The robotic vehicle model, the sampling model is of form (7), and its uncertainty
covariances are given by (8). The sampling space ??– can be a grid.
Constants " > 0, p ?‰? 1 are given.
Step1 (initialize): Assume a starting robot location X0. Pick an initial
covariance estimate P0, and unknown parameter guess estimate a0. Remove
the starting sampling points from ??–. Denote the remaining sampling space as
??–0.
Step2: For each iteration step k starting at k = 0, and for each possible
control vector Uk, propagate the time update equations (9)??’(11) estimates
of the robot position and the current parameter guesses. Propagate the P
matrix measurement update using equation (13).
Step3: Pick the control input Uk that minimizes the p-norm of Pk+1.
Step4: Command the robot using the Uk found in Step3. Update the
robot position and the parameter estimates using equation (14) by utilizing
aposteriori measurements of the robot states and the sampling data while the
robot is in transit.
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Dan O. Popa and Frank L. Lewis
Step5: If the uncertainty measure becomes ???small??? enough, ||Pk+1|| ?‰¤ ",
exit, otherwise set k = k + 1 and repeat Step2.
It is apparent that the algorithm AS-3 is a more systematic way to reposition
the robot and estimate the parametric field than algorithms AS-1 and
AS-2.
5.1 EXAMPLE: Kalman Filter estimation for a parameter-linear
field
Instead of using the closed form numerical or algebraic solutions from Section
4.
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