Solving the robustpeak-to-peak$\mathcal {L}_{1}$filtering problem requires a solution when persistent impulsive disturbances affect the model. In this letter, we solve the$\mathcal {L}_{1}$problem for a state-space model based on the backward Euler method with norm-bounded colored disturbances. Thepeak-to-peaklemma is modified and a new theorem is proved to numerically compute the bias correction gain$\bf {K}$for a recursive$\mathcal {L}_{1}$filter. The gain$\bf {K}$is computed numerically using a linear matrix inequality. Based on a numerical example of a quasi-periodic process subject to Gauss-Markov measurement disturbances with overshooting, it is shown that the gain$\bf {K}$of an$\mathcal {L}_{1}$filter satisfies the rule of thumb, i.e. it ranges between the Kalman gain and the unbiased finite impulse response (UFIR) filter gain. Accordingly, the$\mathcal {L}_{1}$filter occupies an intermediate place between the Kalman and UFIR filters. Herewith, having two additional tuning factors, it is more complex in tuning.

The$H_\infty$problem is reformulated for the bias correction gain of the recursive$H_\infty$-Kalman filter. For uncertain processes, the gain is computed using a linear matrix inequality, a bounded real lemma modified for non-predictive state space models based on Euler's backward method, and a new theorem. It is shown numerically that the gain of the$H_\infty$-Kalman filter is between the optimal Kalman gain and the gain of the robust unbiased finite impulse response filter. The filter performances are compared in terms of root mean square error, as well as the newly introduced robustness and estimation quality factors.

Ultrawideband (UWB)-based localization is widely used in environments inaccessible to global navigation satellite system signals. To improve the precision of UWB-based localization, a robust distributed adaptive extended unbiased finite impulse response (EFIR) filtering algorithm is developed. The algorithm is designed to reduce round-off errors and adaptively adjust noise covariances using the expectation-maximization (EM) approach. Based on extensive experimental testing, the EFIR algorithm is shown to outperform the distributed extended Kalman filter-based algorithm and distributed EFIR filter-based algorithm under harsh conditions.

In indoor robot localization by using ultra-wideband (UWB), the extended Kalman filter (EKF)-based algorithms suffer from the colored measurement noise (CMN) that degrades the localization accuracy and causes the divergence. To overcome this issue, we develop a hybrid colored EKF and colored extended unbiased finite impulse response (EFIR) filter (cEKF/EFIR filter) employing measurement differences. We also develop this algorithm using a filter bank on merged averaging horizons to be adaptive to time-varying CMN and call it the adaptive EKF/EFIR (aEKF/EFIR) filter. Experimental testing is provided in UWB-based indoor mobile robot localization environments. It is shown that the end-to-end colored EKF/EFIR and aEKF/EFIR filtering algorithms have better performances than the EKF, EFIR filter, and their modifications for CMN.

Accurate indoor localization information of the quadrotor plays an important role in many Internet-of-Things applications. To improve the estimation accuracy and robustness, a fixed-lag extended finite impulse response smoother (FEFIRS) algorithm is proposed for fusing the inertial navigation system (INS) and ultra wideband (UWB) data tightly, which employs a distance between the UWB reference nodes and a blind node measured by the INS and UWB. The FEFIRS algorithm consists of an extended unbiased finite impulse response (EFIR) filter and a fixed-lag unbiased FIR (UFIR) smoother. The EFIR filter is employed to improve the robustness, and the fix-lag UFIR smoother is capable of improving the accuracy. Based on extensive test investigations employing real data, the proposed FEFIRS has higher accuracy and robustness than the Kalman-based solutions in the tightly integrated INS/UWB-based indoor quadrotor localization.

A novel approach is proposed to H2finite impulse response (FIR) prediction in discrete-time state-space. The biased-constrained H2optimal unbiased FIR (H2-OUFIR) predictor derived under disturbances and measurement errors is shown to have the maximum likelihood form and be equivalent to the OUFIR predictor under Gaussian noise. The derivation is provided using the backward Euler method by minimizing the squared weighted Frobenius norm. A bias-constrained suboptimal H2FIR filtering algorithm using the linear matrix inequality is also designed. The H2-OUFIR predictor performance is investigated by simulations and experimentally in a comparison with the Kalman and unbiased FIR predictors.

Experience replay is a promising approach to improve the learning efficiency of adaptive dynamic programming. A general model-free adaptive dynamic programming (ADP) approach with the experience replay technology is investigated in this paper to solve the optimal control problems in continuous state and action spaces. Both the critic network and action network are modeled with a feedforward neural network with one hidden layer. During the learning process, a number of recently observed data samples are recorded in a database. When updating the parameters of the neural networks, the data in the sample database are repeatedly used to update the weights of the action network and the critic network. Implementation details of the algorithm are given, and simulation experiments are utilized to verify the learning efficiency of the proposed approach.