Xiaoxu Wang

A Gaussian approximation recursive filter for nonlinear systems with correlated noises

This paper proposes a Gaussian approximation recursive filter (GASF) for a class of nonlinear stochastic systems in the case that the process and measurement noises are correlated with each other. Through presenting the Gaussian approximations about the two-step state posterior predictive probability density function (PDF) and the one-step measurement posterior predictive PDF, a general GASF framework in the minimum mean square error (MMSE) sense is derived. Based on the framework, the GASF implementation is transformed into computing the multi-dimensional integrals, which is solved by developing a new divided difference filter (DDF) with correlated noises. Simulation results demonstrate the superior performance of the proposed DDF as compared to the standard DDF, the existing UKF and EKF with correlated noises.

Gaussian filter for nonlinear systems with correlated noises at the same epoch

This paper proposes a general framework solution of Gaussian filter (GF) for both linear and nonlinear dynamic systems with correlated noises at the same epoch. Detailed discussions and simulation comparisons with existing Gaussian approximation recursive filter and existing de-correlating GF are provided, which show advantages of estimation accuracy of the proposed method in some applications.

Measurement Random Latency Probability Identification

This technical note focuses on efficiently identifying the unknown or time-varying random latency probability (RLP) of the measurements in the networked multi-sensor system by resorting to expectation maximization (EM) framework. Firstly, a novel scheme is proposed for equivalently decomposing the complete data log-likelihood function into a summation form parameterized by RLP. Secondly, the rapid computation of the expectation in E-step is achieved by skillfully introducing Jessens inequality to avoid the state augmentation of the traditional method. Thirdly, the analytical identification result of RLP is obtained in M-step by constructing Lagrange operator to maximize the expectation with the parameter constraint. Naturally, such analytical result is so simple that it can be quickly carried out, which is demonstrated by quantitative computation complexity analysis. Finally, an example motivated by the maneuvering target tracking application is presented to show the superiority of the new method.

General equivalence between two kinds of noise-correlation filters

A recent comment (Chang, 2014) theoretically demonstrated that for the linear system with the correlated process and measurement noises, the GASF framework proposed in the paper Wang et?al. (2012) was equivalent to the conventional de-coupling filtering framework. In this note, we would further show that such equivalence between the two frameworks can be justified in a more general way, even for the nonlinear system.

Application of Unscented Transformation for Nonlinear State Smoothing

Abstract Motivated by the well-known fact that the state estimate of a smoother is more accurate than that of the corresponding filter, this paper is concerned with the state smoothing problem for a class of nonlinear stochastic discrete systems. Firstly, a novel type of optimal smoother, which provides a unified theoretical framework for the solution of state smoothing problem no matter that system is linear or nonlinear, is derived on the basis of minimum mean squared error (MMSE) estimation theory. Further, in the case that the dynamic model and measurement functions are all nonlinear, a new suboptimal smoother is developed by applying the unscented transformation for approximately computing the smoothing gain in the optimal smoothing framework. Finally, the superior performance of the proposed smoother to the existing extended Kalman smoother (EKS) is demonstrated through a simulation example.

Gaussian-consensus filter for nonlinear systems with randomly delayed measurements in sensor networks

The Gaussian filter is presented for nonlinear systems with delayed measurements.The delay in the measurement equation obeys a Markov chain.The posterior probability of delay is estimated based on the multiple model method.A Gaussian-consensus filter gives a decentralized fusion in sensor networks. This paper presents the decentralized state estimation problem of discrete-time nonlinear systems with randomly delayed measurements in sensor networks. In this problem, measurement data from the sensor network is sent to a remote processing network via data transmission network, with random measurement delays obeying a Markov chain. Here, we present the Gaussian-consensus filter (GCF) to pursue a tradeoff between estimate accuracy and computing time. It includes a novel Gaussian approximated filter with estimated delay probability (GEDPF) online in the sense of minimizing the estimate error covariance in each local processing unit (PU), and a consensus strategy among PUs in processing network to give a fast decentralized fusion. A numerical example with different measurement delays is simulated to validate the proposed method.

Multi-region scene matching based localisation for autonomous vision navigation of UAVs

A multi-region scene matching-based localisation system for automated navigation of Unmanned Aerial Vehicles (UAV) is proposed. This system may serve as a backup navigation error correction system to support autonomous navigation in the absence of a global positioning system such as a Global Navigation Satellite System. Conceptually, the system computes the location of the UAV by comparing the sensed images taken by an on board optical camera with a library of pre-recorded geo-referenced images. Several challenging issues in building such a system are addressed, including the colour variability problem and elimination of time-varying details from the pairs of images. The overall algorithm is an iterative process involving four sub-processes: firstly, exact histogram matching is applied to sensed images to overcome the colour variability issues; secondly, regions are automatically extracted from the sensed image where landmarks are detected via their colour histograms; thirdly, these regions are matched against the library, while eliminating inconsistent regions between underlying image pairs in the registration process; and finally the location of the UAV is computed using an optimisation procedure which minimises the localisation error using affine transformations. Experimental results demonstrate the proposed system in terms of accuracy, robustness and computational efficiency.

A dynamic attitude measurement system based on LINS.

A dynamic attitude measurement system (DAMS) is developed based on a laser inertial navigation system (LINS). Three factors of the dynamic attitude measurement error using LINS are analyzed: dynamic error, time synchronization and phase lag. An optimal coning errors compensation algorithm is used to reduce coning errors, and two-axis wobbling verification experiments are presented in the paper. The tests indicate that the attitude accuracy is improved 2-fold by the algorithm. In order to decrease coning errors further, the attitude updating frequency is improved from 200 Hz to 2000 Hz. At the same time, a novel finite impulse response (FIR) filter with three notches is designed to filter the dither frequency of the ring laser gyro (RLG). The comparison tests suggest that the new filter is five times more effective than the old one. The paper indicates that phase-frequency characteristics of FIR filter and first-order holder of navigation computer constitute the main sources of phase lag in LINS. A formula to calculate the LINS attitude phase lag is introduced in the paper. The expressions of dynamic attitude errors induced by phase lag are derived. The paper proposes a novel synchronization mechanism that is able to simultaneously solve the problems of dynamic test synchronization and phase compensation. A single-axis turntable and a laser interferometer are applied to verify the synchronization mechanism. The experiments results show that the theoretically calculated values of phase lag and attitude error induced by phase lag can both match perfectly with testing data. The block diagram of DAMS and physical photos are presented in the paper. The final experiments demonstrate that the real-time attitude measurement accuracy of DAMS can reach up to 20″ (1σ) and the synchronization error is less than 0.2 ms on the condition of three axes wobbling for 10 min.

Simultaneous mean and covariance correction filter for orbit estimation

This paper proposes a novel filtering design, from a viewpoint of identification instead of the conventional nonlinear estimation schemes (NESs), to improve the performance of orbit state estimation for a space target. First, a nonlinear perturbation is viewed or modeled as an unknown input (UI) coupled with the orbit state, to avoid the intractable nonlinear perturbation integral (INPI) required by NESs. Then, a simultaneous mean and covariance correction filter (SMCCF), based on a two-stage expectation maximization (EM) framework, is proposed to simply and analytically fit or identify the first two moments (FTM) of the perturbation (viewed as UI), instead of directly computing such the INPI in NESs. Orbit estimation performance is greatly improved by utilizing the fit UI-FTM to simultaneously correct the state estimation and its covariance. Third, depending on whether enough information is mined, SMCCF should outperform existing NESs or the standard identification algorithms (which view the UI as a constant independent of the state and only utilize the identified UI-mean to correct the state estimation, regardless of its covariance), since it further incorporates the useful covariance information in addition to the mean of the UI. Finally, our simulations demonstrate the superior performance of SMCCF via an orbit estimation example.

Adaptive Gaussian mixture filter for Markovian jump nonlinear systems with colored measurement noises

This paper considers the state estimation of discrete-time Markovian jump nonlinear systems with colored measurement noises obeying a nonlinear autoregressive process of order n, which is motivated by tracking the maneuvering target under electronic countermeasures with high speed sampling or persistent perturbations. In order to remove the measurement noises correlation, the left zero divisor is explored to reconstruct a new measurement equation via difference approach, with the help of applying statistical linear regression to the colored measurement noise model. Then, a novel hypothesis set constituted of all possible values of multi-step Markov jumping parameters is defined and the posterior probability density of the state is derived recursively. By using Gaussian mixtures to approximate the posterior probability densities, an adaptive Gaussian mixture filter for the considered system is proposed, where the Gaussian components with small weights are pruned adaptively through measuring the Alpha (or Beta) divergence for the original and approximated Gaussian mixtures, to achieve a tradeoff between the estimation accuracy and running time. A maneuvering target tracking accompanied by range gate pull-off with different colored measurement noises cases is simulated to validate the proposed method.