Modified Champernowne Function Based Robust and Sparsity-Aware Adaptive Filters

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

This paper presents a new robust adaptive unscented particle filtering algorithm by adopting the concept of the adaptive robust filtering to the unscented particle filter. This algorithm adaptively determines the equivalent weight function and adaptively adjusts the adaptive factor constructed from predicted residuals to resist the disturbances of singular observations and the kinematic model noise, thus preventing particles from degeneracy. It also uses the unscented transformation to improve the accuracy of particle filtering, thus providing the reliable state estimation for improving the performance of adaptive robust filtering. Experiments and comparison analysis demonstrate that the proposed filtering algorithm can effectively resist disturbances due to system state noise and observation noise, and the filtering accuracy is much higher than the extended Kalman filter, unscented Kalman filter, standard particle filter and unscented particle filter.

Robust adaptive filter allowing systematic model errors for transfer alignment

In many applications of adaptive system identification, the output signal of an unknown system is corrupted by additive noise. When the additive noise is strong, the estimated weights of the adaptive filter cannot converge to desired weights with sufficient accuracy. In this report, we propose an interference robust block adaptive digital filter (BADF) which can improve the accuracy of the estimated weights by averaging the adaptive weight vectors. We also formulate the error variance of the estimated weights of the proposed method. >

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

Fault-tolerant SINS/HSB/DVL underwater integrated navigation system based on variational Bayesian robust adaptive Kalman filter and adaptive information sharing factor

In recent years, the hyperbolic family of adaptive algorithms have been widely used to combat impulsive noise. The novel exponential hyperbolic sine adaptive filters (EHSAF) and the normalized exponential hyperbolic sine adaptive filter (NEHSAF) suitable for impulsive noise environments are proposed in this brief. The cost function is based on the exponential hyperbolic sine-based error function. The stability condition based on the learning rate and the steady-state analysis are investigated too. Additionally, a variable scheme for the scaling parameter is proposed to remove the tradeoff between convergence speed and steady-state excess mean square error (EMSE). The computational complexity is presented too. The simulation results in the context of unknown system identification and echo cancellation application have been performed to prove the performance improvement of the proposed algorithms.

This paper proposes Adaptive Step-Size Least Mean Modulus (ASS-LMM) algorithm for fast convergent and robust adaptive filtering in the presence of impulse noise. The ASS-LMM algorithm for use in adaptive filters defined in the complex-number domain is basically the LMM algorithm combined with a new adaptive step-size control algorithm to improve the convergence speed of the LMM algorithm while preserving its robustness against additive impulsive observation noise. Through analysis and experiment, we demonstrate effectiveness of the proposed ASS-LMM algorithm in making adaptive filters fast convergent and highly robust in the presence of impulse noise. Good agreement between simulated and theoretical convergence behavior in the transient phase and in the steady state proves the validity of the analysis.

Aiming at the problems of Non-Line-of-Sight (NLOS) observation errors and inaccurate kinematic model in ultra-wideband (UWB) systems, this paper proposed an improved robust adaptive cubature Kalman filter (IRACKF). Robust and adaptive filtering can weaken the influence of observed outliers and kinematic model errors on filtering, respectively. However, their application conditions are different, and improper use may reduce positioning accuracy. Therefore, this paper designed a sliding window recognition scheme based on polynomial fitting, which can process the observation data in real-time to identify error types. Simulation and experimental results indicate that compared to the robust CKF, adaptive CKF, and robust adaptive CKF, the IRACKF algorithm reduces the position error by 38.0%, 45.1%, and 25.3%, respectively. The proposed IRACKF algorithm significantly improves the positioning accuracy and stability of the UWB system.

In this paper, a new robust adaptive FIR filter algorithm with variable forgetting factor for time-varying parameters estimation in the presence of impulsive noise is discussed. The proposed algorithm is based on the robust recursive least square and extended prediction error variable forgetting factor adaptation algorithms. The feasibility of the approach is demonstrated in a system identification simulation using a FIR filter application.

This paper develops a novel nonlinear adaptive robust filter called the multiple-step randomly delayed variational Bayesian adaptive high-degree cubature Huber-based filter (MRD-VBAHCHF) for a class of nonlinear stochastic systems whose measurements are randomly delayed by multiple sampling times and corrupted by contaminated Gaussian noise with unknown covariance. First, a system with randomly delayed measurement is modeled in terms of multiple Bernoulli random variables. Then, the multiple-step randomly delayed high-degree cubature Kalman filter (MRD-HCKF) is derived by employing the fifth-degree cubature rule to compute the mean and covariance of the nonlinear equations in the system model. Next, the MRD-HCKF is modified to the MRD-VBAHCHF by incorporating the variational Bayesian theory and Huber technique for estimating the measurement noise covariance online and suppressing the influence of non-Gaussian noise. Consequently, the proposed filter is not only adaptive to unknown measurement noise statistics but also robust to random measurement delays and non-Gaussian noise. Finally, the MRD-VBAHCHF is verified for use in inertial navigation system/visual navigation system (INS/VNS) integrated navigation on asteroid missions, and the results of Monte Carlo simulations demonstrate that the MRD-VBAHCHF outperforms the high-degree cubature Kalman filter (HCKF), the MRD-HCKF and the variational Bayesian adaptive high-degree cubature Huber-based filter (VBAHCHF), thus showing the superiority of the proposed filter.

A new solution to the numerical instability of fast recursive least squares adaptive filter algorithms is presented. Using interval arithmetic, an error analysis is effectively performed in parallel with the computations of the algorithm. If necessary the algorithm will be rescued, preventing divergence. This is shown in software simulations and in a hardware implementation of an adaptive equaliser.

With the development of global navigation satellite system (GNSS), the GNSS/inertial navigation system (INS) integrated system offers the users better positioning or navigation performance. This paper proposes an adaptive robust ultra‐tightly coupled GNSS/INS system based on a novel vector tracking strategy for combining both global positioning system (GPS) L1 and BeiDou B1 signals’ tracking together. The inherent mechanism of the vector tracking approach has been analysed to describe the relationship between the replica signals and user's dynamic state. Then, an adaptive robust filter is used to gain the accurate estimates of vehicle states when the vehicle is under a weak‐signal or large manoeuvring environment. Finally, the experimental platform is set up using a GPS/BeiDou signal simulator and an inertial measurement unit simulator and the test results show that the proposed ultra‐tightly coupled system can keep the tracking loops from the high dynamic perturbations, which saves the cost time of signal reacquisition. Moreover, the presented adaptive robust ultra‐tightly coupled system can obtain a higher accuracy than Kalman filtering in a simultaneous weak‐signal and large manoeuvring environment.

In the recent past, logarithmic hyperbolic cosine based-cost function has been widely applied in adaptive filters as it offers robust performance against outliers. However, the performance of such adaptive filters suffers from high steady-state misalignment due to its significant weight update, even in the presence of outliers. This paper proposes a logistic distance metric-based novel robust cost function, and the corresponding logistic distance metric adaptive filter (LDMAF) has been developed. The proposed LDMAF provides negligible weight update when the desired signals are affected by significant outliers, resulting in low steady-state misalignment. The bound on learning rate has been estimated, and computational complexity comparison of the proposed and other existing algorithms has also been carried out. To further exploit the system's sparse nature and robustness against the outliers, zero attraction-based LDMAF (ZA-LDMAF) and re-weighted zero attraction-based LDMAF (RZA-LDMAF) algorithms have also been developed in this paper. In addition, a new sparse penalty function based on a generalized multivariate Geman-McClure function has been introduced, which provides smooth <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{0}$</tex-math></inline-formula> -norm approximation over other existing functions. Based on this new sparse penalty function, this paper has also developed a novel sparsity-aware robust adaptive filter called generalized Geman-McClure LDMAF (GGM-LDMAF). Simulation studies confirmed the improved convergence behaviour achieved by the proposed algorithms over other existing algorithms for system identification and acoustic echo cancellation scenarios.

This paper proposes a multiple adaptive notch filter with the p‐th power average of the estimated error E[ep(n)] ‖as the cost function. The adaptive filter consists of a cascade connection of second‐order adaptive notch filters composed of the allpass filters. In general, the elimination bandwidth of the notch filter is desirably small from the practical point of view. However, as the elimination bandwidth is set smaller, the convergence speed of the tap coefficients of the adaptive filter becomes much slower. From the point of view of convergence theory, the radius of the pole of the second‐order allpass filter needs to be close to 1, so that the elimination bandwidth must be extremely small. Convergence speed must be sacrificed due to the practical and theoretical points of view. In this paper, an adaptive notch filter is studied in which the elimination bandwidth of the notch filter is designed small while the gradient of the tap vector of the cost function used in the adaptive algorithm is made effectively equal to the case in which the elimination bandwidth is rather large. In this way, realization of a multiple adaptive notch filter with a high convergence is possible. The absolute value of the transfer function of the notch filter is close to 0 near the elimination frequency while it is close to 1 at other frequencies. Hence, by setting the power of the absolute value larger, the elimination bandwidth becomes larger and the smoothness near the elimination frequency is increased. By means of the gradient algorithm with a cost function E[ep(n)], this property can be utilized so that excellent convergence speed and steady‐state characteristics can be obtained. Finally, verification of the analytical results and comparison with the conventional method are carried out by computer simulation. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(8): 1–8, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10162