Robust Nonlinear Filtering Research Articles

Multi-frequency GNSS robust carrier tracking for ionospheric scintillation mitigation

Ionospheric scintillation is the physical phenomena affecting radio waves propagating from the space through the ionosphere to earth. The signal distortion induced by scintillation can pose a major threat to some GNSS application. Scintillation is one of the more challenging propagation scenarios, particularly affecting high-precision GNSS receivers which require high quality carrier phase measurements; and safety critical applications which have strict accuracy, availability and integrity requirements. Under ionospheric scintillation conditions, GNSS signals are affected by fast amplitude and phase variations, which can compromise the receiver synchronization. To take into account the underlying correlation among different frequency bands, we propose a new multivariate autoregressive model (MAR) for the multi-frequency ionospheric scintillation process. Multi-frequency GNSS observations and the scintillation MAR are modeled in state-space, allowing independent tracking of both line-of-sight phase variations and complex gain scintillation components. The resulting joint synchronization and scintillation mitigation problem is solved using a robust nonlinear Kalman filter, validated using real multi-frequency scintillation data with encouraging results.

A novel square-root cubature information weighted consensus filter algorithm for multi-target tracking in distributed camera networks.

This paper deals with the problem of multi-target tracking in a distributed camera network using the square-root cubature information filter (SCIF). SCIF is an efficient and robust nonlinear filter for multi-sensor data fusion. In camera networks, multiple cameras are arranged in a dispersed manner to cover a large area, and the target may appear in the blind area due to the limited field of view (FOV). Besides, each camera might receive noisy measurements. To overcome these problems, this paper proposes a novel multi-target square-root cubature information weighted consensus filter (MTSCF), which reduces the effect of clutter or spurious measurements using joint probabilistic data association (JPDA) and proper weights on the information matrix and information vector. The simulation results show that the proposed algorithm can efficiently track multiple targets in camera networks and is obviously better in terms of accuracy and stability than conventional multi-target tracking algorithms.

A robust continuous‐time fixed‐lag smoother for nonlinear uncertain systems

SummaryThis paper presents a scheme for the design of a robust fixed‐lag smoother for a class of nonlinear uncertain systems. The proposed approach combines a nonlinear robust estimator with a stable fixed‐lag smoother, to improve the estimation error covariance. The robust fixed‐lag smoother is based on the use of integral quadratic constraints and minimax linear quadratic regulator estimation and control theory. The state estimator uses a copy of the system nonlinearity in the estimator and combines an approximate model of the delayed states to produce a smoother signal. Also in this work, a characterization of the delay approximation error is presented, and the corresponding integral quadratic constraint is included in the design, which gives a guaranteed bound on the performance cost function. In order to see the effectiveness of the method, it is applied to a quantum optical phase estimation problem. Results show a significant improvement in the error covariance of the estimator when compared with a robust nonlinear filter. Copyright © 2015 John Wiley & Sons, Ltd.

Initial alignment for nonlinear inertial navigation systems with multiple disturbances based on enhanced anti-disturbance filtering

Initial alignment for inertial navigation system (INS) has been widely used in practice under the assumption of Gaussian noises. In most previous works, nonlinear dynamics was ignored and the disturbances were merged into either a Gaussian or norm-bounded variable, where the Kalman filtering or robust filtering can be applied, respectively. In this article, the unmodelled nonlinear dynamics, drifts, parametric uncertainties, as well as other disturbances are considered simultaneously and are formulated into different types of uncertain disturbances described by the exo-system, stochastic and norm-bounded variable, respectively. A nonlinear initial alignment approach for INS is first presented based on a new disturbance attenuation and rejection filtering scheme against multiple disturbances. The INS error model with both nonlinear dynamics and multiple disturbances is established and the initial alignment problem is transformed into a robust nonlinear filter design problem for a class of nonlinear systems with multiple disturbances. In the proposed composite filtering approach, the drift filter is designed to estimate and compensate the inertial sensor drift. Mixed H 2/H ∞ filtering is designed to optimise the estimation error and attenuate the norm-bounded uncertain disturbances, respectively. Simulations for ground stationary base initial alignment of an INS are provided. Comparisons show that the concerned INS has the enhanced disturbance rejection and attenuation performance.

Adaptive complex unscented Kalman filter for frequency estimation of time-varying signals

A simple and robust non-linear filter algorithm has been proposed in this study for estimating the frequency of a time-varying sinusoidal signal under high noise conditions. The real signal is first converted to an analytical signal and its complex state-space model is derived. An unscented complex Kalman filter (CUKF) is then obtained using the complex signal model and the error covariances along with the Kalman gain are updated iteratively. Also, the stability and the convergence characteristics of the proposed filter are presented for a single sinusoid embedded in noise. It has been shown that the proposed algorithm works efficiently for the estimation of abrupt changes in signal frequency under high noise conditions. To evaluate the performance of the proposed algorithm several computer simulation results of real-time and synthetic signals are presented. Further to improve the performance of the proposed filter in the presence of significant noise and distortions, the covariance matrices are tuned iteratively.

Equivariant Holomorphic Filters for Contour Denoising and Rapid Object Detection

It is well known that linear filters are not powerful enough for many low-level image processing tasks. However, it is also very difficult to design robust nonlinear filters that respond exclusively to features of interest and that are, at the same time, equivariant with respect to translation and rotation. This paper proposes a new class of rotation-equivariant nonlinear filters that is based on the principle of group integration. These filters become efficiently computable by an iterative scheme based on repeated differentiation of products and summations of intermediate results. The relations of the proposed approach to Volterra filters and steerable filters are shown. In the context of detection problems, the filter may be interpreted as some kind of generalized Hough transform. The experiments show that the new filter can be used for enhancing noisy contours and rapid object detection in microscopical images. In the detection context, our experiments show that the proposed filter is definitely superior to alternative approaches, when high localization accuracy is required.

Feedback Analysis of Radial Basis Functions Neural Networks via Small Gain Theorem

Radial basis function neural networks are used in a variety of applications such as pattern recognition, nonlinear identification, control, time series prediction, etc. In this paper, feedback analysis of the learning algorithm of radial basis function neural networks is presented. It studies the robustness of the learning algorithm in the presence of uncertainties that might be due to noisy perturbations at the input or to modeling mismatch. The learning scheme is first associated with a feedback structure and then the stability of that feedback structure is analyzed via small gain theorem. The analysis suggests bounds on the learning rate in order to guarantee that the learning algorithm will behave as robust nonlinear filters and optimal choices for faster convergence speeds.

선형화 오차에 강인한 확장칼만필터

In this paper, a new-type Extended Kalman Filter (EKF) is proposed as a robust nonlinear filter for a stochastic nonlinear system. The original EKF is widely used for various nonlinear system applications. But it is fragile to its estimation errors because they give rise to linearization errors that affect the system mode1 as the modeling errors. The linearization errors are nonlinear functions of the estimation errors therefore it is very difficult to obtain the accurate error covariance of the EKF using the linear form. The inaccurately estimated error covariance hinders the EKF from being a sub-optimal estimator. The proposed filter tries to obtain the upper bound of the error covariance tolerating the uncertainty of the error covariance instead of trying to obtain the accurate one. It treats the linearization errors as uncertain modeling errors that can be handled by the robust linear filtering. In order to be more robust to the estimation errors than the original EKF, the proposed filter minimizes the upper bound like the robust linear filter that is applied to the linear model with uncertainty. The in-flight alignment problem of the inertial navigation system with GPS position measurements is a good example that the proposed robust filter is applicable to. The simulation results show the efficiency of the proposed filter in the robustness to initial estimation errors of the filter.

A robust nonlinear filter for image restoration

A class of nonlinear regression filters based on robust estimation theory is introduced. The goal of the filtering is to recover a high-quality image from degraded observations. Models for desired image structures and contaminating processes are employed, but deviations from strict assumptions are allowed since the assumptions on signal and noise are typically only approximately true. The robustness of filters is usually addressed only in a distributional sense, i.e., the actual error distribution deviates from the nominal one. In this paper, the robustness is considered in a broad sense since the outliers may also be due to inappropriate signal model, or there may be more than one statistical population present in the processing window, causing biased estimates. Two filtering algorithms minimizing a least trimmed squares criterion are provided. The design of the filters is simple since no scale parameters or context-dependent threshold values are required. Experimental results using both real and simulated data are presented. The filters effectively attenuate both impulsive and nonimpulsive noise while recovering the signal structure and preserving interesting details.

Threshold decomposition of multidimensional ranked order operations

A useful class of robust nonlinear digital filters is the group of sliding window filters which use ranked order operations at each position of the window to produce the filter output. Median filters, alpha trimmed filters, and weighted rank filters are all included in this class. In this paper, it is shown that for all these filters, filtering an arbitrary level signal is equivalent to decomposing the signal into binary signals, filtering each binary signal, and then reversing the decomposition. This equivalence allows problems in the analysis and the implementation of these filters to be reduced to the equivalent problems for binary signals. Since the effects of ranked filters on binary signals are better understood, this technique is a powerful new tool.