Out-of-sequence Measurements Research Articles

A robust particle filter for ambiguous updates of underwater terrain-aided navigation

This paper proposes a novel method to improve the robustness of particle filtering (PF) in relatively flat terrain that lack sufficient features for accurate positioning. In terrain -aided navigation (TAN), similar terrain profiles lead to multimodality in the posterior distribution. It not only reduces the accuracy of current position estimation, but also affects the subsequent estimation of PF, and even causes filter divergence. When no additional information is available, the historical estimation is employed to correct ambiguous updates caused by multimodal posteriors. First, a strategy for identifying ambiguous updates is proposed by analyzing the particle set distribution using the clustering method and covariance. Inspired by out-of-sequence measurement (OOSM), once the ambiguous updates are detected, the ambiguous estimates are corrected by introducing high-quality previous information. Moreover, an efficient solution is provided for the storage and computation requirements of OOSM within the PF framework. To verify the effectiveness of the proposed algorithm, simulation and experimental validation are designed. By comparing with PF, mixture particle filtering (MPF), and OOSMPF algorithms, the proposed algorithm demonstrates better estimation accuracy and robustness in terrain flat areas.

A Modified Bayesian Framework for Multi-Sensor Target Tracking with Out-of-Sequence-Measurements.

Target detection and tracking is important in military as well as in civilian applications. In order to detect and track high-speed incoming threats, modern surveillance systems are equipped with multiple sensors to overcome the limitations of single-sensor based tracking systems. This research proposes the use of information from RADAR and Infrared sensors (IR) for tracking and estimating target state dynamics. A new technique is developed for information fusion of the two sensors in a way that enhances performance of the data association algorithm. The measurement acquisition and processing time of these sensors is not the same; consequently the fusion center measurements arrive out of sequence. To ensure the practicality of system, proposed algorithm compensates the Out of Sequence Measurements (OOSMs) in cluttered environment. This is achieved by a novel algorithm which incorporates a retrodiction based approach to compensate the effects of OOSMs in a modified Bayesian technique. The proposed modification includes a new gating strategy to fuse and select measurements from two sensors which originate from the same target. The state estimation performance is evaluated in terms of Root Mean Squared Error (RMSE) for both position and velocity, whereas, track retention statistics are evaluated to gauge the performance of the proposed tracking algorithm. The results clearly show that the proposed technique improves track retention and and false track discrimination (FTD).

Generalized LMMSE Filtering with Out‐of‐Sequence Observations in Arbitrary Constant Delay

Focusing on the problem of state estimation in the presence of sensor faults and Out-of-sequence measurement (OOSM) observations synchronously, we derive a formulation of Linear minimum mean squared error (LMMSE) filter with the arbitrary time delay of OOSM, the generalization of the present work lies in simultaneous treatment of correlated faults together with OOSMs that arrive at an arbitrary delay in a linear-optimal manner. The approach is demonstrated in a numerical comparison.

Multisensor Multi-Target Tracking Based on GM-PHD Using Out-Of-Sequence Measurements.

In this paper, we study the issue of out-of-sequence measurement (OOSM) in a multi-target scenario to improve tracking performance. The OOSM is very common in tracking systems, and it would result in performance degradation if we used it inappropriately. Thus, OOSM should be fully utilized as far as possible. To improve the performance of the tracking system and use OOSM sufficiently, firstly, the problem of OOSM is formulated. Then the classical B1 algorithm for OOSM problem of single target tracking is given. Next, the random finite set (RFS)-based Gaussian mixture probability hypothesis density (GM-PHD) is introduced. Consequently, we derived the equation for re-updating of posterior intensity with OOSM. Implementation of GM-PHD using OOSM is also given. Finally, several simulations are given, and results show that tracking performance of GM-PHD using OOSM is better than GM-PHD using in-sequence measurement (ISM), which can strongly demonstrate the effectiveness of our proposed algorithm.

Multisensor-Based Target-Tracking Algorithm with Out-of-Sequence-Measurements in Cluttered Environments.

A localization and tracking algorithm for an early-warning tracking system based on the information fusion of Infrared (IR) sensor and Laser Detection and Ranging (LADAR) is proposed. The proposed Kalman filter scheme incorporates Out-of-Sequence Measurements (OOSMs) to address long-range, high-speed incoming targets to be tracked by networked Remote Observation Sites (ROS) in cluttered environments. The Rauch–Tung–Striebel (RTS) fixed lag smoothing algorithm is employed in the proposed technique to further improve tracking accuracy, which, in turn, is used for target profiling and efficient filter initialization at the targeted platform. This efficient initialization increases the probability of target engagement by increasing the distance at which it can be effectively engaged. The increased target engagement range also reduces risk of any damage from debris of the engaged target. Performance of the proposed target localization algorithm with OOSM and RTS smoothing is evaluated in terms of root mean square error (RMSE) for both position and velocity, which accurately depicts the improved performance of the proposed algorithm in comparison with existing retrodiction-based OOSM filtering algorithms. The effects of assisted target state initialization at the targeted platform are also evaluated in terms of Time to Impact (TTI) and true track retention, which also depict the advantage of the proposed strategy.

An Out-of-sequence Measurement Fusion Method for Guidance Filtering with Delayed Measurements

This paper addresses the problems inherent in the design of a guidance filter with heterogeneous sensor outputs, some of which are subject to a known degree of time delay. The proposed method employs an out-ofsequence measurement fusion scheme in the form of fixed-point Kalman smoothing to effectively incorporate the delayed measurements without needing to significantly alter the underlying nonlinear guidance filtering framework. Two numerical case studies concerning satellite proximity operation and anti-ship missile guidance are presented to demonstrate the effectiveness of the proposed method.

Cooperative target localization using multiple UAVs with out-of-sequence measurements

PurposeThe time delay would occurs when the measurements of multiple unmanned aerial vehicles (UAVs) are transmitted to the date processing center during cooperative target localization. This problem is often named as the out-of-sequence measurement (OOSM) problem. This paper aims to present a nonlinear filtering based on solving the Fokker–Planck equation to address the issue of OOSM.Design/methodology/approachAccording to the arrival time of measurement, the proposed nonlinear filtering can be divided into two parts. The non-delay measurement would be fused in the first part, in which the Fokker–Planck equation is utilized to propagate the conditional probability density function in the forward form. The time delay measurement is fused in the second part, in which the Fokker–Planck is used in the backward form approximately. The Bayes formula is applied in both parts during the measurement update.FindingsUnder the Bayesian filtering framework, this nonlinear filtering is not only suitable for the Gaussian noise assumption but also for the non-Gaussian noise assumption. The nonlinear filtering is applied to the cooperative target localization problem. Simulation results show that the proposed filtering algorithm is superior to the previous Y algorithm.Practical implicationsIn this paper, the research shows that a better performance can be obtained by fusing multiple UAV measurements and treating time delay in measurement with the proposed algorithm.Originality/valueIn this paper, the OOSM problem is settled based on solving the Fokker–Planck equation. Generally, the Fokker–Planck equation can be used to predict the probability density forward in time. However, to associate the current state with the state related to OOSM, it would be used to propagate the probability density backward either.

Data-Aware Retrodiction for Asynchronous Harmonic Measurement in a Cyber-Physical Energy System.

Cyber-physical energy systems provide a networked solution for safety, reliability and efficiency problems in smart grids. On the demand side, the secure and trustworthy energy supply requires real-time supervising and online power quality assessing. Harmonics measurement is necessary in power quality evaluation. However, under the large-scale distributed metering architecture, harmonic measurement faces the out-of-sequence measurement (OOSM) problem, which is the result of latencies in sensing or the communication process and brings deviations in data fusion. This paper depicts a distributed measurement network for large-scale asynchronous harmonic analysis and exploits a nonlinear autoregressive model with exogenous inputs (NARX) network to reorder the out-of-sequence measuring data. The NARX network gets the characteristics of the electrical harmonics from practical data rather than the kinematic equations. Thus, the data-aware network approximates the behavior of the practical electrical parameter with real-time data and improves the retrodiction accuracy. Theoretical analysis demonstrates that the data-aware method maintains a reasonable consumption of computing resources. Experiments on a practical testbed of a cyber-physical system are implemented, and harmonic measurement and analysis accuracy are adopted to evaluate the measuring mechanism under a distributed metering network. Results demonstrate an improvement of the harmonics analysis precision and validate the asynchronous measuring method in cyber-physical energy systems.

Information filters with reduced data storage for out‐of‐sequence measurements update

In target tracking/fusion applications, the measurements often do not become available in the order of measurement times. Out of sequence measurements (OOSMs) are used to update state estimates for the ‘current’ time, using measurements from previous measurement times. The authors propose information filter-based OOSM update solution(s), which forward propagate the OOSMs information filter state. This allows tradeoffs between estimation performance and storage requirements.

Update with out-of-sequence measurements

Out-of-sequence measurements (OOSMs) can create difficulties for discrete time filtering. A number of procedures have been developed for extending the Kalman filter to handle these different types of delay. A common characteristic of these methods is the policy of always incorporating, or fusing delayed measurements at the time they finally become available. In this paper, we proposed a selective threshold (ST) to determine the value of the OOSMs, and based on a proposed information filter (ST-IF) to update the estimate with the useful OOSMs. By the simulation, we show that selective fusion can reduce computational costs while maintaining a good performance.

Rao–Blackwellized Particle Filters With Out-of-Sequence Measurement Processing

This paper addresses the out-of-sequence measurement (OOSM) problem for mixed linear/nonlinear state-space models, which is a class of nonlinear models with a tractable, conditionally linear substructure. We develop two novel algorithms that utilize the linear substructure. The first algorithm effectively employs the Rao–Blackwellized particle filtering framework for updating with the OOSMs, and is based on storing only a subset of the particles and their weights over an arbitrary, predefined interval. The second algorithm adapts a backward simulation approach to update with the delayed (out-of-sequence) measurements, resulting in superior tracking performance. Extensive simulation studies show the efficacy of our approaches in terms of computation time and tracking performance. Both algorithms yield estimation improvements when compared with recent particle filter algorithms for OOSM processing; in the considered examples they achieve up to 10% enhancements in estimation accuracy. In some cases, the proposed algorithms even deliver accuracy that is similar to the lower performance bounds. Because the considered setup is common in various estimation scenarios, the developed algorithms enable improvements in different types of filtering applications.

A Particle Filter Update Algorithm Based on out of Sequence Measurement

Consider out of sequence measurement (oosm) estimation problem in central tracking system of multi-sensor distributed data fusion, which is due to the communication delay. Apply the particle filter algorithm to overcome this problem and propose a update algorithm for the case of an arbitrary (multi-step) lag in case of nonlinear. Then we compare this algorithm with the known EKF oosm algorithm. Results demonstrate the feasibility and effectiveness of this algorithm.

Optimal Update with Multiple Out-of-Sequence Measurements with Arbitrary Arriving Order

In multisensor target tracking systems receiving out-of-sequence measurements (OOSMs) from local sensors is a common situation. In the last decade many algorithms have been proposed to update with an OOSM optimally or suboptimally. However, what one faces in the real world is the multiple OOSMs, which arrive at the fusion center in, generally, arbitrary orders, e.g., in succession or interleaved with in-sequence measurements. A straightforward approach to deal with this multi-OOSM problem is by sequentially applying a given OOSM algorithm; however, this simple solution does not guarantee the optimal update under the multi-OOSM scenario. The work presented here discusses the differences between the single-OOSM processing and the multi-OOSM processing, and presents the general solution to the multi-OOSM problem, which is called the complete in-sequence information (CISI) approach. Given an OOSM, in addition to updating the state at the most recent time, the CISI approach also updates the states between the OOSM time and the most recent time, including the state at the OOSM time. Three novel CISI methods are developed in this paper: the information filter-equivalent measurement (IF-EqM) method, the CISI fixed-point smoothing (CISI-FPS) method and the CISI fixed-interval smoothing (CISI-FIS) method. Numerical examples are given to illustrate the optimality of these CISI methods under various multi-OOSM scenarios.

Out-of-Sequence Measurement Processing for Particle Filter: Exact Bayesian Solution

The problem of out-of-sequence measurement (OOSM) processing when the filtering technique used at the tracker is the particle filter (PF) is considered. First, an exact Bayesian algorithm for updating with OOSMs is derived. Then, the PF implementation of the exact Bayesian algorithm, called A-PF, is developed. Since A-PF is rooted in exact Bayesian inference, if the number of particles is sufficiently large, A-PF is the one (and the only one) that is able to achieve the optimal performance obtained from the in-sequence processing. This is confirmed by the simulation results. Also, it is shown that the performance of A-PF is always superior to previous (heuristic) PF-based algorithms with the same number of particles.

Two-Sensor Information Fusion with Out-of-Sequence Measurement

In sensor tracking system, Out-Of-Sequence Measurement(OOSM) always occur due to communication delays. The system needs to update the OOSM in order to improve the precision. An optimal information fusion estimation weighted by scalars is presented for two-sensor information fusing with OOSM, which considers correlation between local errors, and avoid to compute the weighted matrix. It is easy to apply in real-time.

Comment on "One-Step Solution for the Multistep Out-of-Sequence-Measurement Problem in Tracking

To incorporate out-of-sequence measurements (OOSMs) in a Kalman filter, the cited paper proposed algorithms that reduced the multistep problem into a single-step one, by defining one that has the same dimension as the state vector. However, the authors did not prescribe formulas for the case when such a full-dimension equivalent measurement cannot be defined. This correspondence fills the gap by deriving formulas that are always applicable, regardless of the dimension of the equivalent measurement.

Examination of a Popular Out-of-Sequence Measurement Update Algorithm

We examine an out-of-sequence measurement (OoSM) update algorithm by Bar-Shalom. We demonstrate that C is mathematically equivalent to initializing a track with the OoSM, predicting that track to the current time without process noise, then using the OoSM track as a pseudomeasurement to update the system track. We argue that a more reasonable approximation includes process noise in the OoSM prediction. Like Algorithm C, the proposed algorithm makes use only of current track information.

An Improvement of Ensemble Kalman Filter for OOSM Tracking

AbstractIn multisensor target tracking system, the measurements of the same target are always delayed, come at different rates, and arrive out of sequence. Such measurements are called “out-of sequence” measurements (OOSMs). Examples of such systems are a mobile robot or an unmanned aerial vehicle (UAV) which is observed by both inertial sensors and visual sensors, and delay caused by transmitting or processing time. Solutions via Extended Kalman Filter (EKF), Particle Filter (PF), and Ensemble Kalman Filter (EnKF) have been proposed so far. EnKF yields various advantages, e.g., it can be applied to strong nonlinear system, requires much less particles than PF, and does not require any Jacobian matrix or backward state-transition function. In this paper, we propose an algorithm to improve accuracy of using EnKF with OOSMs. The algorithm concerns estimating an ensemble of the process noises. We validate the proposed algorithm by simulations of the aircraft tracking system. The results show another competitive solution for OOSM filtering.

Single-step-lag OOSM algorithm based on unscented transformation

Aiming at the out-of-sequence measurement (OOSM) problem, the update equations of the nonlinear single-step-lag OOSM are derived based on the existing methods. By introducing the unscented transformation (UT), the covariance between state vector and corresponding measurement vector are computed such that the single-step-lag OOSM can be effectively solved under the nonlinear Gaussian system with nonlinear measurement equation and linear dynamic equation. Furthermore, a single-step-lag OOSM fusion algorithm based on UT is presented to confront the problem of the single-step-lag OOSM in multi-sensor system. The proposed algorithm has some advantages over the EKF A1 based on the extended Kalman filter frame and the optimal method without lags. For example, it can be used when the Jacobian matrix or the Hessian matrix of nonlinear measurement equation is nonexistent; its filtering performance is better; and its complexity has the same order of magnitude as that of the EKF A1 algorithm.

Efficient Delay-Tolerant Particle Filtering

This paper proposes a novel framework for delay-tolerant particle filtering that is computationally efficient and has limited memory requirements. Within this framework the informativeness of a delayed (out-of-sequence) measurement (OOSM) is estimated using a lightweight procedure and uninformative measurements are immediately discarded. The framework requires the identification of a threshold that separates informative from uninformative; this threshold selection task is formulated as a constrained optimization problem, where the goal is to minimize tracking error whilst controlling the computational requirements. We develop an algorithm that provides an approximate solution for the optimization problem. Simulation experiments provide an example where the proposed framework processes less than 40% of all OOSMs with only a small reduction in tracking accuracy.