CN114118528A - Ship track real-time forecasting method based on combination of linear filter and nonlinear filter - Google Patents

Ship track real-time forecasting method based on combination of linear filter and nonlinear filter Download PDF

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CN114118528A
CN114118528A CN202111292868.XA CN202111292868A CN114118528A CN 114118528 A CN114118528 A CN 114118528A CN 202111292868 A CN202111292868 A CN 202111292868A CN 114118528 A CN114118528 A CN 114118528A
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汪震
严震海
刘建设
龙飞
陈姚节
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Wuhan University of Science and Engineering WUSE
Wuhan Institute of Marine Electric Propulsion China Shipbuilding Industry Corp No 712 Institute CSIC
China Ship Development and Design Centre
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Wuhan Institute of Marine Electric Propulsion China Shipbuilding Industry Corp No 712 Institute CSIC
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Abstract

The invention discloses a ship track real-time forecasting method based on combination of linear and nonlinear filters, which comprises the following steps: s1, collecting a target historical track as a data set, and carrying out data preprocessing to obtain a data set with noise removed; s2, fitting the data set by using N-order polynomial fitting to obtain N +1 polynomials for prediction, and selecting an optimal prediction curve from the N +1 prediction polynomials by using K-fold cross validation to obtain a preliminary prediction result; s3, processing the prediction result by using median filtering to obtain the prediction result without nonlinear noise; the invention provides a ship track real-time forecasting method based on combination of linear and nonlinear filters, which is used for forecasting a future track of a target ship. According to the historical track data in a short period, the combined filtering prediction model is updated in real time, the implementation cost is low, the inherent parameters of the ship where the intelligent water cannon equipment is located and the external environment parameters are not needed, and the generalization performance is good.

Description

Ship track real-time forecasting method based on combination of linear filter and nonlinear filter
Technical Field
The invention relates to the field of ship track prediction, in particular to a ship track real-time forecasting method based on combination of linear and nonlinear filters.
Background
In recent years, with the development of computer technology, a water cannon striking system is developed from manual control to intelligent control, an intelligent water cannon automatically adjusts the striking angle of the intelligent water cannon according to the position of a striking target, and the intelligent water cannon is mostly applied to fire fighting and law enforcement at the present stage. When the intelligent water cannon is applied to fire fighting, the position of a fire source cannot be changed, so that the intelligent water cannon can strike a static target, and the striking effect cannot be influenced by the movement of jet flow in the air; when the intelligent water cannon is applied to law enforcement, a target ship is in a motion state when avoiding striking, time consumed by jet flow moving in the air can cause striking miss, a striking drop point always lags behind a target position, and the striking point needs to be corrected by calculating the lead. Therefore, real-time prediction of the target ship track is a key step for improving the hitting precision of the intelligent water cannon, the intelligent water cannon predicts the target position according to the prediction model, the hitting advance is calculated, and the hitting miss problem is solved.
Existing target estimation prediction methods can be classified into a statistical-based method and a deep learning-based method. However, some prediction methods need a large amount of data, the prediction effect is general when the data amount is small, and some models need to be built by using more ship intrinsic parameters and external environment parameters, so that the generalization is not good. Or the short-term track prediction model is established by combining the advantages of the CNN and the LSTM networks, and compared with the traditional mathematical statistics method, the short-term track prediction model has better effect in a specific environment but needs a larger-scale training set. Or a ship track prediction model with strong real-time property is established depending on binocular vision distance measurement, but the cost is high. Or a vessel AIS data is modeled using a polynomial based kalman filter model, but it does not consider the processing of real-time tracking data with a lot of noise.
Disclosure of Invention
Aiming at the problems, the invention provides a ship track real-time forecasting method based on a combination of linear and nonlinear filters, which is used for forecasting the future track of a target ship. According to the historical track data in a short period, the combined filtering prediction model is updated in real time, the implementation cost is low, the inherent parameters of the ship where the intelligent water cannon equipment is located and the external environment parameters are not needed, and the generalization performance is good.
The invention provides a ship track real-time forecasting method based on combination of linear and nonlinear filters, which comprises the following steps: s1, collecting a target historical track as a data set, and carrying out data preprocessing to obtain a data set with noise removed; s2, fitting the data set by using N-order polynomial fitting to obtain N +1 polynomials for prediction, and selecting an optimal prediction curve from the N +1 prediction polynomials by using K-fold cross validation to obtain a preliminary prediction result; and S3, processing the prediction result by using the median filter to obtain the prediction result with nonlinear noise removed.
Further, step S1 specifically includes: s11, tracking the target ship by using the intelligent water cannon system, and acquiring the information of yaw angle and pitch angle for describing a target track; s12, the noise of the collected data is a random variable X, wherein X obeys one-dimensional Gaussian distribution, and the probability density function is
Figure BDA0003335266580000021
Wherein mu is a random variableThe expected value of X, sigma is the standard deviation of X; s13, taking the probability density function as a Gaussian function G (x) prototype of the Gaussian template, and setting the expected value mu as the value x of the convolution element of the current template0Is, then Gaussian template
Figure BDA0003335266580000022
Wherein x is x0Value of field element, if one-dimensional Gaussian template width is N, Gaussian template
Figure BDA0003335266580000023
Traversing the acquired data by using a Gaussian template, and performing convolution to obtain a filtering result
Figure BDA0003335266580000024
The Gaussian filtering is carried out on a large amount of noise in the collected data, the linear filtering is adopted, the larger the standard deviation sigma of the Gaussian function is, the better the smoothing degree after filtering is, and a good smoothing effect can be obtained by adjusting sigma.
Further, in step S2, fitting the data set by using N-order polynomial fitting specifically includes: fitting the sample set by using a least square method to obtain 0-N order polynomial
Figure BDA0003335266580000031
Where N is the highest order of the polynomial, t is time, b is the bias constant, a is the polynomial coefficient, and m is the order.
The prediction effects of different prediction curves of m are different, the overfitting problem can occur when m is too large, and the underfitting problem can occur when m is too small. Therefore, the order m needs to be normalized to obtain a suitable value of m.
Further, in step S2, selecting an optimal prediction curve from the N +1 prediction polynomials by using K-fold cross validation, specifically including: s21, dividing the sample set S into k parts at equal intervals, using (k-1) parts as training set to calculate F (m, t), using one part as cross validation set, S22, calculating error value e between predicted value and true value on validation set as (p-r)2Taking the average value of the error values e to be minimumF (m, t) is an optimal prediction curve, wherein m is a K-fold cross validation specification order, p is a predicted value, and r is a true value; and S23, if there are a plurality of F (m, t) with the same mean value of the error values e, taking the F (m, t) with the minimum order m as the optimal prediction curve.
The K-fold cross validation is suitable for scenes with small data sets, overfitting and under-fitting can be effectively prevented, appropriate model parameters are found, and the order m is normalized by the K-fold cross validation.
Further, step S3 specifically includes: s31, calculating a plurality of prediction results in the neighborhood of the prediction time point by using the optimal prediction curve to obtain a set of prediction results; and S32, filtering the nonlinear noise in the prediction result by using median filtering to obtain a final prediction result.
And further, the method further comprises the step of fitting to obtain preset parameters of linear filtering and nonlinear filtering parameter values based on a plurality of target track data, wherein the preset parameters comprise a Gaussian function standard deviation sigma, a Gaussian template width N, a polynomial highest order D, a sample number k and sample data L of median filtering.
Further, the method also comprises the step of quantitatively evaluating the prediction result based on the Mean Square Error (MSE).
The invention has the following beneficial technical effects:
1. the Gaussian noise and the predicted target track are processed by a linear filter, and then the nonlinear noise in the prediction result is processed by a nonlinear filter, so that the prediction curve has no obvious nonlinear noise and has good smoothness.
2. The coincidence degree of the predicted track and the original track is good, the ship track combined by the linear and nonlinear filters is adopted for real-time prediction and prevention, and when a moving target is hit, the static target can be concentrated, and the moving target can be hit accurately.
3. The combined filtering prediction model can be updated in real time according to the historical track data in a short period, the implementation cost is low, the inherent parameters of the ship where the intelligent water cannon equipment is located and the external environment parameters are not needed, and the generalization performance is good.
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FIG. 1 is a schematic flow chart of an embodiment of a ship track real-time forecasting method based on a combination of linear and nonlinear filters according to the present invention;
FIG. 2 is a schematic diagram of convolution filtering of raw data according to an embodiment of the present invention;
FIG. 3 is a flow chart illustrating median filtering according to an embodiment of the present invention;
FIG. 4 is an exploded view of a target trajectory in an embodiment of the present invention;
FIG. 5 is a sample schematic view of a yaw trajectory in an embodiment of the present invention;
FIG. 6 is a graph of the effect of linear filtering prediction;
FIG. 7 is a diagram of the prediction effect of the ship track real-time forecasting method based on the combination of the linear filter and the nonlinear filter in the embodiment of the present invention;
FIG. 8 is a schematic diagram of a target trajectory in an embodiment of the present invention;
Detailed Description
For a further understanding of the invention, reference will now be made to the preferred embodiments of the invention by way of example, and it is to be understood that the description is intended to further illustrate features and advantages of the invention, and not to limit the scope of the claims.
As shown in fig. 1, the present invention aims to provide a flow diagram of a ship track real-time forecasting method based on a combination of linear and nonlinear filters, wherein the linear filtering algorithm is divided into gaussian filtering and N-order polynomial fitting, and the nonlinear filtering algorithm adopts median filtering. The method comprises the steps of firstly smoothing historical track data by Gaussian filtering, filtering Gaussian noise in a data set, then calculating a prediction curve set by using N-order polynomial fitting for calculating a predicted value, then evaluating a prediction effect by using a K-fold cross validation algorithm, determining a prediction curve according to the evaluation effect, and finally filtering nonlinear noise in a result sequence predicted by the prediction curve by using median filtering to obtain an effective predicted value. In the illustrated embodiments of the present invention, the method steps of the present invention are described individually.
And S1, collecting the target historical track as a data set, and carrying out data preprocessing to obtain a data set with noise removed.
And tracking the target ship by using an intelligent water cannon system, and describing the position of the target according to the information of the yaw angle and the pitch angle. Due to the rolling of equipment-loaded ships, water mist shielding and the like, a large amount of noise can appear in the process of acquiring target position information, and Gaussian filtering is needed to be used for preprocessing data. The noise is set as a random variable X, and experiments show that the X basically follows one-dimensional Gaussian distribution, and the probability density function p (X) is shown as the formula (1).
Figure BDA0003335266580000051
Where μ is the expected value of the random variable X and σ is the standard deviation of X.
Gaussian filtering is a linear filtering method, using equation (1) as a prototype of gaussian function g (x) for calculating a gaussian template, and setting its expected value as the value of the convolution element of the current template, where μ ═ x0，x0The element of the convolution of the current template is the Gaussian template G (x) shown in formula (2).
Figure BDA0003335266580000052
Wherein x is x0The value of the field element. The larger the standard deviation sigma of the Gaussian function is, the better the smoothing degree after filtering is, and a good smoothing effect can be obtained by adjusting sigma.
Setting the width of one-dimensional Gaussian template as N, the Gaussian template G (x)1,x2,Λ,xN) As shown in formula (3).
Figure BDA0003335266580000053
The data is filtered using a gaussian template, as shown in fig. 2, X is the raw data and Y is the filtering result. And traversing the original data from left to right by using a Gaussian template, and performing convolution to obtain a filtering result Y. The method for obtaining the filtering result Y by the convolution of the original data X is shown as the formula (4).
Figure BDA0003335266580000061
And S2, fitting the data set by using N-order polynomial fitting to obtain N +1 polynomials for prediction, and selecting an optimal prediction curve from the N +1 prediction polynomials by using K-fold cross validation to obtain a preliminary prediction result.
Polynomial fitting is a linear filtering method, and the polynomial can approximate the mapping relation between any independent variable and dependent variable, so that the polynomial fitting can be used for predicting the ship track. And (3) setting the highest order of the polynomial as N, setting a set of data preprocessing results as a sample set S, and fitting the sample set by using a least square method to obtain a 0-Nth order polynomial F (m, t), as shown in a formula (5).
Figure BDA0003335266580000062
Where t is time, b is a bias constant, a is a polynomial coefficient, and m is an order. The prediction effects of different prediction curves of m are different, the overfitting problem can occur when m is too large, and the underfitting problem can occur when m is too small. Therefore, the order m needs to be normalized to obtain a suitable value of m.
The K-fold cross validation is suitable for scenes with smaller data sets, can effectively prevent over-fitting and under-fitting, and finds out appropriate model parameters. The K-fold cross-validation specification order m is used herein.
And (3) sampling and dividing a sample set S into k parts at equal intervals, respectively using (k-1) parts as a training set to calculate F (m, t), using the remaining 1 part as a cross validation set, and finally, taking an average error for evaluating the prediction effect of the F (m, t), wherein the error calculation method between the predicted value and the true value is shown as a formula (6).
e＝(p-r)2 (6)
Where e is the error value, p is the predicted value, and r is the true value. And (4) calculating all errors on the verification set when the value of e is larger and the error is larger, and finally taking F (m, t) with the minimum average value of e as an optimal prediction curve.
In some embodiments, if there are a plurality of F (m, t) with the same average value of e, taking F (m, t) with the smallest order m as the optimal prediction curve.
And S3, processing the prediction result by using the median filter to obtain the prediction result with nonlinear noise removed.
As shown in fig. 3, which is a flowchart of using a median filtering algorithm, in the acquired target trajectory information, the gaussian filtering method in the preprocessing process can only process linear noise, but in the preprocessed data set, nonlinear noise generated due to temporary target loss exists. These noises are scaled by the prediction process, so that nonlinear noises exist in the prediction result set, and the drawn result curve has spiky protrusions, which requires filtering the nonlinear noises in the result set. The median filtering is a nonlinear filter, and by sorting the input data element set and taking the median of the data as a filtering result, nonlinear noise data can be effectively filtered. Wherein Z is the set of predicted values, L is the data set length of the first median filtering, and Z (L/2) is the predicted value.
In some embodiments of the present invention, the method further comprises fitting to obtain preset parameters of linear filtering and nonlinear filtering parameter values based on a plurality of target trajectory data.
In one embodiment of the invention, the intelligent water cannon system collects target position information at a rate of 10hz, and the system needs to predict a target track within a time period [ t, t +2], wherein t is the current time. The parameters used are specifically as follows: the standard deviation sigma of the Gaussian function is 1.5, and the width N of the Gaussian template is 20; according to the fitting result of the target trajectory data for multiple times, setting the highest order D of a polynomial fitting curve to be 6, and performing cross validation on the number k of samples used each time to be 3; the number of samples L used at a time for median filtering is 10.
In some embodiments of the invention, the method further comprises quantitatively evaluating the prediction result based on the mean square error MSE.
To quantitatively evaluate embodiments of the present invention, mean Square error mse (mean Square error) was used to evaluate the prediction effect, as shown in equation (7).
Figure BDA0003335266580000071
Wherein
Figure BDA0003335266580000072
To predict value, yiAre true values. The smaller the MSE, the closer the predicted value is to the true value, and the more accurate the predicted result is.
In one embodiment of the invention, the ship track real-time forecasting method based on the combination of the linear filter and the nonlinear filter is applied to an intelligent water cannon system for testing, and a remote control model ship is used as a target. In the intelligent water cannon system, the target motion can be decomposed into motions in the horizontal and vertical directions, as shown in fig. 4, a point P is the current position of the target ship, the x direction is the yaw direction, and the y direction is the pitch direction. In the experiment, the yaw angle value of the intelligent water cannon system is collected to describe the position of the target in the horizontal direction, and the pitch angle value describes the position of the target in the vertical direction.
Taking the yaw direction as an example, a prediction experiment is performed on a target yaw direction trajectory. And collecting about 800 pieces of photoelectric yaw direction data to draw a matlab diagram as shown in fig. 5, wherein the horizontal axis is data collection time, and the vertical axis is a yaw angle, so as to obtain a yaw track sample. And comparing the collected samples with the ship track real-time forecasting method based on the combination of the linear filter and the nonlinear filter in the embodiment of the invention by using linear filtering prediction, the effect is shown in fig. 7. Fig. 6 is a linear filtering prediction effect diagram, and fig. 7 is a prediction effect diagram of a ship track real-time prediction method based on a combination of linear and nonlinear filters. It can be seen that the use of linear filter prediction alone does not deal effectively with nonlinear noise, while the curves predicted using combined filtering do not have significant nonlinear noise and have good smoothness.
The MSE of multiple yaw directions is calculated, the MSE interval of a linear filtering prediction method is 1.2165-3.0027, the MSE interval of the ship track real-time prediction method based on the combination of the linear filter and the nonlinear filter is 0.3025-1.4832, and the combined filtering with the nonlinear filter is obviously higher in prediction effect than the prediction method only using the linear filter.
The pitch direction trajectory is predicted by using the model in the same horizontal direction, and the prediction results of the yaw direction and the pitch direction are displayed in the video frame, the effect is shown in fig. 8, wherein the rectangular frame is an intelligent water cannon tracking frame, the curve a is an original trajectory curve, and the curve b is a prediction curve obtained by using the ship trajectory real-time prediction method based on the combination of the linear filter and the nonlinear filter. Respectively acquiring 100 sample points in a curve a and a curve b by using an equal-interval sampling method to calculate the contact ratio for visually reflecting the prediction effect, setting a sample set as A, and setting the reasonable pixel distance error between the prediction point and the real point as 10, if the linear distance between the sample point of the curve a and the sample point of the corresponding curve b is within the reasonable error range, judging that the prediction is correct, otherwise, judging that the prediction is wrong. If the number of correctly predicted sample points in the sample set a is y and the number of incorrectly predicted sample points is n, the overlap ratio is y/(y + n). The coincidence degree of the predicted track and the original track is calculated to be 88.71%, and the predicted track is basically fit with the original track.
The ship track real-time forecasting method based on the combination of the linear filter and the nonlinear filter firstly processes Gaussian noise and forecasts a target track through the linear filter, and then processes nonlinear noise in a forecast result through the nonlinear filter. The problem of striking lag when the jet device strikes a moving target in engineering is effectively solved, and the target position is predicted in real time according to historical track information and prediction time. Effective target location information is provided for a target-locking method.
The above description of the embodiments is only intended to facilitate the understanding of the method of the invention and its core idea. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.

Claims (7)

1.一种基于线性与非线性滤波器组合的船舶航迹实时预报方法，其特征在于，包括：1. a ship track real-time forecasting method based on linear and nonlinear filter combination, is characterized in that, comprises: S1，采集目标历史轨迹作为数据集，并进行数据预处理，得到去除噪声的数据集；S1, collect the target historical trajectory as a data set, and perform data preprocessing to obtain a noise-removed data set; S2，使用N阶多项式拟合对数据集进行拟合，得到N+1个用于预测的多项式，使用K折交叉验证在N+1个预测多项式中选取最优预测曲线，得到初步预测结果；S2, use N-order polynomial fitting to fit the data set to obtain N+1 polynomials for prediction, and use K-fold cross-validation to select the optimal prediction curve from the N+1 prediction polynomials to obtain preliminary prediction results; S3，使用中值滤波处理预测结果，得到去除非线性噪声的预测结果。S3 , using median filtering to process the prediction result to obtain a prediction result with non-linear noise removed. 2.如权利要求1所述的基于线性与非线性滤波器组合的船舶航迹实时预报方法，其特征在于，步骤S1具体包括：2. the ship track real-time forecast method based on linear and nonlinear filter combination as claimed in claim 1, is characterized in that, step S1 specifically comprises: S11，使用智能水炮系统对目标船舶进行跟踪，采集其中偏航角和俯仰角信息用于描述目标轨迹；S11, use the intelligent water cannon system to track the target ship, and collect the yaw angle and pitch angle information to describe the target trajectory; S12，采集数据的噪声设为随机变量X，其中，X服从一维高斯分布，概率密度函数为
Figure FDA0003335266570000011
其中，μ为随机变量X的期望值，σ为X的标准差；S12, the noise of the collected data is set as a random variable X, where X obeys a one-dimensional Gaussian distribution, and the probability density function is
Figure FDA0003335266570000011
Among them, μ is the expected value of the random variable X, and σ is the standard deviation of X; S13，将所述概率密度函数作为计算高斯模板的高斯函数G(x)原型，将其期望值μ设置为当前模板卷积元素的值x0，则高斯模板
Figure FDA0003335266570000012
其中，x为x0邻域元素的值，若一维高斯模板宽度为N，则高斯模板
Figure FDA0003335266570000013
使用高斯模板遍历采集数据，进行卷积，得到滤波结果
Figure FDA0003335266570000014
S13, using the probability density function as the prototype of the Gaussian function G(x) for calculating the Gaussian template, and setting its expected value μ as the value x 0 of the convolution element of the current template, then the Gaussian template
Figure FDA0003335266570000012
Among them, x is the value of the element in the neighborhood of x 0. If the width of the one-dimensional Gaussian template is N, then the Gaussian template
Figure FDA0003335266570000013
Use the Gaussian template to traverse the collected data, perform convolution, and obtain the filtering result
Figure FDA0003335266570000014
 3.如权利要求2所述的基于线性与非线性滤波器组合的船舶航迹实时预报方法，其特征在于，步骤S2中使用N阶多项式拟合对数据集进行拟合，具体包括：对样本集使用最小二乘法拟合得到0～N阶多项式
Figure FDA0003335266570000021
其中N为多项式最高阶数，t为时间，b为偏置常量，a为多项式系数，m为阶数。3. the ship track real-time forecasting method based on the combination of linear and nonlinear filters as claimed in claim 2, is characterized in that, in step S2, use N-order polynomial fitting to fit data set, specifically comprises: to sample The set is fitted using the least squares method to obtain a polynomial of order 0 to N
Figure FDA0003335266570000021
Where N is the highest order of the polynomial, t is the time, b is the bias constant, a is the polynomial coefficient, and m is the order. 4.如权利要求3所述的基于线性与非线性滤波器组合的船舶航迹实时预报方法，其特征在于，步骤S2中使用K折交叉验证在N+1个预测多项式中选取最优预测曲线，具体包括：4. the ship track real-time forecasting method based on linear and nonlinear filter combination as claimed in claim 3, is characterized in that, in step S2, use K-fold cross-validation to select optimal forecast curve in N+1 forecast polynomial , including: S21，把样本集S等间隔抽样分成k份，分别使用其中的(k-1)份作为训练集计算F(m,t)，一份作为交叉验证集；S21: Divide the sample set S into k parts at equal intervals, and use (k-1) parts of them as the training set to calculate F(m, t), and one part as the cross-validation set; S22，计算验证集上预测值与真实值之间的误差值e＝(p-r)2，取误差值e的平均值最小的F(m,t)为最优预测曲线，其中，m为K折交叉验证规范阶数，p为预测值，r为真实值；S22, calculate the error value e=(pr) 2 between the predicted value and the actual value on the validation set, and take F(m, t) with the smallest mean value of the error value e as the optimal prediction curve, where m is the K-fold Cross-validation normative order, p is the predicted value, r is the true value; S23，若有多个误差值e的均值相同的F(m,t)，则取其中阶数m最小的F(m,t)为最优预测曲线。S23, if there are multiple F(m, t) with the same mean value of error value e, take the F(m, t) with the smallest order m as the optimal prediction curve. 5.如权利要求1所述的基于线性与非线性滤波器组合的船舶航迹实时预报方法，其特征在于，步骤S3具体包括：5. the ship track real-time forecasting method based on linear and nonlinear filter combination as claimed in claim 1, is characterized in that, step S3 specifically comprises: S31，使用最优预测曲线计算预测时间点邻域内的多个预测结果，得到预测结果的集合；S31, using the optimal prediction curve to calculate multiple prediction results in the neighborhood of the prediction time point, to obtain a set of prediction results; S32，使用中值滤波过滤预测结果中的非线性噪声，得到最终预测结果。S32, use median filtering to filter nonlinear noise in the prediction result to obtain a final prediction result. 6.如权利要求4所述的基于线性与非线性滤波器组合的船舶航迹实时预报方法，其特征在于，还包括基于若干目标轨迹数据拟合得到线性滤波和非线性滤波参数值的预设参数，所述预设参数包括高斯函数标准差σ，高斯模板宽度N，多项式最高阶数D，样本份数k，以及，中值滤波的样本数据L。6. the ship track real-time forecasting method based on the combination of linear and nonlinear filters as claimed in claim 4, is characterized in that, also comprises the preset that linear filtering and nonlinear filtering parameter values are obtained based on some target trajectory data fitting The preset parameters include the standard deviation σ of the Gaussian function, the width N of the Gaussian template, the highest order D of the polynomial, the number of samples k, and the sample data L of the median filter. 7.如权利要求1-6任一项所述的基于线性与非线性滤波器组合的船舶航迹实时预报方法，其特征在于，还包括基于均方误差MSE定量评价预测结果。7. The method for real-time forecasting of ship tracks based on a combination of linear and nonlinear filters according to any one of claims 1-6, characterized in that, further comprising quantitatively evaluating the forecast results based on mean square error (MSE).
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114462458A (en) * 2022-04-11 2022-05-10 自然资源部第一海洋研究所 Ship underwater signal noise reduction and target enhancement method
CN114741464A (en) * 2022-06-09 2022-07-12 成都和为时代科技有限公司 Ship AIS target track tracking method based on least square polynomial curve fitting

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114462458A (en) * 2022-04-11 2022-05-10 自然资源部第一海洋研究所 Ship underwater signal noise reduction and target enhancement method
CN114741464A (en) * 2022-06-09 2022-07-12 成都和为时代科技有限公司 Ship AIS target track tracking method based on least square polynomial curve fitting

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