Table 1 Comparison of simulation results for single robot, multi-robot decentralized and federated decentralized filter

Field size (m × m)

300 × 300

300 × 300

300 × 300

Grid size for initial samples collection (n × n)

30 × 30

30 × 30

30 × 30

Number of neurons (B)

40

40

40

RBF variances (σ)

30

30

30

Number of sampling robots (N)

1

4

4

Grid size for adaptive sampling (p × p)

5 × 5

5 × 5

5 × 5

Horizon size (in grids) for next sample selection for each robot

10

30

10

Initial parameters error covariances$\left[\begin{array}{ccccc}\hfill b\hfill & \hfill a_i\hfill & \hfill si\hfill & \hfill x_{0i}\hfill & \hfill y_{0i}\hfill \end{array}\right]$

$\left[\begin{array}{ccccc}\hfill 200\hfill & \hfill 50\hfill & \hfill {10}^{-7}\hfill & \hfill 4\hfill & \hfill 4\hfill \end{array}\right]$

$\left[\begin{array}{ccccc}\hfill 200\hfill & \hfill 50\hfill & \hfill {10}^{-7}\hfill & \hfill 4\hfill & \hfill 4\hfill \end{array}\right]$

$\left[\begin{array}{ccccc}\hfill 200\hfill & \hfill 50\hfill & \hfill {10}^{-7}\hfill & \hfill 4\hfill & \hfill 4\hfill \end{array}\right]$

Sensor measurement error covariance (R)

1

1

1

Initial norm of error covariance of all parameters$(‖P_0‖)$

375.9

375.9

375.9

Final norm of error covariance of all parameters$(‖P_{k+1}‖)$

13.25

241.0

17.27

Norm of error between original and initial estimated field$(‖g-g_{est\_0}‖)$

25.05

25.05

25.05

Norm of error between original and final estimated field$(E_{2F}=‖g-g_{est\_k+1}‖)$

19.67

48.0

19.33

Time taken to reach$(‖g-g_{est\_k+1}‖)<20$

11.92 min

5.48 min

2.89 min

No. of samples (qN)

300

300

320

No. of times KF runs for calculating the parameter estimates

300 (complete estimate)

1 (complete estimate)

320 (partial estimate)

# of samples/robot after which global estimate is calculated (q/r)

1

300

20

No. of times fusion is performed using LEs (r)

N/A

N/A

4