CN102707268A

CN102707268A - Movable radar networking batch-processing type error register

Info

Publication number: CN102707268A
Application number: CN2012101755048A
Authority: CN
Inventors: 何友; 崔亚奇; 熊伟; 王国宏; 董云龙; 王海鹏
Original assignee: Naval Aeronautical University
Current assignee: Naval Aeronautical University
Priority date: 2012-05-23
Filing date: 2012-05-23
Publication date: 2012-10-03

Abstract

The invention discloses a mobile radar network batch processing type error registration device, which belongs to the field of radar data processing. The assumptions and constructed models of the existing mobile radar network error registration technology do not meet the requirements of the actual engineering background, and neither systematically and comprehensively model and solve the mobile radar network error registration problem, and the usability is poor. The invention relates to a batch processing algorithm for measurement, and finally obtains a convergent system error estimate by recursively optimizing the system error along the maximum gradient of the disturbance. The error registerer does not constrain the distance between radars, does not need to use the prior knowledge of fixed reference points, and has fast estimation convergence speed and high accuracy, which has the value of popularization and application.

Description

Batch error registerer for mobile radar network

一、技术领域 1. Technical field

本发明属于多传感器组网融合数据处理技术中的误差配准领域，适用于舰载雷达、机载雷达等机动平台雷达间的组网系统。 The invention belongs to the field of error registration in multi-sensor network fusion data processing technology, and is suitable for a network system between mobile platform radars such as shipboard radars and airborne radars. the

二、背景技术 2. Background technology

机动平台是雷达在实际作战运用中的重要载体，机动雷达网是一种典型的多传感器系统组网模式。在多传感器组网系统中，如何对各传感器的系统误差进行有效的配准和补偿，是其核心关键技术之一。 The mobile platform is an important carrier of radar in actual combat, and the mobile radar network is a typical multi-sensor system networking mode. In a multi-sensor networking system, how to effectively register and compensate the system errors of each sensor is one of the core key technologies. the

目前，关于机动雷达网误差配准技术的研究比较少。Helmick利用卡尔曼滤波技术实现了机动雷达量测和姿态角误差的实时估计，但算法是在假设机动雷达之间距离很近时给出的，只适用于同一机动平台多雷达的误差配准问题。Kastella通过解耦的方式实现了移动平台定位误差的估计，但需要利用固定参考点的先验知识。实际中，机动雷达网主要是由跨平台、大距离范围内分布的雷达构成的，主要包含量测和姿态角系统误差，而在现有机动雷达网误差配准技术中，算法的假设和构建的模型都不符合实际工程背景要求，都没有系统、全面地对机动雷达网误差配准问题进行建模和求解。 At present, there are relatively few studies on the error registration technology of mobile radar networks. Helmick uses the Kalman filter technology to realize the real-time estimation of the maneuvering radar measurement and attitude angle error, but the algorithm is given when the distance between the maneuvering radars is assumed to be very close, and it is only applicable to the error registration problem of multiple radars on the same maneuvering platform . Kastella realizes the estimation of the positioning error of the mobile platform through decoupling, but it needs to use the prior knowledge of the fixed reference point. In practice, the mobile radar network is mainly composed of cross-platform radars distributed over a large distance, mainly including measurement and attitude angle system errors. In the existing mobile radar network error registration technology, the assumption and construction of the algorithm None of the models meets the requirements of the actual engineering background, and there is no systematic and comprehensive modeling and solution for the error registration problem of the mobile radar network. the

三、发明内容 3. Contents of the invention

1.要解决的技术问题 1. Technical problems to be solved

本发明的目的在于提供一种用于机动雷达组网的批处理式误差配准器。该误差配准器利用多机动雷达对处于公共探测区域内非合作目标的量测，根据雷达量测值在目标状态空间的投影和系统误差的扰动数学关系，采用批处理式的算法结构，通过对系统误差和目标状态进行期望最大化递归优化，实现对系统误差的配准，并最终得到消除系统误差后的目标状态融合估计。该误差配准器不对雷达间的距离进行约束，不需要利用固定参考点的先验知识，且估计收敛速度快、精度高，因而应用范围广，实用性较强。 The object of the present invention is to provide a batch-processing error registerer for mobile radar networking. The error registerer uses multi-mobile radars to measure non-cooperative targets in the common detection area. According to the projection of radar measurement values in the target state space and the perturbation mathematical relationship of system errors, it adopts a batch-processing algorithm structure. The expectation maximization recursive optimization is performed on the system error and the target state to realize the registration of the system error, and finally obtain the fusion estimation of the target state after the system error is eliminated. The error registerer does not constrain the distance between radars, does not need to use prior knowledge of fixed reference points, and has a fast convergence speed and high precision, so it has a wide range of applications and strong practicability. the

2.技术方案 2. Technical solution

本发明所述的用于机动雷达组网的批处理式误差配准器，包括以下技术措施：首先根据各雷达包含系统误差的量测方程，利用已经得到的系统误差估计(假设系统误差的初始估计为零)，把各雷达所有时刻的量测投影到目标状态空间中，得到各雷达的目标状态估计，然后根据所有雷达同一时刻目标状态估计和系统误差的扰动数学关系，利用所有雷达所有时刻的目标状态估计对已经得到的系统误差估计进行修正，进一步得到优化后的系统误差估计，最后根据设置的阈值，对系统误差估计的收敛性进行判断：如果没有收敛，继续上述过程；如果收敛，输出系统误差的估计，并利用系统误差的估计对所有雷达所有时刻的目标状态估计进行修正和融合，最终输出目标状态的估计。 The batch-processing error registration device for mobile radar networking according to the present invention includes the following technical measures: firstly, according to the measurement equations that each radar contains system errors, the system error estimates that have been obtained are used (assuming the initial value of the system errors) is estimated to be zero), project the measurement of each radar at all times into the target state space, and obtain the target state estimation of each radar, and then according to the perturbation mathematical relationship between the target state estimation and system error of all radars at the same time, use The target state estimation corrects the already obtained system error estimate, further obtains the optimized system error estimate, and finally judges the convergence of the system error estimate according to the set threshold: if there is no convergence, continue the above process; if it converges, Output the estimate of the system error, and use the estimate of the system error to correct and fuse the target state estimates of all radars at all times, and finally output the target state estimate. the

3.有益效果 3. Beneficial effects

本发明相比背景技术具有如下的优点： Compared with background technology, the present invention has the following advantages:

(1)在满足可观测性条件下，该误差配准器可对具有任意位置关系的雷达进行配准； (1) Under the condition of observability, the error registerer can register the radar with any positional relationship;

(2)该误差配准器可对雷达量测和姿态角系统误差进行估计，且估计精度高，收敛速度快； (2) The error registerer can estimate the system error of radar measurement and attitude angle, and has high estimation accuracy and fast convergence speed;

(3)该误差配准器可得到融合所有雷达量测信息的目标状态估计。 (3) The error registerer can obtain the target state estimation fused with all radar measurement information. the

四、附图说明 4. Description of drawings

图1为本发明的实施原理流程图。 Fig. 1 is the flow chart of the implementation principle of the present invention. the

五、具体实施方式 5. Specific implementation

以下结合说明书附图对本发明作进一步详细描述。参照说明书附图，本发明的具体实施方式分以下几个步骤： The present invention will be described in further detail below in conjunction with the accompanying drawings. With reference to the accompanying drawings in the description, the specific implementation of the present invention is divided into the following steps:

(1)组网系统由n部三维机动雷达i(i＝1，2，...，n)组成，雷达i存在距离误差

方位角误差

俯仰角误差

偏航角误差

纵摇角误差

和横摇角误差且它们都是常量加性误差。在k时刻，雷达i在地球直角坐标系中的坐标为x_is(k)＝[x_is(k)，y_is(k)，z_is(k)]′，对应的地理坐标为x_isp(k)＝[L_i(k)，B_i(k)，H_i(k)]′，其机动载体平台包含误差的姿态角为

。根据载体坐标系、NED坐标系和地球直角坐标系之间的变换关系，机动雷达组网系统存在系统误差的量测方程可表示为 (1) The networking system is composed of n three-dimensional mobile radars i (i=1, 2, ..., n), and the radar i has a distance error

Azimuth error

pitch angle error

Yaw angle error

pitch angle error

and roll angle error And they are all constant additive errors. At time k, the coordinates of radar i in the Earth's Cartesian coordinate system are x _is (k)=[x _is (k), y _is (k), z _is (k)] ', and the corresponding geographic coordinates are x _isp ( k)=[L _i (k), B _i (k), H _i (k)]′, the attitude angle of the mobile carrier platform including error is

. According to the transformation relationship between the carrier coordinate system, the NED coordinate system and the earth's Cartesian coordinate system, the measurement equation for the systematic error of the mobile radar networking system can be expressed as

z(k)＝h(g(x(k)，b^z))+b^l+w (1) z(k)=h(g(x(k), b ^z ))+b ^l +w (1)

其中z(k)＝[z₁(k)′，z₂(k)′，...，z_n(k)′]′为组网系统在k时刻的量测向量；

为系统的量测系统误差向量；

为系统的姿态角系统误差向量；w＝[w₁′，w₂′，...，w_n′]′为系统的高斯白色量测噪声，w_i为雷达i的量测噪声，其协方差

为

且不同雷达w_i之间相互独立；h(g)＝[h₁(g₁)′，h₂(g₂)′，...，h_n(g_n)′]′为系统在地球直角坐标系中对目标状态x(k)的量测函数， Where z(k)=[z ₁ (k)', z ₂ (k)', ..., z _n (k)']' is the measurement vector of the networking system at time k;

is the measurement system error vector of the system;

is the attitude angle system error vector of the system; w=[w ₁ ′, w ₂ ′,...,w _n ′]′ is the Gaussian white measurement noise of the system, w _i is the measurement noise of radar i, and its correlation variance

for

And different radars w _i are independent of each other; h(g)=[h ₁ (g ₁ )′, h ₂ (g ₂ )′,..., h _n (g _n )′]′ is the system at right angles to the earth The measurement function of the target state x(k) in the coordinate system,

${g g}_{i i} ((x x ((k k)),, {b b}_{i i}^{z z})) = = {x x}_{il il} ((k k)) = = [\begin{matrix} {u u}_{i i} ((k k)) \\ {s the s}_{i i} ((k k)) \\ {m m}_{i i} ((k k)) \end{matrix}] = = {A A}^{- - 11} (({v v}_{i i} ((k k)) - - {b b}_{i i}^{z z})) {T T}^{- - 11} (({x x}_{isp isp} ((k k)))) ((x x ((k k)) - - {x x}_{is is} ((k k)))) - - - - - - ((22))$

${h h}_{i i} (({x x}_{il il} ((k k)))) = = [\begin{matrix} \sqrt{{u u}_{i i} {((k k))}^{22} + + {s the s}_{i i} {((k k))}^{22} + + {m m}_{i i} {((k k))}^{22}} \\ arctan arctan ((\frac{{s the s}_{i i} ((k k))}{{u u}_{i i} ((k k))})) \\ arctan arctan ((\frac{{m m}_{i i} ((k k))}{\sqrt{{u u}_{i i} {((k k))}^{22} + + {s the s}_{i i} {((k k))}^{22}}})) \end{matrix}] - - - - - - ((33))$

${A A}_{pitch pitch} ((φ φ)) = = [\begin{matrix} 11 & 00 & 00 \\ 00 & cos cos φ φ & sin sin φ φ \\ 00 & - - sin sin φ φ & cos cos φ φ \end{matrix}] - - - - - - ((66))$

${A A}_{roll roll} ((α α)) = = [\begin{matrix} cos cos α α & 00 & - - sin sin α α \\ 00 & 11 & 00 \\ sin sin α α & 00 & cos cos α α \end{matrix}] - - - - - - ((77))$

${T T}^{- - 11} (({x x}_{isp isp} ((k k)))) = = {T T}^{' '} (({x x}_{isp isp} ((k k)))) = = {[\begin{matrix} - - sin sin {L L}_{i i} ((k k)) & - - sin sin {B B}_{i i} ((k k)) cos cos {L L}_{i i} ((k k)) & cos cos {B B}_{i i} ((k k)) cos cos {L L}_{i i} ((k k)) \\ cos cos {L L}_{i i} ((k k)) & - - sin sin {B B}_{i i} ((k k)) sin sin {L L}_{i i} ((k k)) & cos cos {B B}_{i i} ((k k)) sin sin {L L}_{i i} ((k k)) \\ 00 & cos cos {B B}_{i i} ((k k)) & sin sin {B B}_{i i} ((k k)) \end{matrix}]}^{' '} - - - - - - ((99))$

(2)根据式(1)，利用雷达的量测和系统误差的当前估计值 (如果还未进行系统误差估计，设

计算所有雷达所有时刻的量测z_i(k)在目标状态空间中的投影

(2) According to Equation (1), using radar measurements and the current estimate of the system error (If no systematic error estimation has been performed, set

Calculate the projection of the measurement z _i (k) on the target state space for all radars at all times

${\overset{^^}{x x}}_{i i} ((k k)) = = T T (({x x}_{isp isp} ((k k)))) A A (({v v}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{z z})) {h h}_{i i}^{- - 11} (({z z}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{l l})) + + {x x}_{is is} ((k k)) - - - - - - ((1010))$

其中 in

${h h}_{i i}^{- - 11} (({z z}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{l l})) = = [\begin{matrix} (({r r}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{r r})) cos cos (({θ θ}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{θ θ})) cos cos (({η η}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{η η})) \\ (({r r}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{r r})) sin sin (({θ θ}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{θ θ})) cos cos (({η η}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{η η})) \\ (({r r}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{r r})) sin sin (({η η}_{i i} ((k k)) - - {\overset{^^}{b b}}_{i i 00}^{η η})) \end{matrix}] - - - - - - ((1111))$

(3)利用已经得到的系统误差估计

和各雷达的目标状态估计

按照复合函数的求导公式，近似计算h_i(·)关于x(k)的雅可比矩阵H_ix(k)、关于

的雅可比矩阵

其中令R(k)＝u_i(k)²+s_i(k)²+m_i(k)²、R′(k)＝u_i(k)²+s_i(k)²、

x′_k＝x(k)-x_is(k) (3) Using the already obtained systematic error estimation

and target state estimation for each radar

According to the derivation formula of the composite function, the Jacobian matrix H _ix (k) of h _i (·) about x(k), about

The Jacobian matrix of

where R(k)=u _i (k) ² +s _i (k) ² +m _i (k) ² , R′(k)=u _i (k) ² +s _i (k) ² ,

x′ _k ＝x(k)-x _is (k)

${H h}_{ix ix} ((k k)) = = [\begin{matrix} \frac{{u u}_{i i} ((k k))}{\sqrt{R R}} & \frac{{s the s}_{i i} ((k k))}{\sqrt{R R}} & \frac{{m m}_{i i} ((k k))}{\sqrt{R R}} \\ \frac{- - {s the s}_{i i} ((k k))}{\sqrt{{R R}^{' '} ((k k))}} & \frac{{u u}_{i i} ((k k))}{\sqrt{{R R}^{' '} ((k k))}} & 00 \\ \frac{- - {u u}_{i i} ((k k)) {m m}_{i i} ((k k))}{R R \sqrt{{R R}^{' '} ((k k))}} & \frac{- - {s the s}_{i i} ((k k)) {m m}_{i i} ((k k))}{R R \sqrt{{R R}^{' '} ((k k))}} & \frac{{u u}_{i i}^{22} ((k k)) + + {s the s}_{i i}^{22} ((k k))}{R R \sqrt{{R R}^{' '} ((k k))}} \end{matrix}] A A {(({v v}_{i i} ((k k)) - - {b b}_{i i}^{z z}))}^{- - 11} T T {(({x x}_{isp isp} ((k k))))}^{- - 11} - - - - - - ((1212))$

(4)根据雷达的量测方程，可得系统误差和目标状态的扰动关系为 (4) According to the measurement equation of the radar, the disturbance relationship between the system error and the target state can be obtained as

X(k)≈X₀(k)-Q(k)b (14) X(k)≈X ₀ (k)-Q(k)b (14)

其中 $X_{0} (k) = {\hat{X}}_{0} (k) + Q (k) {\hat{b}}_{0},$ ${\hat{X}}_{0} (k) = {[{\hat{x}}_{1} {(k)}^{'}, {\hat{x}}_{2} {(k)}^{'}, . . ., {\hat{x}}_{n} {(k)}^{'}]}^{'},$ Q(k)由下式求出 in $x_{0} (k) = {\hat{x}}_{0} (k) + Q (k) {\hat{b}}_{0},$ ${\hat{x}}_{0} (k) = {[{\hat{x}}_{1} {(k)}^{'}, {\hat{x}}_{2} {(k)}^{'}, . . ., {\hat{x}}_{no} {(k)}^{'}]}^{'},$ Q(k) is obtained by the following formula

${H h}_{i i}^{- - L L} = = [[{H h}_{ix ix}^{- - L L},, {H h}_{ix ix}^{- - L L} {H h}_{{ib ib}^{z z}}]] - - - - - - ((1515))$

$Q Q ((k k)) = = block block - - diag diag (({H h}_{11}^{- - L L} ((k k)),, {H h}_{22}^{- - L L} ((k k)),, . . . . . .,, {H h}_{n no}^{- - L L} ((k k)))) - - - - - - ((1616))$

(5)根据扰动方程(14)和目标状态的最大似然估计方程，可求出系统误差的最大似然估计为 (5) According to the disturbance equation (14) and the maximum likelihood estimation equation of the target state, the maximum likelihood estimation of the system error can be obtained as

$\overset{^^}{b b} = = {[[{Σ Σ}_{k k = = 11}^{N N} {Q Q}^{' '} ((k k)) {Σ Σ}^{- - 11} ((k k)) Q Q ((k k))]]}^{- - 11} [[{Σ Σ}_{k k = = 11}^{N N} {Q Q}^{' '} ((k k)) {Σ Σ}^{- - 11} ((k k)) {X x}_{00} ((k k))]] - - - - - - ((1717))$

其中 in

${Σ Σ}^{- - 11} ((k k)) = = block block - - diag diag (({Σ Σ}_{{x x}_{11}}^{- - 11} ((k k)),, {Σ Σ}_{{x x}_{22}}^{- - 11} ((k k)),, . . . . . .,, {Σ Σ}_{{x x}_{n no}}^{- - 11} ((k k)))) - - [[{{{Σ Σ}_{{x x}_{i i}}^{- - 11} ((k k)) {[[{Σ Σ}_{i i = = 11}^{n no} {Σ Σ}_{{x x}_{i i}}^{- - 11} ((k k))]]}^{- - 11} {Σ Σ}_{{x x}_{j j}}^{- - 11} ((k k))}}_{ij ij}]] - - - - - - ((1818))$

${Σ Σ}_{{x x}_{i i}}^{- - 11} ((k k)) = = {H h}_{ix ix} {((k k))}^{' '} {Σ Σ}_{{z z}_{i i}}^{- - 11} {H h}_{ix ix} ((k k)) - - - - - - ((1919))$

(6)根据

判定估计值

是否收敛，其中||·||表示某种向量范数，可以自行选取， ε表示接受门限。如果估计值

已收敛，继续向下执行，否则令

然后重新从步骤(2)向下执行。 (6) According to

judgment estimate

Convergence or not, where ||·|| represents a certain vector norm, which can be selected by yourself, and ε represents the acceptance threshold. if estimated value

has converged, continue to execute downward, otherwise let

Then re-execute from step (2).

(7)利用系统误差的收敛估计

和相应的Q(k)、X₀(k)，带入到式(14)，计算目标状态的去偏估计

并根据多雷达目标状态的融合方程，进一步求取融合估计

(7) Convergence estimation using systematic error

and the corresponding Q(k), X ₀ (k), put them into formula (14), and calculate the debiased estimate of the target state

And according to the fusion equation of the multi-radar target state, the fusion estimation is further obtained

$\hat{x} (k) = {[Σ_{i = 1}^{n} Σ_{x_{i}}^{- 1} (k)]}^{- 1} [Σ_{i = 1}^{n} Σ_{x_{i}}^{- 1} (k) {\hat{x}}_{i} (k)] - - - (20)$ 。 $\hat{x} (k) = {[Σ_{i = 1}^{no} Σ_{x_{i}}^{- 1} (k)]}^{- 1} [Σ_{i = 1}^{no} Σ_{x_{i}}^{- 1} (k) {\hat{x}}_{i} (k)] - - - (20)$ .

Claims

1. be used for mobile radar networking batch processing formula error registration device, it is characterized in that:

(1) mobile radar measures at the dbjective state space projection;

(2) utilize linear approximate relationship between measurement equation establishing target state disturbance quantity and the systematic error disturbance quantity.

2. the mobile radar networking batch processing formula error registration device that is used for as claimed in claim 1; It is characterized in that said mobile radar measures at the dbjective state space projection; Performing step is: based on mobile radar at the measurement equation of earth rectangular coordinate system to dbjective state; Under the condition that obtains the systematic error estimation, can obtain mobile radar and measure z _i(k) at the dbjective state space projection

For

{\hat{x}}_{i} (k) = T (x_{isp} (k)) A (v_{i} (k) - {\hat{b}}_{i 0}^{z}) h_{i}^{- 1} (z_{i} (k) - {\hat{b}}_{i 0}^{l}) + x_{is} (k)

V wherein _i(k) be the attitude angle measurement of mobile radar;

Be respectively the radar measurement and the attitude angle systematic error that have obtained and estimate component; x _Is(k), x _Isp(k) be respectively the coordinate of mobile radar in earth rectangular coordinate system and geographic coordinate system;

Be respectively carrier coordinate system and be tied to the rotation matrix of earth rectangular coordinate system conversion to NED coordinate system and NED.

3. the mobile radar networking batch processing formula error registration device that is used for as claimed in claim 1; It is characterized in that the said linear approximate relationship that utilizes between measurement equation establishing target state disturbance quantity and the systematic error disturbance quantity; Performing step is: to the measurement equation of mobile radar about dbjective state; Carry out small sample perturbations at systematic error b and dbjective state X (k) direction, and adopt the linearization approximation technique to launch, the perturbation equation that can get systematic error and dbjective state does

X(k)≈X ₀(k)-Q(k)b

Wherein

measures the vector at the dbjective state space projection constantly for all radar k;

is that the systematic error before this recurrence estimates that Q (k) is a perturbation matrix.