A fuzzy-controlled Kalman filter applied to stereo-visual tracking schemes

Fuzzy extended Kalman filter for dynamic mobile localization in urban area using wireless network

“…Notice that since there is at least one fuzzy rule which is activated at a given time, it holds that for at least one measurement > 0, which makes the expression (15) always definite. (15) assumes that the global estimate of the target corresponds to the weighted estimate of the local estimates in view of (14). This agrees with the intuition pertaining to the outcome of the fuzzy inference system.…”

“…These are based on the difference between the measurement and its predicted value, since, if the filter works correctly, the residual should be zero-mean Gaussian. Examples of typical rules are [13][14]: "If residual is OK then Q is unchanged"; "If residual is very near to zero then Q is reduced"; "If residual is very far from zero, then Q is increased". Another covariance estimation case is when the state transition noise is known or previously estimated, but the sensors state have changed during the process, requiring reestimation of measurement noise variance-covariance matrix.…”

“…A solution based on the use of fuzzy logic to tune the system and measurement noise has been proposed in [13][14], which allows the filter to reduce the risk of divergence. The key idea is to use an adaptive fuzzy logic based controller to continuously adjust the P and Q noise intensity depending on the gap between the theoretical and measured innovation.…”

Distributed Kalman filtering for multiagent systems

“…While this condition appears restrictive, in practice one rarely knows the true cross-covariances and it is often assumed that the covariance matrix is diagonal [13], [14]. Since our goal is to design separate observers for the two subsystems, but still minimize the estimation error covariance of the joint filter, we use separate Kalman filters for each subsystem.…”

“…Case 2: If the covariance of the estimates is also available, then x 1 can be considered as a stochastic input, with estimated covariance P 1 (k), for the second subsystem. For this case, a Kalman-type gain can be computed by minimizing the trace of the error covariance for the second subsystem, assuming that x 1 is a stochastic variable with a known covariance matrix P 1 (14). The covariance for x 2 is calculated as (15), where P 2 (k) is the true covariance obtained for the states of the second subsystem.…”