CN114118528A - Ship track real-time forecasting method based on combination of linear filter and nonlinear filter - Google Patents
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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
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
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
Wherein x is x0Value of field element, if one-dimensional Gaussian template width is N, Gaussian template
Traversing the acquired data by using a Gaussian template, and performing convolution to obtain a filtering result
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
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.
Drawings
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).
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).
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).
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).
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).
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).
Wherein
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. A ship track real-time forecasting method based on combination of linear and nonlinear filters is characterized by comprising 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.
2. The method for forecasting ship tracks in real time based on the combination of linear and nonlinear filters as claimed in claim 1, wherein the 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, setting the noise of the collected data as a random variable X, wherein X obeys one-dimensional Gaussian distribution, and the probability density function is
Wherein mu is an expected value of a random variable X, and sigma is a 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 template0Gauss template
Wherein x is x0The value of the neighborhood element, if the width of the one-dimensional Gaussian template is N, the Gaussian template
Traversing the acquired data by using a Gaussian template, and performing convolution to obtain a filtering result
3. The method for real-time ship track prediction based on combination of linear and nonlinear filters as claimed in claim 2, wherein the step S2 of fitting the data set by using N-order polynomial fitting specifically comprises: fitting the sample set by using a least square method to obtain 0-N order polynomial
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.
4. The method for real-time ship track prediction based on combination of linear and nonlinear filters as claimed in claim 3, wherein the step S2 of using K-fold cross validation to select the optimal prediction curve among N +1 prediction polynomials comprises:
s21, dividing the sample set S into k parts at equal intervals, respectively using (k-1) parts as training sets to calculate F (m, t), and using one part as a cross validation set;
s22, calculating the error value e between the predicted value and the true value on the verification set (p-r)2Taking F (m, t) with the minimum average value of the error values e as 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.
5. The method for forecasting ship tracks in real time based on the combination of linear and nonlinear filters as claimed in claim 1, wherein the 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.
6. The method according to claim 4, further comprising fitting a plurality of target trajectory data to obtain preset parameters of linear filtering and nonlinear filtering parameter values, wherein the preset parameters include standard deviation σ of Gaussian function, width N of Gaussian template, highest order D of polynomial, number of samples k, and sample data L of median filtering.
7. The method for real-time forecasting of ship tracks based on the combination of linear and nonlinear filters according to any of claims 1 to 6, characterized in that it further comprises the quantitative evaluation of the prediction results based on the mean square error MSE.
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Cited By (2)
| 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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Cited By (2)
| 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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