364767A (en) * | 2013-07-08 | 2013-10-23 | 杭州电子科技大学 | Space-time registration method of ground radar and mobile platform radar |
| CN103760556A (en) * | 2014-01-23 | 2014-04-30 | 西安电子科技大学 | Multi-target cognitive tracking method based on concentrated type MIMO radar |
| EP2843439A1 (en) * | 2013-07-26 | 2015-03-04 | Deutsches Zentrum für Luft- und Raumfahrt e.V. | Method for correcting the time and phase references of asynchronous SAR data |
| CN105353359A (en) * | 2015-10-30 | 2016-02-24 | 西安电子科技大学 | Asynchronous netted radar system error correction method |
| CN107315171A (en) * | 2017-07-02 | 2017-11-03 | 中国航空工业集团公司雷华电子技术研究所 | A kind of radar network composite dbjective state and systematic error Combined estimator algorithm |
| CN107390191A (en) * | 2017-05-23 | 2017-11-24 | 中国民航大学 | A kind of ECEF coordinate systems lower probability assumes density filtering radar space error method for registering |
| JP2018146351A (en) * | 2017-03-03 | 2018-09-20 | 株式会社東芝 | Multisensor system, sensor bias estimation device, sensor bias estimation method, and sensor bias estimation program |
| CN109782240A (en) * | 2019-01-25 | 2019-05-21 | 北京电子工程总体研究所 | One kind being based on the modified multisensor syste error registration method of recursion and system |
| CN110058205A (en) * | 2019-05-24 | 2019-07-26 | 中国人民解放军陆军炮兵防空兵学院郑州校区 | A kind of surveillance radar element error calibration method based on iteration closest approach algorithm |
-
2020
- 2020-10-22 CN CN202011135492.7A patent/CN112285701B/en active Active
Patent Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103344946A (en) * | 2013-07-08 | 2013-10-09 | 杭州电子科技大学 | Foundation radar and aerial mobile platform radar real-time error registering method |
| CN103364767A (en) * | 2013-07-08 | 2013-10-23 | 杭州电子科技大学 | Space-time registration method of ground radar and mobile platform radar |
| EP2843439A1 (en) * | 2013-07-26 | 2015-03-04 | Deutsches Zentrum für Luft- und Raumfahrt e.V. | Method for correcting the time and phase references of asynchronous SAR data |
| CN103760556A (en) * | 2014-01-23 | 2014-04-30 | 西安电子科技大学 | Multi-target cognitive tracking method based on concentrated type MIMO radar |
| CN105353359A (en) * | 2015-10-30 | 2016-02-24 | 西安电子科技大学 | Asynchronous netted radar system error correction method |
| JP2018146351A (en) * | 2017-03-03 | 2018-09-20 | 株式会社東芝 | Multisensor system, sensor bias estimation device, sensor bias estimation method, and sensor bias estimation program |
| CN107390191A (en) * | 2017-05-23 | 2017-11-24 | 中国民航大学 | A kind of ECEF coordinate systems lower probability assumes density filtering radar space error method for registering |
| CN107315171A (en) * | 2017-07-02 | 2017-11-03 | 中国航空工业集团公司雷华电子技术研究所 | A kind of radar network composite dbjective state and systematic error Combined estimator algorithm |
| CN109782240A (en) * | 2019-01-25 | 2019-05-21 | 北京电子工程总体研究所 | One kind being based on the modified multisensor syste error registration method of recursion and system |
| CN110058205A (en) * | 2019-05-24 | 2019-07-26 | 中国人民解放军陆军炮兵防空兵学院郑州校区 | A kind of surveillance radar element error calibration method based on iteration closest approach algorithm |
Non-Patent Citations (12)
| Title |
|---|
| 3D asynchronous multisensor target tracking performance with bias compensation;Man Ying 等;2010 2nd International Conference on Computer Engineering and Technology;全文 * |
| A two-stage optimization approach to the asynchronous multi-sensor registration problem;Wenqiang Pu 等;2017 IEEE International Conference on Acoustics, Speech and Signal Processing(ICASSP);全文 * |
| Asynchronous multi-sensor bias estimation with sensor location uncertainty;Suo Xiaofeng 等;2009 Chinese Control and Decision Conference;全文 * |
| optimal asynchronous multi-sensor registration in 3 dimensions;Shunan Jiang 等;2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP);第81-85页 * |
| Optimal estimation of sensor biases for asynchronous multi-sensor data fusion;Pu, WQ 等;MATHEMATICAL PROGRAMMING;全文 * |
| 一种基于合作目标的机动雷达误差配准技术;李润泽;邱火旺;远留会;;舰船电子工程(第07期);全文 * |
| 两坐标雷达组网中目标高度与系统误差联合估计;朱洪伟;何友;;系统工程与电子技术(第09期);全文 * |
| 基于混合遗传算法的雷达组网空间误差估计;卢彦飞;晏靖靖;王子润;丘恺彬;;现代雷达(第03期);全文 * |
| 多站雷达点迹航迹融合方法与仿真研究;郭邦;中国优秀硕士学位论文全文数据库 信息科技辑;全文 * |
| 异步网络的多维测量融合定位方法研究;陆康丽;中国优秀硕士学位论文全文数据库 信息科技辑;全文 * |
| 网络化作战系统中的多雷达时空数据配准;朱蕊;宋建光;;现代防御技术(第02期);全文 * |
| 雷达时差和系统误差的联合估计方法;吴泽民;任姝婕;;兵工学报(第07期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112285701A (en) | 2021-01-29 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107315171B (en) | Radar networking target state and system error joint estimation algorithm | |
| CN108896047B (en) | Distributed sensor network collaborative fusion and sensor position correction method | |
| CN111178385A (en) | Target tracking method for robust online multi-sensor fusion | |
| CN109917333B (en) | Passive positioning method integrating AOA observed quantity and TDOA observed quantity | |
| CN107592671B (en) | Networked multi-agent active variable topology autonomous cooperative positioning method | |
| CN103344946B (en) | Foundation radar and aerial mobile platform radar real-time error registering method | |
| Ahmad et al. | An online scalable approach to unified multirobot cooperative localization and object tracking | |
| CN110231620B (en) | Noise-related system tracking filtering method | |
| CN107576932B (en) | Alternating Kalman spatial registration method for coexistence of cooperative target and non-cooperative target | |
| CN111181529A (en) | Smooth constraint extended Kalman filtering method applied to nonlinear Gaussian model | |
| Xie et al. | An improved algorithm based on particle filter for 3D UAV target tracking | |
| CN112285701B (en) | Error correction method for three-dimensional networking radar system | |
| CN112163052B (en) | Multi-sensor space registration method under information deficiency measurement | |
| CN105353359B (en) | Asynchronous radar network systematic error correction method | |
| CN110133586A (en) | TOA combined synchronization and localization method based on linearity correction | |
| CN104535963B (en) | Cooperative target positioning achievement method of multiple mobile nodes based on distance measurement | |
| CN110426689B (en) | Airborne multi-platform multi-sensor system error registration algorithm based on EM-CKS | |
| CN116156445A (en) | Error correction method for multi-sensor network system under general sense integrated background | |
| Han et al. | A multi-platform cooperative localization method based on dead reckoning and particle filtering | |
| Chen | The SLAM algorithm for multiple robots based on parameter estimation | |
| CN112346032B (en) | Single infrared sensor target orbit determination method based on consistency extended Kalman filtering | |
| CN110595470A (en) | Pure orientation target tracking method based on external bounding ellipsoid collective estimation | |
| CN115615456A (en) | Sensor error registration method and device based on iteration nearest integer point set | |
| Lee et al. | An improved algorithm of UKF-SLAM based on RBF neural network adaptive robot | |
| CN112285697A (en) | Multi-sensor multi-target space-time deviation calibration and fusion method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |