A Fusion Tracking Algorithm for Electro-Optical Theodolite Based on the Three-State Transition Model
Abstract
:1. Introduction
- (1)
- The enhancement of detection performance is achieved by utilizing multiple measurements of the target concurrently. By employing fusion computation, the precision of target state estimation is increased, thereby reducing the level of uncertainty in the information obtained.
- (2)
- The enhancement of the tracking system’s robustness is achieved through the incorporation of multiple sensors, providing redundancy during target field tests to ensure the detection of the target by at least one sensor. This redundancy serves to facilitate the smooth progression of the mission.
2. Adaptive Weighted Fusion Algorithm
2.1. Adaptive Weighted Fusion Algorithm Based on Error Covariance Recursion
2.2. The Enhanced Adaptive Weighted Fusion Algorithm
3. Fusion Tracking Algorithm Based on Three-State Transition Model
3.1. The Three-State Transition Model and Fusion Tracking Principle
- (1)
- In the event that the sensor is in a state of hold, the algorithm assesses whether this particular sensor holds the utmost priority among all sensors also in the hold state. Should this criterion be satisfied, the algorithm then proceeds to derive the measurement values from this sensor for the current time. Conversely, it will switch to the sensor with the highest priority within the hold state and employ its measured values as the output for the current time.
- (2)
- In the fusion state, the algorithm employs the adaptive weighted fusion value of azimuth and elevation measurements as the output for the present time.
- (3)
- If none of the conditions mentioned above are met, signifying that the sensor is in the switch state, the algorithm proceeds to the sensor with the greatest priority in the hold state. Following this, it employs the measurement obtained from this sensor as the output for the present time.
3.2. Measurement with Effective Bits Fusion Tracking Algorithm
4. Experimental Results and Discussion
4.1. Experimental Conditions and Parameters
- (1)
- The existence of background regions sharing similar characteristics with the target could lead to fluctuating off-target amounts in image analysis, especially when the target trajectory intersects these regions. The instability observed may result in fluctuating states in sensor measurements that correspond to the respective areas.
- (2)
- When new moving objects are detected within the sensor’s field of view and are mistakenly identified as the intended target, the sensor will record angles corresponding to the movement path of the incorrect target. Consequently, this may lead to an inability to precisely track the original target.
- In the azimuthal direction, the target’s initial position is defined as 100, accompanied by an initial angular velocity of 0.05 and an angular acceleration of 0.002 for uniform acceleration motion.
- In the elevation direction, the target’s initial position is established at an angle of 60, accompanied by an initial angular velocity of 0.03 and an angular acceleration of −0.0005 for uniform deceleration motion.
- The simulation lasts for 20 s, utilizing a sensor sampling rate of 100 Hz and an attenuation factor of 0.95.The measurement values of each sensor are acquired by introducing random noise to the ideal values. Sensors 1 to 4 are labeled as Z1 to Z4, respectively. Sensor 1 is characterized by the lowest noise variance and the highest priority. The error levels of Z2, Z3, and Z4 escalate sequentially based on their priority.
4.2. Simulation Experiment 1
4.3. Simulation Experiment 2
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Number of Effective Sensors | |
---|---|
2 | 0.35 |
3 | 0.25 |
4 | 0.1 |
Method 1 | Method 2 | Method 3 | ||||
---|---|---|---|---|---|---|
MAX_MSE_A (10−4) | 41.8772 | 33.1794 | 0.1337 | 0.1036 | 0.1323 | 0.1034 |
MAE_A (10−3) | 25.0461 | 14.2845 | 2.6009 | 2.1840 | 2.5908 | 2.1702 |
MAX_MSE_E (10−4) | 41.5964 | 29.5217 | 0.0059 | 0.0059 | 0.0059 | 0.0058 |
MAE_E (10−3) | 24.5366 | 12.4860 | 0.5769 | 0.5702 | 0.5736 | 0.5714 |
Method 1 | Method 2 | Method 3 | ||||
---|---|---|---|---|---|---|
Switching Time (s) | 10.01 | 10.01 | 7.93 | 7.93 | 7.92 | 7.89 |
Delay of Switching Time (s) | 2.51 | 2.51 | 0.43 | 0.43 | 0.42 | 0.39 |
Method 1 | Method 2 | Method 3 | ||||
---|---|---|---|---|---|---|
MAX_MSE_A (10−4) | 18.8702 | 8.4478 | 0.9550 | 0.1998 | 0.6189 | 0.1907 |
MAE_A (10−3) | 10.9451 | 7.5683 | 4.5671 | 3.2638 | 4.4942 | 3.2376 |
MAX_MSE_E (10−4) | 5.6569 | 2.2718 | 0.1343 | 0.0137 | 0.0739 | 0.0114 |
MAE_E (10−3) | 4.9615 | 3.3155 | 1.1386 | 0.8025 | 1.0370 | 0.7854 |
Method 1 | Method 2 | Method 3 | ||||
---|---|---|---|---|---|---|
Switching Time (s) | 9.51 | 9.37 | 8.55 | 8.21 | 8.61 | 8.22 |
Delay of Switching Time (s) | 2.01 | 1.87 | 1.05 | 0.71 | 1.11 | 0.72 |
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Zhang, S.; Wang, H.; Song, L.; Li, H.; Liu, S. A Fusion Tracking Algorithm for Electro-Optical Theodolite Based on the Three-State Transition Model. Sensors 2024, 24, 5847. https://doi.org/10.3390/s24175847
Zhang S, Wang H, Song L, Li H, Liu S. A Fusion Tracking Algorithm for Electro-Optical Theodolite Based on the Three-State Transition Model. Sensors. 2024; 24(17):5847. https://doi.org/10.3390/s24175847
Chicago/Turabian StyleZhang, Shixue, Houfeng Wang, Liduo Song, Hongwen Li, and Shuai Liu. 2024. "A Fusion Tracking Algorithm for Electro-Optical Theodolite Based on the Three-State Transition Model" Sensors 24, no. 17: 5847. https://doi.org/10.3390/s24175847