Kalman filter and FMP filter ··· 41 Figure 2.29 Prediction tracking error of comparison Kalman filter of. The Kalman filter and the FMP filter ··· 42 Figure 3.1 East-West error in the third-order FMP filter observation.
Introduction
- Warship and Its Properties
- Introduction of Fading Memory Polynomial Filter (FMP Filter)
- Related Studies of the Study
- Scope, Methodology and Content of This Study
In the early work of Benedict and Bordner (1962), the dual-based filter analysis remains in the frequency domain (Z-transform). The study focuses on comparing the performance of the Benedict-Bordner filter, also known as the Simpson filter, the Gray & Murray filter, and the third-order FMP filter.
FMP Filter and Its Superiority
Fourth-order FMP Filter
Based on the two main stages of third-order FMP filter algorithm, the prediction stage and smoothing stage can be derived as equations. Equations are the prediction equations for position, velocity, acceleration and jerk respectively where they are updated from the estimated state, thus reducing the tracking error Equations are the smoothing equations calculated by adding a weighted difference between the observed and the predicted position to the prediction . state.
Superiority of FMP Filter
- Comparison of FMP Filter and Other Filter Algorithms
- Benedict-Bordner Model
- Filter Gain Coefficients Selection Using the Gray &
- Performance Comparison of the Filters
- Comparison of FMP Filter and Kalman Filter
- Kalman Filter Algorithm
- Simulation of Kalman Filter and FMP Filter
- Restult Comparison of FMP Filter and Kalman Filter · 37
The position trajectories of the Gray & Murray filter shown in Figure (2.11) appear to track the target quite stably compared to the FMP filter shown in Figure (2.9), which can be seen to have a slight overshoot at various points along the target's curves. As for the Benedict-Bordner filter, shown in Figure (2.10), the filter performs worse than the other two filters based on the visibly clear jerking motion, an indication of its inability to track this kind of target maneuver effectively. These results show that the FMP filter has a higher accuracy in both predicting and smoothing the position of the target warship, followed by the Gray & Murray filter.
Figure (2.28) and Figure (2.29) show the prediction errors resulting from the FMP filter and the Kalman filter, respectively. Figure (2.30) and Figure (2.31) are the smoothing errors obtained from the FMP filter and Kalman filter, respectively. These results show that the Kalman filter has slightly higher accuracy in both predicting and smoothing the position of the target warship than the FMP filter.
As shown in Table 2.3, the comparison result shows that the Kalman filter has slightly higher accuracy than the FMP filter in both prediction and smoothing of the target position.
Summary of Chapter 2
Third-order FMP Filter to Track High Mobility Warship
Noise Addition
Determination of Optimal
Figure (3.6) shows the sum of the total prediction tracking error and the total attenuation tracking error when the value changes from 0 to 1.
Third-order FMP filter to Track High Mobility Motion under the
- Input Model of Own Ship and Target
- Noise Addition
- Determination of Optimal
Figure (3.6) shows the sum of total prediction tracking error and total smoothing tracking error when value varies from 0 to 1. The curves decrease rapidly and reach the minimum, and then they increase rapidly. 3.2) where and are constants that serve to control the velocity of target in the input motion model. Figure (3.12) shows the prediction tracking error which stands for the difference between true position and predicted position, while Figure (3.13) shows the smoothing tracking error which stands for the difference between true and smoothed position.
Then set varying from 0 to 1 in steps of 0.01 and calculate the total prediction tracking error and the total smoothing tracking error for each step. Figure (3.14) shows the total prediction tracking error and the total smoothing tracking error as the value of varies from 0 to 1.
Speed-dependent Third-order FMP Filter to Track High Mobility
- Input Model of Target
- Noise Addition
- Determination of optimal
- Relationship between Speed and Optimal
Therefore, to obtain the optimal smoothing coefficients, the optimization of the FMP filter focuses on experimentally adjusting the value through trial and error. As shown in Table 3.2, it is visibly clear that the rate-dependent third-order FMP filter has higher performance than the classical third-order FMP filter. The prediction tracking error of the third-order velocity-dependent FMP filter is 18,632.96 m, while that of the classical third-order filter.
Similarly, the smoothing accuracy is increased by 161.05 by applying the velocity-dependent third-order FMP filter. Meanwhile, the standard deviation of prediction tracking error and the standard deviation of smoothing tracking error of rate-dependent FMP filter are obviously smaller than those of classical FMP filter, which indicates that the stability of rate-dependent FMP filter is much better.
Speed-dependent Third-order FMP Filter to Track High Mobility
- Input Model
- Noise Addition
- Determination of Optimal
- Relationship between Speed and Optimal
Therefore, to obtain the optimal attenuation coefficients, the optimization of the FMP filter focuses on adjusting the value through trial and error method. As shown in Table 3.3, it is quite clear that the rate-dependent third-order FMP filter has a higher performance than the classical third-order FMP filter. The prediction tracking error of the rate-dependent third-order FMP filter reaches while the classical third-order FMP filter describes its optimal performance with the resulting prediction tracking error.
Similarly, the smoothing accuracy is increased by 143.59 using the speed-dependent third-order FMP filter. Meanwhile, the standard deviation of prediction tracking error and the standard deviation of smoothing tracking error of speed-dependent FMP filter are obviously smaller than those of classical FMP filter, which indicates that the stability of speed-dependent FMP filter is much better.
Summary of Chapter 3
Meanwhile, the standard deviation of the prediction tracking error and the standard deviation of the smoothing tracking error of the rate-dependent FMP filter are obviously smaller than those of the classical FMP filter, which indicates that the stability of the rate-dependent FMP filter is much better. smoothing tracking errors Speed dependent. both own ship and target in motion. Because the relative motion has sudden changes in velocity and acceleration, therefore jerk correction, change in acceleration must be considered in order to improve the tracking accuracy. Therefore, the next chapter will discuss the fourth-order FMP filter for tracking a high-mobility battleship.
Fourth-order FMP Filter to Track High Mobility Warship
Simulation of Fourth-order FMP Filter
The optimization process begins by calculating the total transient error which is the sum of the squares of the difference between the true trajectory and the predicted trajectory. The goal of optimization is to find the discount factor that minimizes this error, then use this information to calculate the optimal damping constants. Therefore, this is achieved by drawing a line of the discount factor, which lies in .
Figure (4.4) shows the consistency with regard to the optimal and therefore maintains the validity of the results, as it indicates a corresponding value of the optimal discount factor. They represent plots of the total error difference between the true and predicted trajectories and between the true and smoothed trajectories, respectively, against corresponding values.
Result Analysis of Fourth-order FMP Filter
Figure (4.8) and Figure (4.9) plot the prediction tracking error and the smoothing tracking error for the third-order FMP filter and the fourth-order FMP filter. As shown in the table below, the third-order FMP filter shows the best performance when =0.64 with the prediction tracking error corresponding to . Meanwhile, the standard deviation of prediction tracking error and smoothing tracking error of the fourth-order FMP filter is slightly smaller than that of the third-order FMP filter.
It indicates that the stability of fourth-order FMP filter is higher than the stability of third-order FMP filter. Meanwhile, the stability of fourth-order FMP filter is higher than the stability of third-order FMP filter.
Fourth-order FMP Filter to Track Trigonometric Function
- Input Model of Own Ship and Target
- Noise Addition
- Determination of Optimal
- Input Model
- Noise Addition
- Determination of Optimal
- Curve Fitting by Least Square Method
- Advantages of Speed-dependent FMP Filter
In contrast, the rate-dependent FMP filter exhibits its optimal performance with a consequent prediction tracking error. Meanwhile, the standard deviation of the prediction tracking error and the smoothing tracking error of the rate-dependent FMP filter are slightly smaller than those of the fourth-order FMP filter. It shows that the stability of the rate-dependent FMP filter is relatively higher than that of the fourth-order FMP filter.
The prediction detection error of speed-dependent fourth-order FMP filter amounts to while the speed-dependent third-order FMP filter exhibits its optimal performance with prediction detection error as a result. Similarly, the smoothing accuracy is increased by 659.04 using the speed-dependent fourth-order FMP filter.
Speed-dependent Fourth-order FMP Filter to Track High Mobility
- Input Model of Own Ship and Target
- Noise Addition
- Determination of Optimal
- Relationship between Speed and Optimal
- Advantages of Speed-dependent FMP Filter
On the contrary, the rate-dependent FMP filter shows its optimal performance with a total prediction tracking error resulting from . FMP filter to track high mobility targets under the condition of own ship and moving targets. The prediction tracking error of the rate-dependent fourth-order FMP filter is equal to , while the rate-dependent third-order FMP filter shows its optimal performance with a total prediction tracking error due to .
Similarly, the smoothing accuracy increases by 944.68 using the velocity-dependent fourth-order FMP filter. Meanwhile, the standard deviation of the prediction tracking error and the smoothing tracking error of the rate-dependent fourth-order FMP filter are smaller than the rate-dependent third-order FMP filter, indicating that the stability of the rate-dependent fourth-order FMP filter is relatively higher.
Performance of Fourth-order FMP Filter to Track Random
- Generation of Trajectory Function
- Determination of Parameters in Motion Model
- Simulation
Therefore, it is necessary to verify the performance of the fourth-order FMP filter while the trajectories are different. This section therefore investigates the performance of the fourth-order FMP filter for tracking random motion cases. The motion model of the own ship and the target is generated by a multi-level combined trigonometric function, whose amplitude and wavelength parameters are randomly generated.
To simulate tracking in a relatively similar environment, the parameterization of the motion models requires that the speed of the target and own ship must lie in the range of. Figure (4.29) - Figure (4.36) shows four cases of data generation results, and it is obvious that they have obvious differences in each case.
Summary of Chapter 4
Conclusion
Basic investigation of performance comparison of α-β-γ filter and Kalman filter for use in a tracking module for arpa system aboard high dynamic warships. Performance comparison of alpha-beta-gamma filter and Kalman filter for target tracking using radar measurements. Basic study comparing performance of α-β-γ filter and Kalman filter for use in a tracking module for ARPA system aboard high dynamic warships.
Comparison of performance of α-β-γ -η filter and Kalman filter for ARPA system to detect high dynamic target. Basic study on the comparison of performance of α-β-γ filter and Kalman filter for use in a detection module for ARPA system on board high dynamic warships.
