Unknown Noise Covariance Research Articles

DOA estimation with a rotational uniform linear array (RULA) and unknown spatial noise covariance

Direction of Arrival (DOA) estimation is one of the major tasks in array signal processing. In this paper, a new DOA estimation method is proposed using a rotational uniform linear array (RULA) consisting of omnidirectional sensors. The main contribution of the proposed method is that the number of distinguishable signals is larger than the methods in the literature with a uniform linear array consisting of the same number of omnidirectional sensors. Moreover, the new method can effectively reduce unknown spatial noises using a generalized complement projection matrix under the RULA framework. Simulations are presented to illustrate the effectiveness of the proposed method and comparison with some existing DOA estimation methods is also made.

Enhancement in Li-Ion Battery Cell State-of-Charge Estimation Under Uncertain Model Statistics

Accurate battery state-of-charge (SOC) estimation in real time is desired in many applications. Among other methods, the extended Kalman filter (EKF) allows for high-accuracy real-time tracking of the SOC. However, an accurate SOC model is needed to guarantee convergence. Additionally, knowledge of the statistics of the process noise and the measurement noise is needed for high-accuracy SOC estimation. In this paper, two methods, namely, the multiple-model EKF (MM-EKF) and the autocovariance least squares technique, are proposed for estimating the SOC of lithium-ion (Li-ion) battery cells. The first method has the advantage of minimizing the EKF algorithm's dependence on the correct assumptions of the measurement's noise statistics, thus, minimizing the impact of model mismatch. The MM-EKF assumes a number of hypotheses for the unknown measurement noise covariance. An EKF is assigned for each assumed measurement noise covariance. The SOC estimate is then obtained by probabilistically summing up the estimates of the hypothesized EKFs. On the other hand, the second method assumes that the measurement noise is unknown and determines its value from the statistics of the EKF. Given an initial and possibly wrong assumption of the measurement noise covariance, the method accounts for possible correlation in the measurement innovations. The estimated measurement noise covariance is subsequently used to obtain an optimal SOC estimate. The proposed methods are evaluated and compared with the conventional EKF method on experimental test data obtained from a 3.6-V Li-ion battery cell.

Kullback–Leibler divergence for interacting multiple model estimation with random matrices

The problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance is studied. The system state and the unknown covariance are jointly estimated, where the unknown covariance is modelled as a random matrix according to an inverse-Wishart distribution. For the IMM estimation with random matrices, one difficulty encountered is the combination of a set of weighted inverse-Wishart distributions. Instead of using the moment matching approach, this difficulty is overcome by minimising the weighted Kullback–Leibler divergence for inverse-Wishart distributions. It is shown that a closed-form solution can be derived for the optimisation problem and the resulting solution coincides with an inverse-Wishart distribution. Simulation results show that the proposed filter outperforms the previous work using the moment matching approach.

Adaptive Gauss–Hermite filter for non‐linear systems with unknown measurement noise covariance

A non-linear adaptive state estimator based on the Gauss–Hermite (GH) quadrature rule has been proposed to suit non-linear signal models where the measurement noise covariance remains unknown. The proposed algorithm which may be used for both parameter and state estimation incorporates online adaptation of the measurement noise covariance ( R ) following maximum-likelihood estimation-based method. The GH quadrature approach has been considered so that the proposed filter may inherit the enhanced estimation accuracy as exhibited by its non-adaptive counterpart. The proposed adaptation algorithm, in contrast to some other reported methods, automatically ensures positive definiteness of the adapted measurement noise covariance. The efficacy of the adaptive algorithm over the non-adaptive GH filter has been demonstrated using Monte Carlo simulation and two case studies. Performance comparison has also been carried out with respect to adaptive unscented Kalman filter with the help of same case studies.

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

Unscented Kalman filter (UKF) has been extensively used for state estimation of nonlinear stochastic systems, which suffers from performance degradation and even divergence when the noise distribution used in the UKF and the truth in a real system are mismatched. For state estimation of nonlinear stochastic systems with non-Gaussian measurement noise, the Masreliez–Martin extended Kalman filter (EKF) gives better state estimates in relation to the standard EKF. However, the process noise and the measurement noise covariance matrices should be known, which is impractical in applications. This paper presents a robust Masreliez–Martin UKF which can provide reliable state estimates in the presence of both unknown process noise and measurement noise covariance matrices. Two numerical examples involving relative navigation of spacecrafts demonstrate that the proposed filter can provide improved state estimation performance over existing robust filtering approaches. Vision-aided robot arm tracking experiments are also provided to show the effectiveness of the proposed approach.

Adaptive central difference filter for non‐linear state estimation

A new algorithm for adaptive non-linear filter suitable for signal models with unknown measurement noise covariance is presented here. The proposed adaptive filter is based on numerically efficient central difference algorithm which is potentially suitable for on board implementation. Unlike some competing adaptation scheme the proposed method guarantees positive definiteness of the estimated covariance matrix and avoids consequent singularity. Superiority of the proposed filter in comparison with non-adaptive central difference filter (CDF), an adaptive unscented Kalman filter and also another CDF based adaptive filter with alternative adaptation scheme has been demonstrated by Monte Carlo simulations. The signal models used are a well-known reentry ballistic target tracking problem and a high dimensional, relatively complex spacecraft attitude determination problem. The algorithm has provisions for (i) iterative refinement, (ii) modulating the degree of adaptation and also (iii) for incorporating tradeoff mechanisms between computational load and estimation error.

Approximate Bayesian Smoothing with Unknown Process and Measurement Noise Covariances

We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is computationally efficient, easy to implement, and can be applied to high dimensional linear systems. The performance of the algorithm is illustrated on a target tracking example.

Extended Kalman filter for modal identification of structures equipped with a pendulum tuned mass damper

Pendulum tuned mass dampers (PTMDs) have been employed in several full-scale applications to attenuate excessive structural motions, which are mostly due to wind. Conducting periodic condition assessments of the devices to ascertain their health is necessary to ensure their continued optimal performance, which involves identifying the modal parameters of the underlying (bare) structure to which they are tuned to. Such an identification is also necessary for the design of control systems such as adaptive tuned mass dampers. Existing methods of arresting the motion of the damper to estimate the modal properties are expensive, time-consuming, and not suitable for online tuning. Instead, in this paper, parameter estimation using the Extended Kalman Filter (EKF) is proposed to undertake this task. The central task accomplished here is to estimate the dynamic characteristics of the bare structure (structure without the PTMD) from response measurements of the coupled main structure and PTMD system. The proposed methodology relies on ambient acceleration measurements of TMD-attenuated responses to estimate the bare structural modal frequencies, damping, and mode shapes, which can then be used either for condition assessment or for control. The application of EKF to modal parameter estimation is not new. However, a methodology to address the problem in wind engineering arising from stochastic disturbances present in both the measurement and state equations, and unknown process and noise covariances arising due to ambient excitations, is presented for the first time. Extensively studied for synthetic data, these two challenges have limited thus far the application of Kalman filtering to practical wind engineering parameter estimation problems using experimentally obtained measurements. In this paper, a detailed methodology is presented to address these challenges by using a modified form of the standard EKF equations, together with an algorithm to estimate the unknown disturbance and measurement noise covariances. Numerical simulations and an experimental study are both presented. Results demonstrate that the method proposed provides reliable estimates for the modal parameters required to perform condition assessment and control tasks for pendulum tuned mass dampers.

Recursive Generalized Total Least Squares with Noise Covariance Estimation

We propose a recursive generalized total least-squares (RGTLS) estimator that is used in parallel with a noise covariance estimator (NCE) to solve the errors-in-variables problem for multi-input-single-output linear systems with unknown noise covariance matrix. Simulation experiments show that the suggested RGTLS with NCE procedure outperforms the common recursive least squares (RLS) and recursive total instrumental variables (RTIV) estimators when all measured inputs and the measured output are noisy. Moreover, when all measured inputs are noise-free, RGTLS with NCE performs similarly to RLS, which in this special case is the optimal estimator, and again RTIV was inferior compared with the RGTLS and NCE procedure.

Particle filters for probability hypothesis density filter with the presence of unknown measurement noise covariance

In Bayesian multi-target filtering, knowledge of measurement noise variance is very important. Significant mismatches in noise parameters will result in biased estimates. In this paper, a new particle filter for a probability hypothesis density (PHD) filter handling unknown measurement noise variances is proposed. The approach is based on marginalizing the unknown parameters out of the posterior distribution by using variational Bayesian (VB) methods. Moreover, the sequential Monte Carlo method is used to approximate the posterior intensity considering non-linear and non-Gaussian conditions. Unlike other particle filters for this challenging class of PHD filters, the proposed method can adaptively learn the unknown and time-varying noise variances while filtering. Simulation results show that the proposed method improves estimation accuracy in terms of both the number of targets and their states.

Adaptive filtering for jump Markov systems with unknown noise covariance

The paper proposed an adaptive filter for jump Markov systems with unknown measurement noise covariance. The filter is derived by treating covariance as a random matrix and an inverse-Wishart distribution is adopted as the conjugate prior. The variational Bayesian approximation method is employed to derive mode-conditioned estimates and mode-likelihood functions in the framework of interacting multiple model. A numerical example is provided to illustrate the performance of the proposed filter.

The Application of Adaptive Kalman Filter in Traffic Flow Forecasting

The urban traffic usually has the characteristics of time-variation and nonlinearity, real-time and accurate traffic flow forecasting has become an important component of the Intelligent Transportation System (ITS). The paper gives a brief introduction of the basic theory of Kalman filter, and establishes the traffic flow forecasting model on the basis of the adaptive Kalman filter, while the traditional Kalman filtering model has the shortcomings of lower forecasting accuracy and easily running into filtering divergence. The Sage&Husa adaptive filtering algorithm will appropriately estimate and correct the unknown or uncertain noise covariance, so as to improve the dynamic characteristics of the model. The simulation results demonstrate that the adaptive Kalman filtering forecasting model has stronger tracking capability and higher forecasting precision, which is applicable to the traffic flow forecasting.

Antenna Array Based GNSS Signal Acquisition for Interference Mitigation

This work addresses the signal acquisition problem using an array of antennas in the general framework of Global Navigation Satellite Systems (GNSS) receivers. We propose a statistical approach, using the Neyman-Pearson (NP) detection theory and the generalized likelihood ratio test (GLRT), to obtain a new detector which is able to mitigate temporally uncorrelated interferences even if the array is unstructured and moderately uncalibrated. The key statistical feature is the assumption of an arbitrary and unknown covariance noise matrix, which attempts to capture the statistical behavior of the interferences and of other nondesirable signals, while exploiting the spatial dimension provided by antenna arrays. Closed-form expressions for detection and false alarm probabilities are provided. The performance and interference rejection capability are modeled and compared with their theoretical bound. Furthermore the proposed detector is analyzed under realistic conditions, which accounts for the presence of errors in the covariance matrix estimation, the residual Doppler and delay errors, and the signal quantization effects. The theoretical results are supported by Monte Carlo simulations.

Performance Enhancement of Subspace Detection With a Diversely Polarized Antenna

Based on a diversely polarized antenna, we address the problems of adaptive detection and performance enhancement in partially homogeneous environments where the test and training data samples share the same noise covariance matrix up to an unknown scaling factor. The matched subspace detector and adaptive subspace detector are employed to handle the detection problem for the cases of known and unknown noise covariance matrix structure, respectively. The performance of the two detectors is evaluated in terms of their probabilities of false alarm and detection. In particular, a waveform design algorithm to enhance the detection performance of the two detectors is proposed. A numerical analysis is presented to demonstrate the potential performance improvement obtained with this algorithm.

Adaptive State‐Feedback Stabilization for High‐Order Stochastic Nonlinear Systems Driven by Noise of Unknown Covariance

This paper further considers more general high‐order stochastic nonlinear system driven by noise of unknown covariance and its adaptive state‐feedback stabilization problem. A smooth state‐feedback controller is designed to guarantee that the origin of the closed‐loop system is globally stable in probability.

Reconstructing signals from noisy data with unknown signal and noise covariance

We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle of minimum Gibbs free energy, which was previously used to derive a signal reconstruction algorithm handling uncertainties in the signal covariance. We extend this algorithm to simultaneously uncertain noise and signal covariances using the same principles in the derivation. The resulting equations are general enough to be applied in many different contexts. We demonstrate the performance of the algorithm by applying it to specific example situations and compare it to algorithms not allowing for uncertainties in the noise covariance. The results show that the method we suggest performs very well under a variety of circumstances and is indeed qualitatively superior to the other methods in cases where uncertainty in the noise covariance is present.

Diffuse Noise Suppression Using Crystal-Shaped Microphone Arrays

This paper describes novel methods for diffuse noise suppression using crystal-shaped microphone arrays. The two-stage processing of the observed signals by the Minimum Variance Distortionless Response (MVDR) beamformer and the subsequent Wiener post-filter is effective for diffuse noise suppression and gives the linear minimum mean square error (LMMSE) estimator of the target signal. It is essential in this framework to accurately estimate the short-time power spectrum and the steering vectors of the target signal from the noisy observations. Our methods diagonalize the spatial noise covariance matrix and utilizes the denoised off-diagonal entries of the spatial covariance matrix to accurately estimate the short-time power spectrum and the steering vectors of the target signal. We employ crystal arrays, certain classes of crystal-shaped array geometries, which make it possible to diagonalize the unknown noise covariance matrix by a constant unitary matrix regardless of its value as long as noise meets an isotropy condition. It is shown through experiments with simulated and real environmental noise that the proposed methods outperform previous methods substantially for real world noise and in the presence of reverberation.

DOA Estimation of Quasi-Stationary Signals With Less Sensors Than Sources and Unknown Spatial Noise Covariance: A Khatri–Rao Subspace Approach

In real-world applications such as those for speech and audio, there are signals that are nonstationary but can be modeled as being stationary within local time frames. Such signals are generally called quasi-stationary or locally stationary signals. This paper considers the problem of direction-of-arrival (DOA) estimation of quasi-stationary signals. Specifically, in our problem formulation we assume: i) sensor array of uniform linear structure; ii) mutually uncorrelated wide-sense quasi-stationary source signals; and iii) wide-sense stationary noise process with unknown, possibly nonwhite, spatial covariance. Under the assumptions above and by judiciously examining the structures of local second-order statistics (SOSs), we develop a Khatri-Rao (KR) subspace approach that has two notable advantages. First, through an identifiability analysis, it is proven that this KR subspace approach can operate even when the number of sensors is about half of the number of sources. The idea behind is to make use of a ¿virtual¿ array structure provided inherently in the local SOS model, of which the degree of freedom is about twice of that of the physical array. Second, the KR formulation naturally provides a simple yet effective way of eliminating the unknown spatial noise covariance from the signal SOSs. Extensive simulation results are provided to demonstrate the effectiveness of the KR subspace approach under various situations.

Accurate Angle-of-Arrival Measurement Using Particle Swarm Optimization

As one of the major methods for location positioning, angle-of-arrival (AOA) estimation is a significant technology in radar, sonar, radio astronomy, and mobile communications. AOA measurements can be exploited to locate mobile units, enhance communication efficiency and network capacity, and support location-aided routing, dynamic network management, and many location-based services. In this paper, we propose an algorithm for AOA estimation in colored noise fields and harsh application scenarios. By modeling the unknown noise covariance as a linear combination of known weighting matrices, a maximum likelihood (ML) criterion is established, and a particle swarm optimization (PSO) paradigm is designed to optimize the cost function. Simulation results demonstrate that the paired estimator PSO-ML significantly outperforms other popular techniques and produces superior AOA estimates.

Noise-insensitive image optimal flow estimation using higher-order statistics

A new algorithm is presented that estimates the displacement vector field from two successive image frames. In the case where the sequence is severely corrupted by additive (Gaussian or not, colored) noise of unknown covariance, then second-order statistics methods do not work well. However, we have studied this topic from a viewpoint different from the above to explore the fundamental limits in image optimal flow estimation. Our scheme is based on subpixel optimal flow estimation using the bispectrum in the parametric domain. The displacement vector of a moving object is estimated by solving linear equations involving third-order holograms and the matrix containing the Dirac delta function. To prove the feasibility of the proposed method, we compared it with a phase correlation technique and the nonparametric bispectrum method described in Res. Lett. Signal Process., ID 417915 (2008). Our results show that our method is considerably more immune to the presence of noise.