Multi-sensor online track fusion method based on multiple outputs

Abstract

The application relates to a multi-sensor online track fusion method based on multi-output, a multi-element linear regression model is trained by using historical data, current track data fusion is realized through the model, on the basis, when new sensor track data and target real track data exist in the fusion process, real-time updating of model parameters is completed by using an online gradient descent algorithm, further next fusion is completed, otherwise the model parameters are not updated. Through the multi-sensor online track fusion method based on multi-output, the precision of track fusion is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of based on comprehensive weighting method's rubidium clock state monitoring method.Belong to control engineering technical field. BACKGROUND

[0002] Currently widely used in multi-sensor track fusion practical application is Kalman filter algorithm and weighted average fusion algorithm.The prediction function of Kalman filter algorithm is often used to realize track sequence time synchronization.Kalman filter algorithm uses the observation value of current time to update the estimation of state variable in combination with the estimation of previous time, to realize the prediction of current time estimation value.

[0003] Information fusion is a process of correlating, relating and synthesizing data and information obtained from single and multiple information sources to obtain accurate position and identity estimates. Multi-sensor track fusion technology, as a multi-level and multi-aspect information fusion process in a specific field, can integrate data under certain criteria to obtain state estimates closer to the true value of the measured physical quantity and more valuable comprehensive information than single sensor data, laying a solid foundation for target tracking and recognition tasks, and being widely used in military and civilian integration fields.

[0004] Although the traditional weighted average fusion algorithm can effectively improve the measurement quality of sensors with poor measurement quality, the measurement accuracy obtained by fusion is still limited, because in actual operation, the measurement error of the sensor is not only related to its own device resolution, but also closely related to the change of measurement environment and even the change of current target motion state. Therefore, adaptively adjusting the fusion weight to achieve the best fusion result in each cycle has become a research focus in the field of track fusion. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a multi-output multi-sensor online track fusion method to improve the accuracy of track fusion.

[0006] The technical scheme adopted by the present application to solve the above problems is: a multi-output multi-sensor online track fusion method, a multivariate linear regression model is trained using historical data, and current track data fusion is realized through the model. On this basis, in the fusion process, when there are new sensor track data and target true trajectory data, the online gradient descent algorithm is used to complete the real-time update of model parameters for the next fusion, otherwise the model parameters are not updated.

[0007] The multi-output linear regression model used in this invention is defined as follows: In multi-output learning, the regression task requires obtaining the values ​​of multiple output variables. If the correlation between output variables is not considered, and the model is learned only for each output variable individually, the effectiveness of the results will be severely compromised. Multiple linear regression models are typically used to represent the relationship between a dependent variable and the changes in multiple independent variables, i.e.:

[0008] y = β0 + β1x1 + ... + β k x k +ξ

[0009] Where x1, ..., x k y is a non-random variable, β0, ..., β is a random dependent variable. k ξ is the regression coefficient, and ξ is the random error term. In a multi-output multiple linear regression model, the output consists of m dependent variables, i.e.:

[0010] y i =β0+β1x 1i +…+β k x ki +ξ i

[0011] The multi-output multiple linear regression model can be expressed as:

[0012]

[0013] The above expression can be represented as:

[0014] Y = βX + ξ

[0015] Where Y is an m-dimensional output vector, β is a k-dimensional regression coefficient vector, X is an m×(k+1) input matrix, and ξ is an error vector.

[0016] The detailed process of the multi-output, multi-sensor online trajectory fusion method of this invention can be described as follows:

[0017] 1. Pretreatment

[0018] Assume that the coordinate transformation, time-scale alignment, and target track association have been completed for each sensor's individual station tracks. Preprocessing mainly focuses on the first-order difference of the individual station tracks; the preprocessed first-order difference data essentially retains only the relative position information of the object's motion. Assume sensors A and B at time t... k The coordinates of the time are respectively and Performing a first-order difference on the coordinates yields the preprocessed coordinates. and Calculate using the following formula:

[0019]

[0020]

[0021]

[0022] 2. Multi-output linear regression model fusion

[0023] The multi-output linear regression model trained by samples can learn the movement law of the target and the error information. The model uses an online gradient descent algorithm to complete the training. In each round of training, it always corrects the model parameters in the direction of the negative gradient of the instantaneous loss function.

[0024] The training process is as follows:

[0025] Let

[0026] (1) Arbitrarily select a 3D model parameter vector β 2 ;

[0027] (2) Prediction

[0028] (3) Calculate the loss f(β 2 ) = (Y 2 - β 2 X 2 ) 2 ;

[0029] (4) Calculate

[0030] (5) Calculate

[0031] (6) Repeat steps 2-5 to update the model parameters β one by one in the order of sample time;

[0032] (7) Output the final β as the model parameter.

[0033] 3. Data recovery

[0034] The inverse operation of the first-order difference of the coordinates is as follows:

[0035]

[0036]

[0037]

[0038] 4. Online update of the model

[0039] Online model updates are mainly implemented when the multi-output linear regression model receives new target coordinate data X during its use, and updates the parameter vector using steps 2-5 of the model training process.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] This invention, based on a multi-output, multi-sensor online track fusion method, improves the accuracy of track fusion by updating model parameters in real time after training the model with historical track data. Attached Figure Description

[0042] Figure 1 This is a flowchart of the multi-output, multi-sensor online trajectory fusion method of the present invention. Detailed Implementation

[0043] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0044] The experiment used real three-dimensional coordinate trajectory data of a satellite and real measurement data from two sensors. The dataset contained 6000 coordinate data points, in meters, with a data interval of 50 milliseconds. The step size η of the TR-OGD algorithm in the experiment was 10. -11 To evaluate the effectiveness of the algorithm, this experiment compares the root mean square error (RMSE). RMSE is the square root of the ratio of the sum of squares of the differences between the fused results and the true values ​​to the data length. It truly reflects the accuracy of the fusion method; the smaller the RMSE value, the better the prediction performance. The formula for calculating RMSE is as follows:

[0045]

[0046] In the experiment, the multi-output linear regression online track fusion algorithm, based on the multi-output linear regression algorithm, uses 2.5% of the data (95%-97.5%) to update the algorithm parameters according to the data time scale. All three methods fuse the remaining 2.5% of the data. The RMSE is shown in Table 1. Comparison reveals that the multi-output linear regression online fusion algorithm has higher accuracy than the other two algorithms, demonstrating the effectiveness of online parameter updates.

[0047] Table 1 RMSE of the three methods

[0048]

[0049] In addition to the above embodiments, the present invention also includes other embodiments. All technical solutions formed by equivalent transformation or equivalent substitution should fall within the protection scope of the claims of the present invention.

Claims

1. A multi-sensor online trajectory fusion method based on multiple outputs, characterized in that, The method includes performing first-order difference analysis on single-station tracks, and then using a multi-output linear regression model trained on samples to complete track fusion. The multi-output multivariate linear regression model is expressed as: Y = βX + ξ, where Y is an m-dimensional output vector, β is a k-dimensional regression coefficient vector, X is an m×(k+1) input matrix, and ξ is an error vector. Then, the inverse operation of first-order difference is performed on the coordinates to achieve data recovery. When new sensor track data and target real trajectory data are available, the online gradient descent algorithm is used to update the model parameters in real time for the next track fusion. The first-order difference for a single-station track includes: Assume sensors A and B are at time t k The coordinates of the time are respectively and Performing a first-order difference on the coordinates yields the preprocessed coordinates. and Calculate using the following formula: Track fusion is accomplished using a multi-output linear regression model trained on samples, including: The multi-output linear regression model trained on samples can learn the motion patterns and error information of the target. The model is trained using an online gradient descent algorithm. In each training round, the regression model always corrects the model parameters along the negative gradient direction of the instantaneous loss function. The specific training process is as follows: make (1) Arbitrarily select the 3D model parameter vector β 2 ; (2) Prediction (3) Calculate the loss l(β) 2 )=(Y 2 -β 2 X 2 ) 2 ; (4) Calculation (5) Calculation (6) Repeat steps 2-5 to update the model parameter β one by one according to the sample time sequence; output the final β as the model parameter; Data recovery by performing the inverse operation of the first-order difference on the coordinates includes: The inverse operation of the first-order difference of the coordinates is performed as follows:

2. The multi-output, multi-sensor online trajectory fusion method according to claim 1, characterized in that, When new sensor track data and target real trajectory data are available, the online gradient descent algorithm is used to update the model parameters in real time for the next track fusion. The specific process includes: The online model update is mainly used when the multi-output linear regression model receives new target coordinate data X during its use. The model updates the parameters in real time by using the specific logic of (2) predicting output, (3) calculating loss function, (4) solving gradient, and (5) updating parameter vector during the model training process.

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