CN113324546B - Robust filtering method for self-adaptive adjustment of multi-submersible cooperative positioning under compass failure - Google Patents

Robust filtering method for self-adaptive adjustment of multi-submersible cooperative positioning under compass failure Download PDF

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CN113324546B
CN113324546B CN202110563429.1A CN202110563429A CN113324546B CN 113324546 B CN113324546 B CN 113324546B CN 202110563429 A CN202110563429 A CN 202110563429A CN 113324546 B CN113324546 B CN 113324546B
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徐博
王潇雨
赵玉新
吴磊
郭瑜
王朝阳
陈崇
余志强
费亚林
国运鹏
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Abstract

The invention provides a multi-underwater vehicle collaborative positioning self-adaptive regulation robust filtering method under compass failure, which comprises the following steps: the method comprises the following steps: establishing a multi-underwater vehicle co-location model with unknown course angle; step two: calculating a heading angle input unknown state estimation value to be corrected; step three: the influence of outlier noise on state estimation is weakened by adaptively updating a measurement noise variance matrix; step four: constructing a nuclear band width self-adaptive adjustment factor; step five: and calculating a course estimation value and a corrected position vector estimation value. The method realizes accurate positioning under the condition that the course angle is unknown along with non-Gaussian noise on the basis of ensuring that the state dimension is not expanded. The method can be used in the field of multi-underwater vehicle co-location under non-ideal conditions.

Description

罗经失效下的多潜航器协同定位自适应调节鲁棒滤波方法Robust filtering method for self-adaptive adjustment of multi-submersible cooperative positioning under compass failure

技术领域technical field

本发明属于非理想条件下的多潜航器协同定位领域，涉及一种罗经失效下的多潜航器协同定位自适应调节鲁棒滤波方法。The invention belongs to the field of multi-submersible cooperative positioning under non-ideal conditions, and relates to a multi-submersible cooperative positioning adaptive adjustment robust filtering method under compass failure.

背景技术Background technique

协同定位是目前中间层区域多潜航器最有效的导航方法之一。然而，协同系统的定位性能经常受多种因素的制约，在协同定位过程中，一个重要的问题是如何在非理想条件下对潜航器的位置进行估计。多潜航器协同定位系统是一个非线性系统，当其航向信息缺失伴随噪声非高斯分布时，将对定位精度产生极大的影响。罗经的电路结构复杂，低成本罗经的使用也会造成故障出现概率的增大。一般情况下，当罗经失效时，通常采用扩展状态维数的方法来估计航向角，然而，计算量将随之增加，特别是当未知故障向量维数与系统状态维数相当时，计算代价更大。针对维数问题，二阶扩展卡尔曼滤波、二阶无迹卡尔曼滤波相继被提出，但其受限于故障向量的统计模型未知且不适用于噪声呈非高斯分布的环境。Co-localization is currently one of the most effective navigation methods for multiple submersibles in the mesosphere. However, the positioning performance of the cooperative system is often restricted by many factors. In the process of cooperative positioning, an important issue is how to estimate the position of the underwater vehicle under non-ideal conditions. The multi-submersible cooperative positioning system is a nonlinear system. When the heading information is missing and the noise is non-Gaussian distribution, it will have a great impact on the positioning accuracy. The circuit structure of the compass is complicated, and the use of low-cost compass will also increase the probability of failure. In general, when the compass fails, the method of expanding the state dimension is usually used to estimate the heading angle, however, the amount of calculation will increase accordingly, especially when the dimension of the unknown fault vector is equivalent to the dimension of the system state, the calculation cost is even higher big. For the problem of dimensionality, the second-order extended Kalman filter and the second-order unscented Kalman filter have been proposed, but they are limited by the unknown statistical model of the fault vector and are not suitable for environments with non-Gaussian noise distribution.

因此，探讨罗经失效与非高斯噪声对协同定位系统定位精度的影响机理，考虑如何在不扩展状态维数且克服非高斯噪声干扰的前提下对实时变化的航向角进行估计，是协同定位方向需要解决的技术问题。Therefore, it is necessary to discuss the influence mechanism of compass failure and non-Gaussian noise on the positioning accuracy of the collaborative positioning system, and consider how to estimate the real-time changing heading angle without expanding the state dimension and overcoming the interference of non-Gaussian noise. Solved technical problems.

发明内容Contents of the invention

针对上述现有技术，本发明要解决的技术问题是提供一种在不扩展状态维数且航向噪声序列未知的前提下、在克服非高斯噪声干扰的同时对变化的航向角进行实时估计的罗经失效下的多潜航器协同定位自适应调节鲁棒滤波方法，以提高协同定位精度。Aiming at the above-mentioned prior art, the technical problem to be solved by the present invention is to provide a compass that can estimate the changing heading angle in real time while overcoming the non-Gaussian noise interference under the premise that the state dimension is not expanded and the heading noise sequence is unknown. Co-localization of multi-submersible vehicles under failure Adaptive adjustment robust filtering method to improve co-location accuracy.

为解决上述技术问题，本发明的一种罗经失效下的多潜航器协同定位自适应调节鲁棒滤波方法，包括以下步骤：In order to solve the above technical problems, a multi-submersible cooperative positioning adaptive adjustment robust filtering method under the failure of the compass of the present invention comprises the following steps:

步骤一：建立航向角未知的多潜航器协同定位模型；Step 1: Establish a multi-submersible cooperative positioning model with unknown heading angle;

步骤二：计算航向角输入未知的待校正状态估计值；Step 2: Calculate the estimated value of the state to be corrected whose heading angle input is unknown;

步骤三：通过自适应更新量测噪声方差矩阵削弱野值噪声对状态估计的影响；Step 3: Weaken the influence of outlier noise on state estimation by adaptively updating the measurement noise variance matrix;

步骤四：构建核带宽度自适应调节因子；Step 4: Construct the kernel bandwidth adaptive adjustment factor;

步骤五：计算航向估计值与校正后的位置向量估计值。Step 5: Calculating the heading estimate and the corrected position vector estimate.

本发明还包括：The present invention also includes:

1.步骤一中建立航向角未知的多潜航器协同定位模型具体为：1. In step 1, the multi-submersible cooperative positioning model with unknown heading angle is established as follows:

状态方程与量测方程如下：The state equation and measurement equation are as follows:

Figure BDA0003079966230000021
Figure BDA0003079966230000021

Figure BDA0003079966230000022
Figure BDA0003079966230000022

式中ak和bk分别为随从潜航器k时刻的东向与北向位置，Δt为采样周期，va,k,vb,k为随从潜航器k时刻的右向与前向速度，θk为k时刻前向与北向的夹角，wa,k,wb,k为零均值高斯白噪声，Zk为领航潜航器与随从潜航器间的相对距离量测信息，

Figure BDA0003079966230000023
为领航潜航器k时刻的位置，εk为量测噪声；where a k and b k are the eastward and northward positions of the accompanying submersible at time k, respectively, Δt is the sampling period, v a,k , v b,k are the rightward and forward velocities of the following submersible at time k, θ k is the angle between forward direction and north direction at time k, w a, k , w b, k are zero-mean Gaussian white noise, Z k is the relative distance measurement information between the leading submersible and the following submersible,
Figure BDA0003079966230000023
is the position of the pilot submersible at time k, ε k is the measurement noise;

将θk作为估计变量，满足Taking θ k as an estimated variable, satisfying

Figure BDA0003079966230000024
Figure BDA0003079966230000024

式中

Figure BDA0003079966230000025
为零均值白噪声；In the formula
Figure BDA0003079966230000025
is zero-mean white noise;

离散时间状态空间模型建立具体为：The discrete-time state-space model is established specifically as follows:

Figure BDA0003079966230000026
Figure BDA0003079966230000026

Figure BDA0003079966230000027
Figure BDA0003079966230000027

式中

Figure BDA0003079966230000028
xk＝[ak bk]T为k时刻随从潜航器的位置，na＝n+1，n为xk的维数，
Figure BDA0003079966230000029
和
Figure BDA00030799662300000210
分别为非线性状态函数和量测函数，假设
Figure BDA00030799662300000211
为高斯白噪声序列，
Figure BDA00030799662300000212
且有：In the formula
Figure BDA0003079966230000028
x k =[a k b k ] T is the position of the following submersible at time k, n a =n+1, n is the dimension of x k ,
Figure BDA0003079966230000029
with
Figure BDA00030799662300000210
are the nonlinear state function and measurement function, respectively, assuming
Figure BDA00030799662300000211
is a Gaussian white noise sequence,
Figure BDA00030799662300000212
and have:

Figure BDA00030799662300000213
Figure BDA00030799662300000213

式中，uk＝[va,k vb,k]T为DVL测得的前向与右向速度，

Figure BDA00030799662300000214
为k-1时刻航向角的估计值；In the formula, u k =[v a,k v b,k ] T is the forward and right speed measured by DVL,
Figure BDA00030799662300000214
is the estimated value of heading angle at time k-1;

式中In the formula

Figure BDA00030799662300000215
Figure BDA00030799662300000215

Figure BDA00030799662300000216
Figure BDA00030799662300000216

式中，

Figure BDA00030799662300000217
为非线性状态函数。In the formula,
Figure BDA00030799662300000217
is a nonlinear state function.

2.步骤二中计算航向角输入未知的待校正状态估计值具体为：2. In step 2, the estimated value of the state to be corrected for the unknown input of the heading angle is calculated as follows:

状态估计值的误差协方差

Figure BDA0003079966230000031
可以被分解为：Error covariance of state estimates
Figure BDA0003079966230000031
can be broken down into:

Figure BDA0003079966230000032
Figure BDA0003079966230000032

式中Sk-1/k-1为

Figure BDA0003079966230000033
经过三角分解后的下三角矩阵；where S k-1/k-1 is
Figure BDA0003079966230000033
The lower triangular matrix after triangular decomposition;

容积点计算具体为：The volume point calculation is specifically:

χk-1,i＝Sk-1/k-1ρi+xk-1/k-1 χ k-1,i ＝S k-1/k-1 ρ i +x k-1/k-1

式中

Figure BDA0003079966230000034
[In]i表示n维单位矩阵In的第i列；In the formula
Figure BDA0003079966230000034
[I n ] i represents the i-th column of the n-dimensional identity matrix I n ;

容积点传播具体为：The volume point propagation is specifically:

Figure BDA0003079966230000035
Figure BDA0003079966230000035

Figure BDA0003079966230000036
Figure BDA0003079966230000036

Figure BDA0003079966230000037
Figure BDA0003079966230000037

Figure BDA0003079966230000038
Figure BDA0003079966230000038

yk/k-1,i＝hk(χk/k-1,i)y k/k-1,i ＝h k (χ k/k-1,i )

Figure BDA0003079966230000039
Figure BDA0003079966230000039

式中

Figure BDA00030799662300000310
为非线性状态函数fk-1(·)展开的采样点，
Figure BDA00030799662300000311
为状态预测值，
Figure BDA00030799662300000312
为
Figure BDA00030799662300000313
的误差协方差矩阵，χk/k-1,i为二次采样点，yk/k-1,i为非线性量测函数hk(·)展开的采样点，
Figure BDA00030799662300000314
为量测预测值，Qk为过程噪声协方差矩阵，ξi与ρi的取值方式相同。In the formula
Figure BDA00030799662300000310
is the sampling point expanded by the nonlinear state function f k-1 (·),
Figure BDA00030799662300000311
is the state prediction value,
Figure BDA00030799662300000312
for
Figure BDA00030799662300000313
The error covariance matrix of , χ k/k-1,i is the secondary sampling point, y k/k-1,i is the sampling point expanded by the nonlinear measurement function h k ( ),
Figure BDA00030799662300000314
In order to measure the predicted value, Q k is the process noise covariance matrix, and the values of ξ i and ρ i are the same.

量测更新为：Measurements updated to:

Figure BDA00030799662300000315
Figure BDA00030799662300000315

Figure BDA00030799662300000316
Figure BDA00030799662300000316

Figure BDA00030799662300000317
Figure BDA00030799662300000317

Figure BDA00030799662300000318
Figure BDA00030799662300000318

Figure BDA00030799662300000319
Figure BDA00030799662300000319

式中

Figure BDA00030799662300000320
为互协方差矩阵，
Figure BDA00030799662300000321
为量测自协方差矩阵，Rk为量测噪声协方差矩阵，Kk为增益矩阵，yk为真实量测信息，
Figure BDA0003079966230000041
分别为无航向输入时的状态估计值与误差协方差矩阵。In the formula
Figure BDA00030799662300000320
is the cross-covariance matrix,
Figure BDA00030799662300000321
is the measurement autocovariance matrix, R k is the measurement noise covariance matrix, K k is the gain matrix, y k is the real measurement information,
Figure BDA0003079966230000041
are the state estimation value and error covariance matrix when there is no heading input, respectively.

3.步骤三中通过自适应更新量测噪声方差矩阵削弱野值噪声对状态估计的影响具体为：3. In step 3, the impact of outlier noise on state estimation is weakened by adaptively updating the measurement noise variance matrix as follows:

量测噪声方差矩阵的自适应更新，即：The adaptive update of the measurement noise variance matrix, namely:

Figure BDA0003079966230000042
Figure BDA0003079966230000042

且有

Figure BDA0003079966230000043
其中TP,k|k-1与Tr,k分别为
Figure BDA0003079966230000044
与量测噪声方差阵Rk经过三角分解后的下三角矩阵；在协同定位模型中，假设系统噪声为高斯噪声，因此有：and have
Figure BDA0003079966230000043
Where T P,k|k-1 and T r,k are respectively
Figure BDA0003079966230000044
and the lower triangular matrix after the triangular decomposition of the measurement noise variance matrix R k ; in the co-location model, it is assumed that the system noise is Gaussian noise, so there are:

Figure BDA0003079966230000045
Figure BDA0003079966230000045

式中σ为核带宽度，且有：where σ is the width of the nuclear band, and there are:

ek＝ζk-Gkxk e k ＝ζ k -G k x k

式中

Figure BDA0003079966230000046
Figure BDA0003079966230000047
m为量测值的维数。In the formula
Figure BDA0003079966230000046
Figure BDA0003079966230000047
m is the dimension of the measured value.

4.步骤四中构建核带宽度自适应调节因子具体为：4. In step 4, the adaptive adjustment factor of the kernel bandwidth is constructed as follows:

新息向量定义为

Figure BDA0003079966230000048
通过新息矩阵
Figure BDA0003079966230000049
和量测误差协方差矩阵
Figure BDA00030799662300000410
构建自适应调节因子：The innovation vector is defined as
Figure BDA0003079966230000048
Via the Innovation Matrix
Figure BDA0003079966230000049
and measurement error covariance matrix
Figure BDA00030799662300000410
Build an adaptive regulator:

Figure BDA00030799662300000411
Figure BDA00030799662300000411

式中

Figure BDA00030799662300000412
当新息矩阵的迹小于等于量测误差方差矩阵的迹时，自适应因子取值为1，否则，利用构造的自适应因子对带宽σ进行实时校正，即σt＝λtσt-1，t为迭代次数。In the formula
Figure BDA00030799662300000412
When the trace of the innovation matrix is less than or equal to the trace of the measurement error variance matrix, the value of the adaptive factor is 1, otherwise, the bandwidth σ is corrected in real time by using the constructed adaptive factor, that is, σ t = λ t σ t-1 , t is the number of iterations.

5.步骤五中计算航向估计值与校正后的位置向量估计值具体为：5. The calculation of the estimated heading value and the estimated value of the corrected position vector in step five are specifically:

航向角的误差协方差矩阵为：The error covariance matrix of heading angle is:

Figure BDA00030799662300000413
Figure BDA00030799662300000413

式中

Figure BDA0003079966230000051
In the formula
Figure BDA0003079966230000051

位置与航向估计的增益矩阵分别为：The gain matrices for position and heading estimation are:

Figure BDA0003079966230000052
Figure BDA0003079966230000052

Figure BDA0003079966230000053
Figure BDA0003079966230000053

航向估计值为：The heading estimate is:

Figure BDA0003079966230000054
Figure BDA0003079966230000054

由航向角估计值校正后的位置估计与位置估计误差协方差矩阵分别为：The covariance matrices of position estimation and position estimation error corrected by the estimated value of heading angle are respectively:

Figure BDA0003079966230000055
Figure BDA0003079966230000055

Figure BDA0003079966230000056
Figure BDA0003079966230000056

式中

Figure BDA0003079966230000057
In the formula
Figure BDA0003079966230000057

本发明的有益效果：本发明同时考虑罗经失效与噪声的非高斯特性，基于U-V转换解耦思路与互相关熵理论，对航向角未知伴随非高斯噪声条件下的协同定位方法进行了研究。现有的二阶扩展卡尔曼滤波、二阶无迹卡尔曼滤波等可实现扩展状态量的解耦从而减小计算代价，但其受故障向量统计模型未知的限制，且前者并不适用于强非线性模型。另外，当噪声异常值的出现导致噪声呈现非高斯特性时，现有算法并不能做到在减小计算代价的同时克服非高斯噪声的干扰。Beneficial effects of the present invention: the present invention considers both compass failure and non-Gaussian noise characteristics, and based on U-V conversion decoupling ideas and cross-correlation entropy theory, the collaborative positioning method under the condition of unknown heading angle accompanied by non-Gaussian noise is studied. The existing second-order extended Kalman filter, second-order unscented Kalman filter, etc. can realize the decoupling of extended state quantities to reduce the calculation cost, but they are limited by the unknown fault vector statistical model, and the former is not suitable for strong nonlinear model. In addition, when the appearance of noise outliers causes the noise to exhibit non-Gaussian characteristics, the existing algorithms cannot overcome the interference of non-Gaussian noise while reducing the computational cost.

针对目前协同定位中航向角的估计需要扩展状态估计维数，导致计算代价增大，且算法不适用于非高斯噪声环境的问题，本发明在适用于强非线性模型的容积卡尔曼滤波(CKF)中引入U-V变换，完成位置估计与航向估计的解耦，同时引入最大互相关熵(MCC)理论，协助量测噪声方差矩阵在量测异常值出现时完成自适应更新。最终在保证不扩展状态维数的基础上，实现航向角未知伴随非高斯噪声条件下的准确定位。本发明可用于非理想条件下的多潜航器协同定位领域。Aiming at the problem that the estimation of the heading angle in the current co-location needs to expand the dimension of the state estimation, which leads to an increase in the calculation cost, and the algorithm is not suitable for the non-Gaussian noise environment, the present invention applies to the volumetric Kalman filter (CKF ) introduces the U-V transformation to complete the decoupling of position estimation and heading estimation, and at the same time introduces the maximum cross-correlation entropy (MCC) theory to assist the measurement noise variance matrix to complete the adaptive update when the measurement outlier occurs. Finally, on the basis of ensuring that the state dimension is not expanded, accurate positioning under the condition of unknown heading angle and non-Gaussian noise is realized. The invention can be used in the field of multi-submersible cooperative positioning under non-ideal conditions.

本发明的主要优点体现在：Main advantage of the present invention is embodied in:

本发明将航向角作为未知的输入项重构非线性系统方程，引入CKF处理非线性系统方程和测量方程，具有更高的实用价值；The present invention uses the course angle as an unknown input item to reconstruct the nonlinear system equation, introduces CKF to process the nonlinear system equation and measurement equation, and has higher practical value;

本发明通过U-V变换，采用鲁棒两级CKF估计航向角和定位信息，完成位置估计与航向估计的解耦，有效降低计算代价；The present invention uses a robust two-stage CKF to estimate the heading angle and positioning information through U-V transformation, completes the decoupling of position estimation and heading estimation, and effectively reduces the calculation cost;

本发明结合MCC方法，建立了一种基于未知输入非线性方程的递推模型，用于更新状态子滤波器的后验估计和协方差矩阵，可有效削弱非高斯噪声的干扰，针对实际场景中可能出现的问题有较好的应对方案；In combination with the MCC method, the present invention establishes a recursive model based on an unknown input nonlinear equation, which is used to update the posterior estimation and covariance matrix of the state sub-filter, which can effectively weaken the interference of non-Gaussian noise. There are better solutions for possible problems;

本发明利用新息矩阵和先验量测协方差矩阵构造自适应因子，利用自适应因子在线调整带宽，具有更高的实用价值。The invention utilizes the innovation matrix and the prior measurement covariance matrix to construct the self-adaptive factor, and uses the self-adaptive factor to adjust the bandwidth on-line, which has higher practical value.

附图说明Description of drawings

图1为协同定位相对距离信息声学通信示意图；Fig. 1 is a schematic diagram of acoustic communication of relative distance information of co-location;

图2为协同定位系统多潜航器实际航行轨迹图；Fig. 2 is the actual navigation track diagram of multi-submersible vehicles of the cooperative positioning system;

图3为协同定位过程中实际量测噪声与噪声概率分布示意图；Fig. 3 is a schematic diagram of actual measurement noise and noise probability distribution in the co-location process;

图4为定位误差比较图；Figure 4 is a comparison diagram of positioning errors;

图5为航向角估计值比较图；Fig. 5 is a comparison chart of heading angle estimates;

图6为航向角误差比较图。Figure 6 is a comparison chart of heading angle errors.

具体实施方式detailed description

下面结合附图与具体实施方式对本发明作进一步详细描述。The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

步骤一：建立航向角未知的多潜航器协同定位模型；Step 1: Establish a multi-submersible cooperative positioning model with unknown heading angle;

本发明以主-从协同定位模式为例，考虑两个领航潜航器交替为一个随从潜航器提供量测信息的经典场景。通讯示意图如附图1所示。状态方程与量测方程如下The present invention takes the master-slave cooperative positioning mode as an example, and considers a classic scenario in which two leading submersibles alternately provide measurement information for a follower submersible. The communication diagram is shown in Figure 1. The state equation and measurement equation are as follows

Figure BDA0003079966230000061
Figure BDA0003079966230000061

Figure BDA0003079966230000062
Figure BDA0003079966230000062

式中ak和bk分别为随从潜航器k时刻的东向与北向位置，Δt为采样周期，va,k,vb,k为随从潜航器k时刻的右向与前向速度，θk为k时刻前向与北向的夹角，wa,k,wb,k为零均值高斯白噪声。Zk为领航潜航器与随从潜航器间的相对距离量测信息，

Figure BDA0003079966230000063
为领航潜航器k时刻的位置，εk为量测噪声。where a k and b k are the eastward and northward positions of the accompanying submersible at time k, respectively, Δt is the sampling period, v a,k , v b,k are the rightward and forward velocities of the following submersible at time k, θ k is the angle between forward direction and north direction at time k, w a,k ,w b,k are zero-mean Gaussian white noise. Z k is the relative distance measurement information between the leading submersible and the following submersible,
Figure BDA0003079966230000063
is the position of the leading submersible at time k, and ε k is the measurement noise.

罗经电路结构复杂，特别是使用低成本罗经时，故障概率将大大增加。将θk作为估计变量，满足The structure of the compass circuit is complex, especially when using a low-cost compass, the probability of failure will increase greatly. Taking θ k as an estimated variable, satisfying

Figure BDA0003079966230000064
Figure BDA0003079966230000064

式中

Figure BDA0003079966230000071
为零均值白噪声。In the formula
Figure BDA0003079966230000071
is zero-mean white noise.

离散时间状态空间模型建立如下The discrete-time state-space model is established as follows

Figure BDA0003079966230000072
Figure BDA0003079966230000072

Figure BDA0003079966230000073
Figure BDA0003079966230000073

式中

Figure BDA0003079966230000074
xk＝[ak bk]T为k时刻随从潜航器的位置，na＝n+1，n为xk的维数，
Figure BDA0003079966230000075
和
Figure BDA0003079966230000076
分别为非线性状态函数和量测函数，假设
Figure BDA0003079966230000077
为高斯白噪声序列，
Figure BDA0003079966230000078
且有In the formula
Figure BDA0003079966230000074
x k =[a k b k ] T is the position of the following submersible at time k, n a =n+1, n is the dimension of x k ,
Figure BDA0003079966230000075
with
Figure BDA0003079966230000076
are the nonlinear state function and measurement function, respectively, assuming
Figure BDA0003079966230000077
is a Gaussian white noise sequence,
Figure BDA0003079966230000078
and have

Figure BDA0003079966230000079
Figure BDA0003079966230000079

式中xk＝[ak bk]T为k时刻随从潜航器的位置，uk＝[va,k vb,k]T为DVL测得的前向与右向速度，

Figure BDA00030799662300000710
为k-1时刻航向角的估计值。In the formula, x k ＝[a k b k ] T is the position of the following submersible at time k, u k ＝[v a,k v b,k ] T is the forward and rightward velocity measured by DVL,
Figure BDA00030799662300000710
is the estimated value of heading angle at time k-1.

式中In the formula

Figure BDA00030799662300000711
Figure BDA00030799662300000711

Figure BDA00030799662300000712
Figure BDA00030799662300000712

式中，

Figure BDA00030799662300000713
为非线性状态函数。In the formula,
Figure BDA00030799662300000713
is a nonlinear state function.

步骤二：航向角输入未知的待校正状态估计值的计算；Step 2: Calculation of the estimated value of the state to be corrected whose heading angle input is unknown;

状态估计值的误差协方差

Figure BDA00030799662300000714
可以被分解为Error covariance of state estimates
Figure BDA00030799662300000714
can be broken down into

Figure BDA00030799662300000715
Figure BDA00030799662300000715

式中Sk-1/k-1为

Figure BDA00030799662300000716
经过三角分解后的下三角矩阵。接着，容积点如下式计算where S k-1/k-1 is
Figure BDA00030799662300000716
Lower triangular matrix after triangular decomposition. Then, the volume point is calculated as follows

χk-1,i＝Sk-1/k-1ρi+xk-1/k-1 (10)χ k-1,i ＝S k-1/k-1 ρ i +x k-1/k-1 (10)

式中

Figure BDA00030799662300000717
[In]i表示n维单位矩阵In的第i列。In the formula
Figure BDA00030799662300000717
[I n ] i represents the i-th column of the n-dimensional identity matrix I n .

容积点传播如下The volume point spread is as follows

Figure BDA00030799662300000718
Figure BDA00030799662300000718

Figure BDA00030799662300000719
Figure BDA00030799662300000719

Figure BDA0003079966230000081
Figure BDA0003079966230000081

Figure BDA0003079966230000082
Figure BDA0003079966230000082

yk/k-1,i＝hk(χk/k-1,i) (15)y k/k-1,i ＝h k (χ k/k-1,i ) (15)

Figure BDA0003079966230000083
Figure BDA0003079966230000083

式中

Figure BDA0003079966230000084
为非线性状态函数fk-1(·)展开的采样点，
Figure BDA0003079966230000085
为状态预测值，
Figure BDA0003079966230000086
为
Figure BDA0003079966230000087
的误差协方差矩阵，χk/k-1,i为二次采样点，yk/k-1,i为非线性量测函数hk(·)展开的采样点，
Figure BDA0003079966230000088
为量测预测值，Qk为过程噪声协方差矩阵，ξi与ρi的取值方式相同。In the formula
Figure BDA0003079966230000084
is the sampling point expanded by the nonlinear state function f k-1 (·),
Figure BDA0003079966230000085
is the state prediction value,
Figure BDA0003079966230000086
for
Figure BDA0003079966230000087
The error covariance matrix of , χ k/k-1,i is the secondary sampling point, y k/k-1,i is the sampling point expanded by the nonlinear measurement function h k ( ),
Figure BDA0003079966230000088
In order to measure the predicted value, Q k is the process noise covariance matrix, and the values of ξ i and ρ i are the same.

量测更新如下The measurements are updated as follows

Figure BDA0003079966230000089
Figure BDA0003079966230000089

Figure BDA00030799662300000810
Figure BDA00030799662300000810

Figure BDA00030799662300000811
Figure BDA00030799662300000811

Figure BDA00030799662300000812
Figure BDA00030799662300000812

Figure BDA00030799662300000813
Figure BDA00030799662300000813

式中

Figure BDA00030799662300000814
为互协方差矩阵，
Figure BDA00030799662300000815
为量测自协方差矩阵，Rk为量测噪声协方差矩阵，Kk为增益矩阵，yk为真实量测信息，
Figure BDA00030799662300000816
分别为无航向输入时的状态估计值与误差协方差矩阵。In the formula
Figure BDA00030799662300000814
is the cross-covariance matrix,
Figure BDA00030799662300000815
is the measurement autocovariance matrix, R k is the measurement noise covariance matrix, K k is the gain matrix, y k is the real measurement information,
Figure BDA00030799662300000816
are the state estimation value and error covariance matrix when there is no heading input, respectively.

步骤三：通过自适应更新量测噪声方差矩阵削弱野值噪声对状态估计的影响；Step 3: Weaken the influence of outlier noise on state estimation by adaptively updating the measurement noise variance matrix;

量测噪声方差矩阵的自适应更新，即The adaptive update of the measurement noise variance matrix, namely

Figure BDA00030799662300000817
Figure BDA00030799662300000817

且有

Figure BDA00030799662300000818
其中TP,k|k-1与Tr,k分别为
Figure BDA00030799662300000819
与量测噪声方差阵Rk经过三角分解后的下三角矩阵。在协同定位模型中，假设系统噪声为高斯噪声，因此有and have
Figure BDA00030799662300000818
Where T P,k|k-1 and T r,k are respectively
Figure BDA00030799662300000819
and the lower triangular matrix after the triangular decomposition of the measurement noise variance matrix R k . In the co-location model, it is assumed that the system noise is Gaussian noise, so there is

Figure BDA00030799662300000820
Figure BDA00030799662300000820

式中σ为核带宽度，将在步骤四中介绍其自适应调节的过程，且有In the formula, σ is the kernel bandwidth, and its adaptive adjustment process will be introduced in step 4, and there is

ek＝ζk-Gkxk (24)e k ＝ζ k -G k x k (24)

式中

Figure BDA0003079966230000091
Figure BDA0003079966230000092
m为量测值的维数。In the formula
Figure BDA0003079966230000091
Figure BDA0003079966230000092
m is the dimension of the measured value.

步骤四：构建核带宽度自适应调节因子；Step 4: Construct the kernel bandwidth adaptive adjustment factor;

新息向量定义为

Figure BDA0003079966230000093
通过新息矩阵
Figure BDA00030799662300000913
和量测误差协方差矩阵
Figure BDA0003079966230000094
构建自适应调节因子如下The innovation vector is defined as
Figure BDA0003079966230000093
Via the Innovation Matrix
Figure BDA00030799662300000913
and measurement error covariance matrix
Figure BDA0003079966230000094
Build the adaptive adjustment factor as follows

Figure BDA0003079966230000095
Figure BDA0003079966230000095

式中

Figure BDA0003079966230000096
当新息矩阵的迹小于等于测量误差方差矩阵的迹时，自适应因子取值为1，否则，它意味着在量测信息中存在异常值。在这种情况下，利用构造的自适应因子对带宽σ进行实时校正，即σt＝λtσt-1，t为迭代次数。In the formula
Figure BDA0003079966230000096
When the trace of the innovation matrix is less than or equal to the trace of the measurement error variance matrix, the adaptive factor takes the value of 1, otherwise, it means that there are outliers in the measurement information. In this case, the bandwidth σ is corrected in real time using the constructed adaptive factor, that is, σ t =λ t σ t-1 , where t is the number of iterations.

步骤五：航向估计值与校正后的位置向量估计值的计算；Step 5: Calculation of the heading estimate and the corrected position vector estimate;

航向角的误差协方差矩阵为The error covariance matrix of heading angle is

Figure BDA0003079966230000097
Figure BDA0003079966230000097

式中

Figure BDA0003079966230000098
In the formula
Figure BDA0003079966230000098

位置与航向估计的增益矩阵分别为The gain matrices of position and heading estimation are respectively

Figure BDA0003079966230000099
Figure BDA0003079966230000099

Figure BDA00030799662300000910
Figure BDA00030799662300000910

航向估计值为The heading estimate is

Figure BDA00030799662300000911
Figure BDA00030799662300000911

由航向角估计值校正后的位置估计与位置估计误差协方差矩阵分别为The covariance matrix of position estimation and position estimation error corrected by the estimated value of heading angle are respectively

Figure BDA00030799662300000912
Figure BDA00030799662300000912

Figure BDA0003079966230000101
Figure BDA0003079966230000101

式中

Figure BDA0003079966230000102
In the formula
Figure BDA0003079966230000102

图1为协同定位相对距离信息声学通信示意图，此处，我们考虑2个领航潜航器轮流为1个随从潜航器提供量测信息的经典场景。领航者配备高精度导航设备，作为通信和导航辅助设备，跟随者配备罗经和DVL等低精度设备，获取速度和航向信息，进行航迹推算。此外，领航者和跟随者均配备水声调制解调器。在协同定位过程中，通过水声设备每隔一段时间测量领航者与跟随者之间的相对距离。图2为协同定位系统多潜航器实际航行轨迹图，可以看出，随从潜航器位于两个领航潜航器之间，这种队形可以提高系统的可观测性。图3为协同定位过程中实际量测噪声与噪声概率分布示意图，可以看出，由于量测异常值的存在，量测噪声不再服从高斯分布。我们的目的是通过估计航向角，保证定位精度。图4为RCKF、核带宽σ不同取值下的MCRCKF以及所提出AMCRCKF的定位误差比较图，可见，在非高斯量测噪声和罗经无效条件下，RCKF定位误差曲线发散剧烈，最大定位误差达到380m，这说明罗经失效方法RCKF在非高斯量测噪声环境下不能保持良好的定位精度。因此，引入MCC来处理非高斯噪声，但是，由图4可见，不合适的带宽也会导致滤波发散。所提出的AMCRCKF算法可以做到自适应调节核带宽度至合理取值，定位误差在20m以内，在罗经失效和量测噪声非高斯分布的情况下仍具有较好的定位精度。图5和图6分别为航向角估计值与航向角误差比较图，可以看出，RCKF和MCRCKF的航向角误差波动较大，对定位精度有很大的负面影响，而AMCRCKF的估计航向角更接近实际航向角。Figure 1 is a schematic diagram of the acoustic communication of relative distance information for co-location. Here, we consider a classic scenario where two leading submersibles take turns to provide measurement information for one follower submersible. The navigator is equipped with high-precision navigation equipment as a communication and navigation aid, and the follower is equipped with low-precision equipment such as compass and DVL to obtain speed and heading information and perform dead reckoning. In addition, both the leader and follower are equipped with hydroacoustic modems. During the co-location process, the relative distance between the leader and the follower is measured by the hydroacoustic device at regular intervals. Figure 2 is the actual trajectories of multiple submersibles in the collaborative positioning system. It can be seen that the follower submersible is located between the two leading submersibles, and this formation can improve the observability of the system. Fig. 3 is a schematic diagram of the actual measurement noise and the noise probability distribution in the co-location process. It can be seen that due to the existence of measurement outliers, the measurement noise no longer obeys the Gaussian distribution. Our purpose is to ensure the positioning accuracy by estimating the heading angle. Figure 4 is a comparison diagram of the positioning error of MCRCKF and the proposed AMCRCKF under different values of RCKF and kernel bandwidth σ. It can be seen that under the conditions of non-Gaussian measurement noise and invalid compass, the RCKF positioning error curve diverges sharply, and the maximum positioning error reaches 380m , which shows that the compass failure method RCKF cannot maintain good positioning accuracy in the non-Gaussian measurement noise environment. Therefore, MCC is introduced to deal with non-Gaussian noise, but, as can be seen from Figure 4, inappropriate bandwidth will also lead to filtering divergence. The proposed AMCRCKF algorithm can adaptively adjust the kernel bandwidth to a reasonable value, the positioning error is within 20m, and it still has good positioning accuracy in the case of compass failure and non-Gaussian distribution of measurement noise. Figure 5 and Figure 6 are the comparison diagrams of the estimated heading angle and the heading angle error respectively. It can be seen that the heading angle error of RCKF and MCRCKF fluctuates greatly, which has a great negative impact on the positioning accuracy, while the estimated heading angle of AMCRCKF is more close to the actual heading angle.

Claims (3)

1. A multi-underwater vehicle collaborative positioning self-adaptive adjustment robust filtering method under compass failure is characterized by comprising the following steps:
the method comprises the following steps: establishing a multi-underwater vehicle co-location model with unknown course angle;
step two: calculating a heading angle input unknown state estimation value to be corrected;
step three: the influence of outlier noise on state estimation is weakened by adaptively updating the measurement noise variance matrix, and the method specifically comprises the following steps:
adaptive updating of the metric noise variance matrix, namely:
Figure FDA0003820851330000011
and is provided with
Figure FDA0003820851330000012
Wherein T is P,k|k-1 And T r,k Are respectively as
Figure FDA0003820851330000013
And the measured noise variance matrix R k A lower triangular matrix after triangular decomposition; in the co-location model, the system noise is assumed to be gaussian noise, so there are:
Figure FDA0003820851330000014
where σ is the nuclear band width and has:
e k ＝ζ k -G k x k
in the formula
Figure 1
m is the dimension of the measured value, ε k To measure noise;
step four: constructing a nuclear band width self-adaptive adjustment factor, which specifically comprises the following steps:
an innovation vector is defined as
Figure FDA0003820851330000016
By an innovation matrix
Figure FDA0003820851330000017
And a measurement error covariance matrix
Figure FDA0003820851330000018
Constructing an adaptive adjustment factor:
Figure FDA0003820851330000019
Figure FDA00038208513300000110
in the formula
Figure FDA00038208513300000111
When the trace of the innovation matrix is less than or equal to the trace of the measurement error variance matrixWhen the bandwidth sigma is corrected, the adaptive factor value is 1, otherwise, the bandwidth sigma is corrected in real time by using the constructed adaptive factor, namely sigma t ＝λ t σ t-1 T is the number of iterations;
step five: calculating a course estimation value and a corrected position vector estimation value, specifically:
the error covariance matrix of the course angle is:
Figure FDA0003820851330000021
in the formula
Figure FDA0003820851330000022
The gain matrix of the position and course estimation is respectively:
Figure FDA0003820851330000023
Figure FDA0003820851330000024
the course estimation value is as follows:
Figure FDA0003820851330000025
the covariance matrices of the position estimation and position estimation errors after correction by the course angle estimation value are respectively:
Figure FDA0003820851330000026
Figure FDA0003820851330000027
in the formula
Figure FDA0003820851330000028
2. The method for multi-underwater-vehicle cooperative localization adaptive regulation robust filtering under compass failure according to claim 1, characterized in that: step one, establishing a multi-underwater vehicle co-location model with unknown course angle specifically comprises the following steps:
the equation of state and the measurement equation are as follows:
Figure FDA0003820851330000029
Figure FDA00038208513300000210
in the formula a k And b k East and north positions of the slave underwater vehicle at the moment k, delta t is a sampling period, v a,k ,v b,k Is the right and forward speed, theta, at time k, of the slave vehicle k Is the angle between the forward direction and the north direction at time k, w a,k ,w b,k Is zero mean white Gaussian noise, Z k The relative distance measurement information between the pilot underwater vehicle and the slave underwater vehicle,
Figure FDA00038208513300000211
for the position of the piloting vehicle at time k, epsilon k To measure noise;
will theta k As an estimated variable, satisfy
Figure FDA00038208513300000212
In the formula
Figure FDA0003820851330000031
Is zero mean white noise;
the discrete time state space model establishment specifically comprises the following steps:
Figure FDA0003820851330000032
Figure FDA0003820851330000033
in the formula
Figure FDA0003820851330000034
x k ＝[a k b k ] T Is the position of the slave vehicle at time k, n a N +1, n is x k The dimension(s) of (a) is,
Figure FDA0003820851330000035
and
Figure FDA0003820851330000036
respectively, the nonlinear state function and the measurement function at the time k after state expansion, assuming
Figure FDA0003820851330000037
Is a sequence of white gaussian noise, and is,
Figure FDA0003820851330000038
y k is the real measurement information, and comprises:
Figure FDA0003820851330000039
in the formula u k ＝[v a,k v b,k ] T The forward and right speed measured for the DVL,
Figure FDA00038208513300000310
the estimated value of the course angle at the k-1 moment is obtained;
in the formula
Figure FDA00038208513300000311
Figure FDA00038208513300000312
In the formula (I), the compound is shown in the specification,
Figure FDA00038208513300000313
as a non-linear state function at time k.
3. The method for multi-underwater-vehicle co-location adaptive adjustment robust filtering under compass failure according to claim 1 or 2, wherein: step two, the calculation of the unknown state estimation value to be corrected of the course angle input is specifically as follows:
error covariance of state estimates
Figure FDA00038208513300000314
Can be decomposed into:
Figure FDA00038208513300000315
in the formula S k-1/k-1 Is composed of
Figure FDA00038208513300000316
A lower triangular matrix after triangular decomposition;
the volume point calculation is specifically:
Figure FDA00038208513300000317
in the formula
Figure FDA00038208513300000318
[I n ] i Representing an n-dimensional identity matrix I n The ith column;
volume point propagation is specifically:
Figure FDA00038208513300000319
Figure FDA0003820851330000041
Figure FDA0003820851330000042
Figure FDA0003820851330000043
y k/k-1,i ＝h k (χ k/k-1,i )
Figure FDA0003820851330000044
in the formula
Figure FDA0003820851330000045
As a function of the nonlinear state at time k-1 k-1 (c) the spread out sample points,
Figure FDA0003820851330000046
in order to be a predicted value of the state,
Figure FDA0003820851330000047
is composed of
Figure FDA0003820851330000048
Of the error covariance matrix χ k/k-1,i Is a secondary sampling point, y k/k-1,i As a function of the non-linear measurement h k (ii) the spread out sample points,
Figure FDA0003820851330000049
for measuring the predicted value, Q k Is a process noise covariance matrix, ξ i And rho i The value taking modes are the same;
the measurement is updated as follows:
Figure FDA00038208513300000410
Figure FDA00038208513300000411
Figure FDA00038208513300000412
Figure FDA00038208513300000413
Figure FDA00038208513300000414
in the formula
Figure FDA00038208513300000415
Is a cross-covariance matrix of the two-dimensional data,
Figure FDA00038208513300000416
to measure the autocovariance matrix, R k Covariance for measuring noiseDifference matrix, K k Is a gain matrix, y k In order to obtain the real measurement information,
Figure FDA00038208513300000417
respectively a state estimation value and an error covariance matrix when no course input exists.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2013130042A1 (en) * 2012-02-28 2013-09-06 Intel Corporation Dynamic optimization of carrier recovery performance for communications systems
CN104090271A (en) * 2014-07-30 2014-10-08 广西大学 Space time adaptive processing (STAP) method of high-speed radar at accelerated movement state
WO2018073626A1 (en) * 2016-10-20 2018-04-26 Harman Becker Automotive Systems Gmbh Noise control
CN109858454A (en) * 2019-02-15 2019-06-07 东北大学 A Dual-Model Adaptive Kernel Correlation Filtering Tracking Method

Family Cites Families (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2252170A1 (en) * 1998-10-27 2000-04-27 Bruno Bessette A method and device for high quality coding of wideband speech and audio signals
US9020088B2 (en) * 2012-09-12 2015-04-28 Topcon Positioning Systems, Inc. Digital system and method of estimating quasi-harmonic signal non-energy parameters using a digital Phase Locked Loop
KR20170124590A (en) * 2013-06-21 2017-11-10 프라운호퍼 게젤샤프트 쭈르 푀르데룽 데어 안겐반텐 포르슝 에. 베. Audio decoder having a bandwidth extension module with an energy adjusting module
CN104866715A (en) * 2015-05-14 2015-08-26 同济大学 Electrical power system robust state estimation method based on self-adaptive kernel density estimation
CN109459040B (en) * 2019-01-14 2021-06-18 哈尔滨工程大学 Multi-AUV co-localization method based on RBF neural network-assisted volumetric Kalman filter
EP3816672A1 (en) * 2019-10-28 2021-05-05 FRAUNHOFER-GESELLSCHAFT zur Förderung der angewandten Forschung e.V. Adaptive weighting matrix for adaptive tracking loops
CN110779519B (en) * 2019-11-18 2021-04-27 哈尔滨工程大学 A single beacon localization method for underwater vehicle with global convergence
CN110779518B (en) * 2019-11-18 2021-04-27 哈尔滨工程大学 A single beacon localization method for underwater vehicle with global convergence
CN112099060B (en) * 2020-08-25 2022-11-25 北京理工大学 Loop-based adaptive carrier frequency tracking method and device
CN112566060B (en) * 2020-12-18 2022-04-22 天津工业大学 Marine ranching underwater and overwater integrated communication system based on small-float anchor chain networking

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2013130042A1 (en) * 2012-02-28 2013-09-06 Intel Corporation Dynamic optimization of carrier recovery performance for communications systems
CN104090271A (en) * 2014-07-30 2014-10-08 广西大学 Space time adaptive processing (STAP) method of high-speed radar at accelerated movement state
WO2018073626A1 (en) * 2016-10-20 2018-04-26 Harman Becker Automotive Systems Gmbh Noise control
CN109858454A (en) * 2019-02-15 2019-06-07 东北大学 A Dual-Model Adaptive Kernel Correlation Filtering Tracking Method

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