Military Communications and Information Technology: A Trusted ...
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Military Communications and Information Technology: A Trusted ... Military Communications and Information Technology: A Trusted ...

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290 Military Communications and Information Technology... • Distributed Kalman Filter using Relaxed Evolution (DKF-RE): The relaxed evolution model describes the transition kernel with an increased process noise covariance by a factor of S. The prediction is therefore given by s s kk | 1 , kk | 1 k1| k1 kk | 1 S kk | 1 P F P F Q (29) s s x . kk | 1 Fkk | 1xk1| k1 (30) This approach spares out the decorrelation by remote covariance matrices. Instead, an approximation which relies only on local parameters and the constant number of sensors is used. x 10 4 Target state estimates 3 2 1 Y 0 −1 −2 −3 −3 −2 −1 0 1 2 3 X x 10 4 Figure 4. Example trajectory of the simulated target in the field of view of 20 sensors V. Evaluation In this section the previous fusion schemes are assessed through simulation. In a single simulation run each algorithm uses the same measurement data. The trajectory is sampled accordingly to the Discrete White Noise Acceleration Model (DWNAM) [1] and all filters use perfectly matched models for the dynamics and the sensors, respectively. A Gaussian distributed zero-mean measurement noise is simulated for each sensor measuring the position of a single target with a variance of 500 m 2 in x- and y-direction. Figure 4 shows an example trajectory of the target. Packet losses by network effects such as congestion and buffer overflows or unreliable Layer-2-Links are simulated by randomly discarding data, which is sent over the connecting network. Figure 5 (a) – (d) shows the Root Mean Squared Er-

Chapter 3: Information Technology for Interoperability and Decision... 291 ror (RMSE) of the aforementioned multi sensor fusion schemes at different levels of communication losses. The probability of a successful transmission was set to (a) 100% (full communication) and (b) 60%, (c) 30% or (d) 10% respectively. It can be seen with full communication, which is shown in Figure 5 (a), the CKF, DKF-GP and DKF-RE have identical performance. This is in agreement with the established assertion in the literature that optimal track to track fusion, in terms of the MSE metric, can be achieved under full communication. It can also be seen that there is a significant improvement in performance by adopting a fusion scheme in comparison to just a single Kalman filter. However, the performance of the Naive fusion scheme is worse than the optimal achieved by CKF, DKF-GP and DKF-RE, as Naive fusion maintains an inconsistent covariance due to ignoring the cross correlations. CKF Single KF DKF_Gp DKF_Relaxed_Evolution Naive_Fusion CKF Single KF DKF_Gp DKF_Relaxed_Evolution Naive_Fusion RMSE RMSE 10 1 0 20 40 60 80 100 120 140 160 180 200 Time (s) 10 1 0 20 40 60 80 100 120 140 160 180 200 Time (s) (a) 100% (full communication) (b) 60% CKF Single KF DKF_Gp DKF_Relaxed_Evolution Naive_Fusion RMSE RMSE CKF Single KF DKF_Gp DKF_Relaxed_Evolution Naive_Fusion 10 1 0 20 40 60 80 100 120 140 160 180 200 Time (s) 0 20 40 60 80 100 120 140 160 180 200 10 1 Time (s) (c) 30% (d) 10% Figure 5. Log-scaled plots of the Root Mean Squared Error for 200 Monte Carlo simulations. The probability of a successful transmission was set to (a) 100% (full communication), (b) 60%, (c) 30% or (d) 10% respectively Figure 5 (b) shows the RMSE when the communication capability is reduced and only 60% of the transmissions are successful. As the complete information can no longer be transmitted to the fusion center, the RMSE of the fused esti-

Chapter 3: <strong>Information</strong> <strong>Technology</strong> for Interoperability <strong>and</strong> Decision...<br />

291<br />

ror (RMSE) of the aforementioned multi sensor fusion schemes at different levels<br />

of communication losses. The probability of a successful transmission was set to<br />

(a) 100% (full communication) <strong>and</strong> (b) 60%, (c) 30% or (d) 10% respectively.<br />

It can be seen with full communication, which is shown in Figure 5 (a),<br />

the CKF, DKF-GP <strong>and</strong> DKF-RE have identical performance. This is in agreement<br />

with the established assertion in the literature that optimal track to track fusion,<br />

in terms of the MSE metric, can be achieved under full communication.<br />

It can also be seen that there is a significant improvement in performance by<br />

adopting a fusion scheme in comparison to just a single Kalman filter. However,<br />

the performance of the Naive fusion scheme is worse than the optimal achieved by<br />

CKF, DKF-GP <strong>and</strong> DKF-RE, as Naive fusion maintains an inconsistent covariance<br />

due to ignoring the cross correlations.<br />

CKF<br />

Single KF<br />

DKF_Gp<br />

DKF_Relaxed_Evolution<br />

Naive_Fusion<br />

CKF<br />

Single KF<br />

DKF_Gp<br />

DKF_Relaxed_Evolution<br />

Naive_Fusion<br />

RMSE<br />

RMSE<br />

10 1 0 20 40 60 80 100 120 140 160 180 200<br />

Time (s)<br />

10 1 0 20 40 60 80 100 120 140 160 180 200<br />

Time (s)<br />

(a) 100% (full communication) (b) 60%<br />

CKF<br />

Single KF<br />

DKF_Gp<br />

DKF_Relaxed_Evolution<br />

Naive_Fusion<br />

RMSE<br />

RMSE<br />

CKF<br />

Single KF<br />

DKF_Gp<br />

DKF_Relaxed_Evolution<br />

Naive_Fusion<br />

10 1 0 20 40 60 80 100 120 140 160 180 200<br />

Time (s)<br />

0 20 40 60 80 100 120 140 160 180 200<br />

10 1 Time (s)<br />

(c) 30% (d) 10%<br />

Figure 5. Log-scaled plots of the Root Mean Squared Error for 200 Monte Carlo simulations.<br />

The probability of a successful transmission was set to (a) 100% (full communication), (b) 60%,<br />

(c) 30% or (d) 10% respectively<br />

Figure 5 (b) shows the RMSE when the communication capability is reduced<br />

<strong>and</strong> only 60% of the transmissions are successful. As the complete information<br />

can no longer be transmitted to the fusion center, the RMSE of the fused esti-

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