Time-correlated Measurement Noise Research Articles

Globally Optimal Distributed Fusion Filter for Descriptor Systems with Time-Correlated Measurement Noises.

This paper concerns the distributed fusion filtering problem for descriptor systems with time-correlated measurement noises. The original descriptor is transformed into two reduced-order subsystems (ROSs) based on singular value decomposition. For the first ROS, a new measurement is obtained using measurement difference technology. Each sensor produces a local filter based on the fusion predictor from the fusion center and its own new measurement and then sends it to the fusion center. In the fusion center, based on local filters, a distributed fusion filter with feedback (DFFWF) in the linear minimum variance (LMV) sense is proposed by applying an innovative approach. The DFFWF for the second ROS is also obtained based on the DFFWF for the first ROS. Then, the DFFWF for the original descriptor is obtained. The proposed DFFWF can achieve the same estimation accuracy as the centralized fusion filter (CFF) under the condition that all local filter gain matrices are of full column rank. Its optimality is strictly proved. Moreover, it has robustness and reliability due to the parallel processing of local filters. Two simulation examples demonstrate the effectiveness of the developed fusion algorithm.

Distributed State Estimation for Continuous-Time Linear Systems With Correlated Measurement Noise

In this article, the problem of distributed state estimation for a continuous-time linear system with a sensor network is investigated, where each sensor can only communicate with its neighbors and contains time-correlated measurement noise. To solve this problem, a novel augmented leader-following information fusion strategy is first proposed to collect measurements and system matrices. Then, a class of distributed state estimators is developed with bounded estimation error covariances. Further, a closed-form relation between the designed distributed estimator and the centralized estimator is established. It is found that the estimation performance of the former converges to that of the latter when the consensus gain tends to infinity. The proposed estimator is further extended to the fully distributed case by introducing an adaptive law for the consensus gain without using any global information. Moreover, it is shown that the designed estimator is applicable for systems with deterministic noise. Finally, several comparative numerical simulations are provided to demonstrate the effectiveness and superiority of the theoretical results.

Globally Optimal Centralized and Sequential Fusion Filters for Uncertain Systems With Time-Correlated Measurement Noises

This paper is concerned with the fusion filtering problem for stochastic uncertain multi-sensor systems with time-correlated measurement noises, where the stochastic uncertainties are described by white multiplicative noises, and the additive measurement noises are first-order Gauss-Markov Processes. By introducing the recursive measurement noise estimators, the centralized fusion filter (CFF) based on the idea of batch process and sequential fusion filter (SFF) based on the idea of sequential process are designed in the linear minimum variance (LMV) sense by an innovation analysis approach, respectively. The proposed SFF can achieve the same estimation accuracy as the CFF. It is also globally optimal. The equivalence on estimation accuracy of the SFF and CFF is strictly proved by mathematical induction method. The stability and steady-state properties of the proposed fusion filters are analyzed. Two examples show the effectiveness of the proposed fusion algorithms.

Generalized bias compensated pseudolinear Kalman filter for colored noisy bearings-only measurements

Bias compensated pseudolinear Kalman filter (BC-PLKF) has been shown to solve the bias problem of pseudolinear Kalman filter (PLKF) and outperform Extended Kalman Filter (EKF) and many others in bearings-only target estimation applications with a low computational cost. However, BC-PLKF assumes that measurement noise is white, which is not a valid approximation for some applications such as weather-vane-used guided missiles where wind disturbance appears as a strongly time-correlated measurement noise, estimators performing high-frequency measurement updates, or cascaded Kalman filter-based algorithms. When the well-known noise augmentation method is applied to BC-PLKF, no straightforward solution for the bias compensation is available. First, process noise and observer matrix become coupled leading to unique bias. Second, the measurement autocovariance turns into zero whose inverse is used at the bias compensation step of BC-PLKF. Therefore, a bias analysis is performed for PLKF where the measurement noise is colored. Moreover, the generalized BC-PLKF algorithm (GBC-PLKF) for colored noise-corrupted measurements is derived. Simulations are performed to compare performances of GBC-PLKF, EKF, Cubature Kalman Filter (CKF), BC-PLKF, and colored noise augmented EKF and CKF (C-EKF and C-CKF) with typical air-to-surface missile engagement scenarios. Results verify that GBC-PLKF outperforms all comparison filters with a low computational cost for bearings-only estimation applications.

Finite-time higher-order moment state estimation for Markov jump linear system with time-correlated measurement noise

In the present study, a higher-order moment state estimation problem in a finite time interval for the discrete-time Markov jump linear systems (MJLS) is investigated. Moreover, time-correlated noise in measurements is considered. Initially, the measruement differencing approach is applied to convert the time-correlated measurement noise to an uncorrelated noise. Then the cumulant generating function is utilized to solve the stochastic jumping problem of MJLS, by which the discrete-time MJLS is transformed into a deterministic system. In this way, the transformed deterministic system has the same norm with a higher-order moment of the original state. Finally, a finite-time state estimation algorithm is proposed to guarantee that the higher-order moment of error trajectory remains within a pre-specified bound over a given time interval. In order to evaluate the performance of the proposed method, some test cases are applied. Obtained results prove the accuracy and efficiency of the proposed method.

State estimation for discrete-time Markov jump linear systems with time-correlated measurement noise

In this paper, the state estimation problem for discrete-time Markov jump linear systems affected by time-correlated measurement noise is considered where the time-correlated measurement noise is described by a linear system model with white noise. As a result, two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence. The first algorithm is optimal in the sense of minimum mean-square error, which is obtained based on the measurement differencing method, Bayes’ rule and some results derived in this paper. The second algorithm is a suboptimal algorithm obtained by using a lot of Gaussian hypotheses. The proposed suboptimal algorithm is finite-dimensionally computable and does not increase computational and storage load with time. Computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm.

Distributed filtering for discrete-time linear systems with fading measurements and time-correlated noise

This paper studies the problem of distributed filtering for discrete-time linear systems with fading measurements and time-correlated noise over a sensor network. To address the problem of the time-correlated measurement noise, the measurement differencing approach is adopted to define a new measurement such that the noise in the new measurement is not time-correlated any longer. Based on the new measurement, the innovation-based and the consensus-based distributed filters are proposed for each sensor by using its neighboring information. By resorting to the graph properties, the filter gain matrices are designed for each sensor to develop optimal distributed filters in the sense of minimum variance. Moreover, suboptimal distributed filters are proposed to reduce the computational cost and the communication cost. The performance of the distributed filters is analyzed with respect to the fading factor. Simulation results are provided to show the effectiveness of the proposed filters.

Discrete EKF with pairwise Time Correlated Measurement Noise for Image-Aided Inertial Integrated Navigation

Abstract. An image-aided inertial navigation implies that the errors of an inertial navigator are estimated via the Kalman filter using the aiding measurements derived from images. The standard Kalman filter runs under the assumption that the process noise vector and measurement noise vector are white, i.e. independent and normally distributed with zero means. However, this does not hold in the image-aided inertial navigation. In the image-aided inertial integrated navigation, the relative positions from optic-flow egomotion estimation or visual odometry are pairwise correlated in terms of time. It is well-known that the solution of the standard Kalman filter becomes suboptimal if the measurements are colored or time-correlated. Usually, a shaping filter is used to model timecorrelated errors. However, the commonly used shaping filter assume that the measurement noise vector at epoch k is not only correlated with the one from epoch k – 1 but also with the ones before epoch k – 1 . The shaping filter presented in this paper uses Cholesky factors under the assumption that the measurement noise vector is pairwise time-correlated i.e. the measurement noise are only correlated with the ones from previous epoch. Simulation results show that the new algorithm performs better than the existing algorithms and is optimal.

Linear optimal estimation with state dependent disturbances and time-correlated measurement noise

The linear filtering, prediction, and smoothing problems are treated for linear message processes with state-dependent noise and time-correlated measurement noise. In particular, a general smoothing formula for these classes of message processes is developed. The derivation evolves directly from the Wiener-Hopf equation and does not use the innovations process.