1. Introduction
Multi-sensor fusion is the monitoring and tracking of targets in the surveillance area by means of networking, which has been widely used in air traffic control, air defense surveillance and other fields. Commonly used sensors are: radar (RA), secondary radar (SSR), enemy and self recognizer (IFF), photoelectric infrared (IF), etc. The main purpose of sensor resource scheduling and control is to make full use of these sensors to collect relevant information to satisfy the all-around surveillance and tracking of multiple targets, or to get the optimal metrics (such as probability of detection, trajectory accuracy, etc.) for a specific characteristic required by the system to scientifically control the sensor resources by this optimal criterion. This optimization criterion is used to allocate the sensor resources in a scientific and reasonable way. Another purpose of sensor resource scheduling and control is to realize the overall optimization of the multi-sensor system, by checking the interrelationship between the tracking situation and the demand criteria to generate a feedback, and continuously adjust and control the sensor work. Through the resource scheduling control of different characteristics and functions of the sensor to take full advantage of multiple sensors or the advantages of their respective operations, you can improve the effectiveness of the multi-sensor fusion system, resource scheduling control is the core of the multi-sensor data fusion system in the use and management of multi-sensor data fusion system to achieve the goal of the target monitoring system, the target characteristics of the main way to obtain. It is mainly through the optimal allocation of resources within the multi-sensor data fusion system. Through unified resource scheduling, a collaborative detection mode is formed, more resources are focused on key observation areas and targets, and more attention is paid to key targets while taking into account regional surveillance. Evaluate the utilization of multi-sensor resources, form an optimized method and effective strategic layout, provide guidance methods for optimization and deployment, and enhance the effectiveness of the system; in terms of system control, consider the change of discovery probability, collaborative detection, human intervention, and other factors, and carry out the integrated management of system detection and collaborative control; resource control is mainly based on the guidance information of the command center, human control commands, and target posture information, to complete the control of sensor resources, and to ensure that the system can be used in a timely manner. Resource control is mainly based on the guidance information, human control commands, and target posture information of the command center to complete the task allocation, work mode and resource scheduling of the sensor resources.
Adopting the strategy based on covariance control to optimize the resource scheduling control, the first is to pre-set a desired tracking accuracy for the target observed by the sensors, i.e., desired covariance matrix, and then control the sensors to make the actual covariance approximate the desired covariance in some sense in some metrics and criteria of the system, this is a general optimization model, which can be expressed by the following form of resource allocation model.
2. Resource allocation optimization model
In the process of multi-sensor observation of targets, it is assumed that the expected covariance matrix is set for D known observed targets as \( p_{0}^{i},(i=1,2,3,.....D), \) The control vector for the sensor is \( U({t_{k}})=\lbrace u(t)\rbrace 丨u(t)=0,1,2,....D;t={t_{1}},{t_{2}}...{t_{k}} \) }。Where u(t) denotes the working mode used by a certain sensor working at moment t u(t)=0 indicates that the sensor is performing a search task; u(t)=j indicates that the jth target is being tracked, then the optimal control model for resource scheduling and control in the process of observing the target by multiple sensors can be set up as follows [1]:
\( u({t_{k+1}})={j_{0}}({t_{k+1}})=ar{g_{min}}F[p_{0}^{i},{p^{i}}({t_{k+1}}丨U({t_{k}}),u({t_{k+1}})=j),i=0,1,2,.....D] \)
included among these \( {p^{i}}({t_{k+1}}丨U({t_{k}}),u({t_{k+1}})=j \) denotes the tracking error covariance matrix of the ith target at the moment tk+1 under the condition that the sensor is known to be tracking the ith target at that moment, and F is the metric function for calculating the deviation of the two sets of matrices. The above formula indicates that the criterion for the selection of the working mode of the sensor at the next moment is to make the tracking error covariance of all the targets closest to its desired covariance set under some metric criterion, that is, when the value of the [F] function is taken to be the smallest, it is the principle of the sensor resource scheduling and control. The specific representation of the function F can be further refined into two resource allocation criteria, i.e., the criterion of minimizing the maximum covariance deviation and the criterion of minimizing the mean value of the covariance deviation, which are hypothetically denoted as the F-1 criterion and the F-2 criterion [2].
For the F-1 criterion, the expression of the sensor resource allocation optimization management model is:
\( u({t_{k+1}})={j_{0}}({t_{k+1}})=ar{g_{min}}[maxf p_{0}^{i},{p^{i}}({t_{k+1}}丨U({t_{k}}),u({t_{k+1}})=j)] \)
For the F-2 criterion, the expression of the optimal management model for sensor resource allocation is:
\( u({t_{k+1}})={j_{0}}({t_{k+1}})=ar{g_{min}}[\frac{1}{D}f p_{0}^{i},{p^{i}}({t_{k+1}}丨U({t_{k}}),u({t_{k+1}})=j)] \)
where the function f(A,B) denotes the dissimilarity measure between matrix A and matrix B, which can be selected in a number of different matrix representations as needed. The general optimization model for sensor resource allocation described above is not limited by the number of dimensions of the state estimates of individual targets in the surveillance area and the number of targets to be tracked, since the core basis of this optimization model is to preset a desired tracking accuracy, i.e.,[3] a desired covariance matrix, and then allocate the sensor resources in the grouping according to some metric criterion that is chosen. Suppose that the most recent filtered update states of the D observed targets prior to the long moment are known to be:
\( \lbrace {t_{k(i)}},{p^{i}}t({k_{(i)}})\rbrace ,(t({k_{(i)}} \lt {t_{k}}) \) ,
where the k(i) subscript denotes the discrete ordinate of the kth filtering for the ith target.
Assume that the discretized equation of state for the ith target is:
\( {x^{i}}({t_{k+1}})={F^{i}}(T_{k}^{i}){x^{i}}({t_{k(i)}})+{G^{i}}(T_{k}^{i}){W^{i}}(T_{k}^{i}) \)
where \( {x^{i}}({t_{k(i)}}) \) represents the state vector of the ith target at the moment. \( {W^{i}}(T_{k}^{i}) \) is the white noise vector of the system with covariance matrix \( {Q^{i}}(T_{k}^{i}) \) , \( {F^{i}}(T_{k}^{i}) \) is the state transfer matrix at the period tk, \( {G^{i}}(T_{k}^{i}) \) is the input matrix at the moment tk, and \( T_{k}^{i}={t_{k+1}}-{t_{k(i)}} \) is the sampling interval of this target for the moment tk+1.
The measurement equation of the system is:
\( {Z^{i}}({t_{k}})={H^{i}}{x^{i}}({t_{k}})+{v^{i}}({t_{k}}) \)
where \( {Z^{i}}({t_{k}}) \) denotes the measurement vector of the radar system for target i at moment tk, \( {v^{i}}({t_{k}}) \) is the measurement noise whose covariance matrix is \( {R^{i}}({t_{k}}) \) , \( {H^{i}}({t_{k}}) \) is the observation matrix, and the noise \( {W^{i}}(T_{k}^{i}) \) is relatively independent of \( {v^{i}}({t_{k}}) \) and is independent of the \( {x^{i}}({t_{k}}) \) initial state.
Let the filter covariance and prediction covariance array in the filtering algorithm be \( {P^{i}}({t_{k+1}}) \) and \( {P^{i}}(t_{k+1}^{-}) \) ,, respectively, and the sensor control vector be \( U({t_{k}})=\lbrace u(t)\rbrace 丨u(t)=0,1,2,....D;t={t_{1}},{t_{2}}...{t_{k}} \) }. The tracking error covariance matrix of each target at moment tk+1 can be expressed as:
\( {p^{i}}({t_{k+1}}丨U({t_{k}}),u({t_{k+1}})=j)=\begin{cases}{P^{i}}({t_{k+1}}),i≠j \\ {P^{i}}(t_{k+1}^{-}),i=j\end{cases} \)
From the above equation tk+1, we can derive the error covariance matrix of all observation targets at the moment, which is brought into the sensor resource allocation model, and according to the current tracking state of the sensors and the expected covariance index [4], we can derive the form of resource allocation of the sensors at the next moment, so as to re-execute the resource scheduling control.
3. The matrix metric function selection
Comparing the difference between two matrices has a variety of metrics, often used matrices are column paradigm, 2-paradigm, Frobenius paradigm, matrix trace, determinant, and matrix singular value decomposition and so on. Comparing the variability between the actual covariance and the expected covariance array can be considered using the above matrix metrics.
Definition of Matrix Metric: A set X∈R is a linear space mapping \( :X*X→R,∀A,B∈X \) . over the number field illumination. f is said to be a matrix metric on a set X if the f mapping satisfies:(1) symmetry: f(A,B)=f(B,A); and (2) non-negativity: f(A,B)≥0. Thus the singular value decomposition of the matrices listed above, as well as the paradigm, trace, etc., can be used as a measure of the variability of the covariance matrices. Assuming two covariance matrices P1P2,, due to the covariance matrix has non-negative and symmetric properties available P1 = PT ≥ 0 and B2 = P2T ≥ 0 two representations of the situation, assuming that the difference between these two matrices is △P = [△P][5], there is a △P = P1-P2, without loss of generality, you can select the 2-paradigm of the matrix and the absolute value of the traces of the two matrix measures for the following analysis, the definition of the two matrix measures can be expressed as follows.
Table 1. Comparison of Matrix Properties and Metrics between P1 and P2
Matrix Property/Metric | P1 | P2 | ΔP = P1 - P2 |
Matrix Dimension | n x n | n x n | n x n |
Trace | Tr(P1) | Tr(P2) | ΔTr |
Determinant | det(P1) | det(P2) | Δdet |
2-Norm | ‖P1‖2 | ‖P2‖2 | ‖ΔP‖2 |
Singular Value Decomposition | σ1(P1) | σ1(P2) | Δσ1 = σ1(P1) - σ1(P2) |
Matrix Norm Difference | ‖P1‖F | ‖P2‖F | ‖ΔP‖F |
M-l metric: absolute value tracing.
\( f({P_{1}},{P_{2}})=trace[abs(△P)]=\sum _{i=1}^{n}|△{P_{ii}}| \)
M-2 metric: Matrix 2-paradigm:
\( f({P_{1}},{P_{2}})={||△P||_{2}}={||{P_{1}}-{P_{2}}||_{2}} \)
When comparing the difference between the expected covariance and the actual covariance, the choice of matrix metrics is not limited to the variability metrics of the two matrices, but can be flexibly selected for the working modes and parameters of the sensors in the group network, etc [6].
4. Conclusion
This paper describes the study of resource scheduling control in multi-sensor fusion based on covariance control strategy, and describes the resource optimization in multi-sensor fusion system under the premise of maintaining the target covariance in the range of desired covariance, and utilizing the characteristics of different sensors according to the system needs to carry out resource management control for multiple sensors. Using the advantages of multiple sensors with different characteristics, the network can improve the spatial resolution and target discovery probability in a large surveillance area as much as possible, and can also treat all the tracked targets in its surveillance area differently, such as concentrating more resources on the key observation area and the key observation targets, and paying more attention to the key targets while taking into account the regional surveillance.
Authors contribution
The two authors contributed equally to this paper.
References
[1]. Du Wei,Wang Yu,Meng Linan. Security distribution system of experimental center based on sensor data fusion[J]. Electronic Fabrication, 2023, 31(24):66-70.
[2]. LU Xiuli, HU Tianyu, Jisong, et al. Research on wireless sensor network positioning based on improved bat optimization algorithm[J]. Foreign Electronic Measurement Technology, 2023, 42(6):103-109.
[3]. WU Yao,ZHU Nongtai. Multi-sensor fusion method for lane lines based on graph optimization,system,electronic device:CN202211616852.4[P].CN115984654A[2024-06-05].
[4]. Y. J. Zheng,X. D. Liu,T. Zhou,et al. Research on optimization strategy of robotics and automation technology in process intelligent upgrading[J]. Manufacturing Automation, 2023, 45(10):216-220.
[5]. Dai Liang, Zhang Jinlong, Qin Wen. Optimization strategy of roadside unit transfer control for transportation energy integration[J]. Control and Decision, 2023, 38(12):3354-3362.
[6]. M. J. Beschooner, J. D. Spetzinger, Shogo Tada, et al. Method and system for controlling fluid pressure in a machine using sensor fusion feedback.CN201810614298.3 [2024-06-05].
Cite this article
Ma,Y.;Tie,Y. (2024). Co-optimization of sensor fusion and control strategies in electrical and electronic systems. Applied and Computational Engineering,70,226-229.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
Disclaimer/Publisher's Note
The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of EWA Publishing and/or the editor(s). EWA Publishing and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
About volume
Volume title: Proceedings of the 2nd International Conference on Functional Materials and Civil Engineering
© 2024 by the author(s). Licensee EWA Publishing, Oxford, UK. This article is an open access article distributed under the terms and
conditions of the Creative Commons Attribution (CC BY) license. Authors who
publish this series agree to the following terms:
1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons
Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this
series.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published
version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial
publication in this series.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and
during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See
Open access policy for details).
References
[1]. Du Wei,Wang Yu,Meng Linan. Security distribution system of experimental center based on sensor data fusion[J]. Electronic Fabrication, 2023, 31(24):66-70.
[2]. LU Xiuli, HU Tianyu, Jisong, et al. Research on wireless sensor network positioning based on improved bat optimization algorithm[J]. Foreign Electronic Measurement Technology, 2023, 42(6):103-109.
[3]. WU Yao,ZHU Nongtai. Multi-sensor fusion method for lane lines based on graph optimization,system,electronic device:CN202211616852.4[P].CN115984654A[2024-06-05].
[4]. Y. J. Zheng,X. D. Liu,T. Zhou,et al. Research on optimization strategy of robotics and automation technology in process intelligent upgrading[J]. Manufacturing Automation, 2023, 45(10):216-220.
[5]. Dai Liang, Zhang Jinlong, Qin Wen. Optimization strategy of roadside unit transfer control for transportation energy integration[J]. Control and Decision, 2023, 38(12):3354-3362.
[6]. M. J. Beschooner, J. D. Spetzinger, Shogo Tada, et al. Method and system for controlling fluid pressure in a machine using sensor fusion feedback.CN201810614298.3 [2024-06-05].