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Traditionally, inverse synthetic aperture radar (ISAR) imaging and target tracking are two separate and independent processes. ISAR imaging is usually achieved after data collecting and tracking for a long time, resulting in the problems of low imaging efficiency, information loss, and probing resource allocation difficulty. In this article, we proposed an integration method of tracking and imaging with wideband radar by constructing the relation among signal, data, and image domains, which can realize accurate tracking and high data-rate imaging at the same time. In this integrated imaging and tracking method, a complex-valued reference high-resolution range profile (HRRP) is generated and predicted by exploiting the relation among range-Doppler image, echo in time domain, and target's motion state. Then, a Bayes estimation model is built to extract range phase error between the predicted HRRP and the real-measured HRRP, and the Kalman filter can update the motion state. In addition, in order to increase the efficiency, the decentralized Kalman filter is also introduced to realize the subaperture parallel processing and data fusion in this article. Finally, the sequential motion compensation is carried out to realize accurate motion compensation and sequential imaging. The simulated and real-measured data confirm the proposed algorithm's robust imaging and tracking performance. Experimental results show that the proposed method has excellent efficiency and can simultaneously realize sequential imaging and accurate tracking. [ABSTRACT FROM AUTHOR]

The ARMAS-SOM framework fuses collaborative all-source sensor information in a resilient manner with fault detection, exclusion, and integrity solutions recognizable to a GNSS user. This framework uses a multifilter residual monitoring approach for fault detection and exclusion, which is augmented with an additional “observability” extended Kalman filter sublayer for resilience. We monitor the a posteriori state covariances in this sublayer to provide intrinsic awareness when navigation state observability assumptions required for integrity are in danger. The framework leverages this to selectively augment with offboard information and preserve resilience. By maintaining split parallel collaborative and proprioceptive instances and employing the “stingy collaboration” technique, we are able to maximize efficient use of network resources, limit the propagation of unknown corruption to a single donor, and maintain consistent collaborative navigation without fear of double-counting in a scalable processing footprint. Last, we preserve the ability to return to autonomy and are able to use the same intrinsic awareness to notify the user when it is safe to do so. [ABSTRACT FROM AUTHOR]

In harsh environments, tracking is organized assuming disturbances, initial errors, and data errors that requires robust algorithms. In this article, we develop, in discrete-time state space, a robust a posteriori $H_{2}$ optimal finite impulse response ($H_{2}$ -OFIR) filter of disturbed systems under initial and measurement errors. The derivation is provided using a novel $H_{2}$ finite impulse response ($H_{2}$ -FIR) state estimation approach by minimizing the squared Frobenius norm of the weighted transfer function. The robust $H_{2}$ -OFIR filter is designed for full block error matrices, and its recursive forms are shown for diagonal error matrices. Also presented is the suboptimal $H_{2}$ -FIR filtering algorithm using the linear matrix inequality. It is shown that, in global-positioning-system-based tracking of moving vehicles, the $H_{2}$ -OFIR filter outperforms the Kalman and unbiased FIR filters in terms of accuracy and robustness. Moreover, the ability to operate on short horizons makes the $H_{2}$ -OFIR filter computationally efficient. [ABSTRACT FROM AUTHOR]

Sample clock offset must be estimated in order to correctly demodulate an OFDM signal. Estimates are also required in passive radar processing, to produce a reference signal, which is properly matched to the transmission. A recently proposed clock offset estimation method for passive radar is found to be overly sensitive to measurement noise. However, the radar ambiguity surface is found to be unaffected by the specific errors engendered by this noise. The reasons for this are explored. An updated method based on state-space modeling and Kalman smoothing is proposed. This is found to restore clock offset estimation performance in cases of higher noise, achieving this with low processing latency. These improvements enable the method to be employed for other applications requiring high quality, time-critical clock offset estimation. [ABSTRACT FROM AUTHOR]

In this article, an $SE(3)$ -constrained extended Kalman filter is proposed in continuous time as well as in a more practical continuous-discrete framework. The filter allows for the state estimation of the 6-DOF rigid body motion while accounting for measurement error statistics and using the rotation matrix instead of quaternions or other attitude parameterizations. The proposed filter differs from the recently proposed $SO(3)$ -constrained attitude filter in that only a subset of the configuration states are constrained in the present filter. Its effectiveness is demonstrated in a numerical example in which its performance is compared with that of an existing $SE(3)$ estimator from the literature and a Monte Carlo simulation is carried out to provide credence to the accuracy of the proposed filter. [ABSTRACT FROM AUTHOR]

Highly maneuverable target tracking under glint noise and nonlinear uncertainties during course changes and terminal maneuvers has been solved suboptimally for many years via the interacting multiple model algorithm with the use of the Kalman filter (KF), unscented Kalman filter, and the extended Kalman filter (EKF). Also, nonlinear KFs such as the cubature Kalman filter have been proposed to improve nonlinear tracking without being able to filter out glint noise. To this end, the particle filter and some KF based on variational Bayesian approach have been proposed with very good results in filtering out glint noise. Nonetheless, it is difficult for state-of-the-art methods to achieve efficient filtering of glint noise and nonlinear tracking at the same time. On the other hand, robust exact differentiators, based on the super-twisting algorithm, have been used for many years in output-feedback control and state observation in order to obtain the derivatives of an input signal with theoretical finite-time exactness. However, their potential for target tracking applications has not been explored sufficiently. In this article, a uniform robust exact filtering differentiator with intrapulse median filtering is proposed to filter out glint noise at the sliding manifold, while offering nonlinear tracking robustness via high-degree super-twisting terms outside the sliding manifold. Numerical simulations comparing the proposed solution to other state-of-the-art methods were conducted, showing promising results. [ABSTRACT FROM AUTHOR]

This article deals with error models for a trident quaternion framework proposed in the companion paper (Part I) and further uses them to investigate the odometer-aided static/in-motion inertial navigation attitude alignment for land vehicles. By linearizing the trident quaternion kinematic equation, the left- and right-trident-quaternion error models are obtained, which are found to be equivalent to those derived from profound group affine. The two error models are used to design their corresponding extended Kalman filters (EKFs), namely, the left-quaternion EKF (LQEKF) and the right-quaternion EKF (RQEKF). Simulations and field tests are conducted to evaluate their actual performances. Owing to the high estimation consistency, the LQEKF and the RQEKF converge much faster in the static alignment than the traditional error-model-based EKF, even under arbitrary large heading initialization. For the in-motion alignment, the LQEKF and the RQEKF possess much larger convergence region than the traditional EKF does, although they still require the aid of attitude initialization so as to avoid large initial attitude errors. [ABSTRACT FROM AUTHOR]

This article focuses on the adaptive Kalman filtering problem for linear systems with unknown covariances of both dynamic multiplicative noise (multiplicative measurement noise) and additive noises (additive process and measurement noises). A recursive-noise adaptive Kalman filter is proposed to estimate both states and covariances of noises by using the variational Bayesian (VB) inference and an indirect method. First, we characterize inverse Wishart priors for both measurement noise covariance and process noise covariance and employ the Student’s t-distribution to represent the likelihood function, which is non-Gaussian and affected by mixing multiplicative noise and additive measurement noise. Then, an adaptive Kalman filtering for recursive both noise covariance matrices and dynamic state is proposed following VB inference. Performance analysis for VB procedures and the proposed filter is provided to ensure the convergence and stability. A target tracking example is provided to validate the effectiveness of the proposed filtering algorithm. [ABSTRACT FROM AUTHOR]

Very often, a measurement is transmitted through network systems before it is available for filtering. The network systems, designed with several communication channels, are prone to cyber-attacks. The cyber-attack often injects false data to alter the original measurement. This article develops a modified Bayesian approximation filtering method for nonlinear filtering with measurements altered due to cyber-attack. The proposed development is within the scope of nonlinear Gaussian filtering. It considers the false data to have either additive or multiplicative effect over the original measurement. Subsequently, two modified measurement models are introduced to model the possibility of false data stochastically. Then, the traditional nonlinear Gaussian filtering method is redesigned for the modified measurement models to deal with the false data attack. The proposed modification is applicable to any of the existing nonlinear Gaussian filters, such as extended Kalman filter, unscented Kalman filter, cubature Kalman filter, and Gauss–Hermite filter. The simulation results show an enhanced estimation accuracy for the proposed modification over the traditional nonlinear Gaussian filtering in the presence of false data. [ABSTRACT FROM AUTHOR]

This article is concerned with the development of two novel Kalman filters for satellite relative pose estimation. The relative pose, which is represented by a dual quaternion, is estimated from noisy lines-of-sight via a single camera, along with biases of linear velocity and angular rate measurements. The constraints on the dual quaternion are handled by brute-force and virtual measurement techniques. The partial reset analysis shows how to propagate the estimation error biases and covariances. Closed-form expressions for the Jacobians are provided. A quantitative observability analysis for the position states is provided. Compared with traditional representations, the dual quaternion model increases the position observability by a factor of four for each line-of-sight. The additive dual quaternion model enhances the observability of the rotation states thanks to a specific coupling term in the pose dynamics. Extensive Monte-Carlo simulations of a flight formation case verify that the proposed novel filters are asymptotically unbiased and statistically consistent for all practical purposes. They outperform the other candidate estimators in particular during the transient phase. The numerical simulations validate the observability analysis. [ABSTRACT FROM AUTHOR]

We address the problem of determining optimal sensor precisions for estimating the states of linear time-varying discrete-time stochastic dynamical systems, with guaranteed bounds on the estimation errors. This is performed in the Kalman filtering framework, where the sensor precisions are treated as variables. They are determined by solving a constrained convex optimization problem, which guarantees the specified upper bound on the posterior error variance. Optimal sensor precisions are determined by minimizing the $l_1$ norm, which promotes sparseness in the solution and indirectly addresses the sensor selection problem. The theory is applied to realistic flight mechanics and astrodynamics problems to highlight its engineering value. These examples demonstrate the application of the presented theory to 1) determine redundant sensing architectures for linear time invariant systems, 2) accurately estimate states with low-cost sensors, and 3) optimally schedule sensors for linear time-varying systems. [ABSTRACT FROM AUTHOR]

Observations from high rate sensors are known to be time-correlated. When processed in a Kalman filter (KF) without accounting for correlations, i) a discrepancy with the true solution occurs, up to a divergence of the filter and ii) the covariance estimates are overestimated, which is equally problematic. Two main solutions exist to account for correlations in a KF: The time differenced and the state augmentation approach. They both model the correlated noise corresponding to an autoregressive process of the first order (AR(1), also called the Gauss Markov process) as it has a short memory, is linear and can be easily implemented. In this contribution, we propose a new method to account for measurement correlations by means of a variance inflation factor (VIF). The latter is derived from an AR(1) assumption for the measurement noise, and its parameters can be estimated by whitening the KF residuals. Our proposal, called the KF_VIF, is further extended to an AR(p) model to account for finer correlation structures. We compare the different approaches and address the impact of noise mismodeling. We use simulations to test the sensitivity of the KF solution to misspecifications and show that the KF_VIF proposed is a powerful answer to account for correlated measurement noise. A real case analysis corresponding to a precomputed flight trajectory with a constant velocity validates the results of the simulations. [ABSTRACT FROM AUTHOR]

In this article, the target tracking of phased array radars with measurements specified in the direction cosine coordinate system is considered. The converted measurement Kalman filter is a widely adopted technique since it allows tracking in the coordinate system in which the dynamics of targets are described. The converted measurement Kalman filter has two types of inherent bias: conversion and estimation biases. The compensation of conversion bias has been examined by earlier studies using the debiasing technique in the presence of estimation bias. This article, therefore, introduces decorrelated debiased converted measurement Kalman filter (DDCMKF) in the direction cosine coordinate system to relieve the estimation bias. The decorrelation between the Kalman gain and measurement residual by applying conditioning on predicted position estimates is first introduced. The range-rate measurement is subsequently incorporated as a pseudo-measurement form after the derivation of decorrelated converted position. Finally, a sequential DDCMKF in direction cosine coordinates is developed using the derived converted position and range-rate measurement models. Adopting sequential filtering for incorporating the range-rate measurement reduces computation complexity and alleviates its strong nonlinearity. Numerical simulations are conducted to evaluate the performance of DDCMKF against other types of tracking filters in the direction cosine coordinate system. Simulation results show that the proposed DDCMKF achieves preferable error performance while maintaining consistency, especially in short-range tracking with relatively large direction cosine errors. [ABSTRACT FROM AUTHOR]

This article addresses a problem of spacecraft orbit estimation with measurement transmission restrictions through an event-triggered state estimation approach. Specifically, we consider the scenario that the ground station communicates with the spacecraft through multiple channels and each channel decides whether or not to transmit the measurements to the spacecraft based on separate deterministic event-triggering conditions. Considering $J_2$ perturbations, an event-triggered unscented Kalman filter-based state estimation algorithm is designed on the basis of a model of orbit dynamics and a measurement model of the ground station. The performance of the estimator is evaluated based on real-time two-line element data. The obtained results indicate that the proposed algorithm can achieve satisfactory estimation performance at reduced measurement transmission rates. [ABSTRACT FROM AUTHOR]

In low-cost wireless sensor networks, the communication bandwidth between sensors may be variable due to power constraints on the sensors. Considering that quantization is an effective method to save communication bandwidth, a novel distributed adaptive quantization state estimation algorithm with variable bandwidth is proposed, where the quantization steps are time varying. Based on the minimum mean squared error criterion and diffusion strategy, the optimal local gain and neighborhood gain are designed to utilize quantized information for fusion estimation. These gains can be adjusted adaptively through local information fusion. Moreover, we also analyze the mean and mean-square performance of the proposed algorithm and find that the covariance is bounded under variable bandwidth. Finally, the effectiveness of the proposed algorithm is verified via numerical simulation. [ABSTRACT FROM AUTHOR]

The development and performance of an endpoint-constrained (EPC) extended Kalman filter (EKF) were published by Haug and Ford, where the EPC EKF was shown to outperform similar non-EPC EKFs against highly maneuverable antiship cruise missile (ASCM) trajectories. The purpose of this article is to resolve two issues identified during the original study. The first issue is that EKFs may not offer superior performance when the target's motion is highly nonlinear. The second issue is that the EPC EKF performs poorly against the high diver trajectory, where the target does not satisfy the EPC until the dive begins. This article presents a new filter that uses a modified version of the EPC and a multiple-model algorithm to achieve superior performance against a larger set of ASCM trajectories than the EPC EKF. [ABSTRACT FROM AUTHOR]

This article proposes a recursive Gaussian process regression with a joint optimization-based iterative learning control algorithm to estimate and predict disturbances and model uncertainties affecting a flight. The algorithm proactively compensates for the predicted disturbances, improving precision in aircraft trajectory tracking. Higher precision in trajectory tracking implies an improvement of the aircraft trajectory predictability and, therefore, of the air traffic management system efficiency. Airlines can also benefit from this higher predictability by reducing the number of alterations when following their designed trajectories, which entails a reduction of costs and emissions. The iterative learning control algorithm is divided into two steps: first, a recursive Gaussian process regression estimates and predicts perturbations and model errors with no need for prior knowledge about their dynamics and with low computational cost, and second, this information is used to update the control inputs so that the subsequent aircraft intending to fly the same planned trajectory will follow it with greater precision than the previous ones. This method is tested on a simulated commercial aircraft performing a continuous climb operation and compared to an iterative learning algorithm using a Kalman filter estimator in a similar scenario. The results show that the proposed approach provides 62 and 42% precision improvement in tracking the desired trajectory, as compared to the Kalman filter approach, in two experiments, where no prior knowledge of the unmodeled dynamics was available, also achieving it in less iterations. [ABSTRACT FROM AUTHOR]

This article proposes a Gaussian filtering method to approximate the single-target updates and normalizing constants for multitarget tracking with nonlinear, non-Gaussian measurements, and a state-dependent probability of detection. The Gaussian approximation is based on the posterior linearization technique, which seeks the optimal affine approximation of the nonlinearities in a mean square error sense. The normalizing constant is approximated using sigma-points based on the posterior. The proposed approach is implemented in a Poisson multi-Bernoulli mixture filter and compared against standard methods to approximate single-target posteriors and normalizing constants in two range-bearings tracking scenarios. [ABSTRACT FROM AUTHOR]

This article is concerned with the distributed fusion estimation problem for nonlinear systems without knowledge of noise statistical information. By using the Taylor expansion, the linearization errors are modeled by the state-dependent terms with uncertain parameters when constructing nonlinear estimation error systems. Then, based on the idea of bounded recursive optimization, a robust design approach is developed to obtain local nonlinear estimators and distributed fusion criterion such that the designed local/fusion estimators are stable. Notice that, by establishing different convex optimization problems, the gains of stable nonlinear local/fusion estimators can be directly obtained using the standard softwares. Finally, two illustrative examples are exploited to show the advantages and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Tracking on the rotation group is a key component of many modern systems for estimation and tracking of the orientation of rigid bodies. To address this problem, here, we describe a Bayesian algorithm that relies on directional measurements, acquired, for example, by an inertial measurements unit (IMU), for tracking on the special orthogonal (rotation) group. Its novelty lies in the use of maximum entropy distributions on these groups as models for the priors, and justifiable relaxation algorithms that permit the recursive implementation of such a model to provide a filter. We provide the solutions in a recursive closed form. In the two-dimensional case, the parameters of the prior and posterior distributions can be computed exactly and the solution has low complexity. Adoption of this approach eliminates the problem of angle wrapping. In higher dimensions, the exact solution cannot be computed, and it is necessary to make appropriate relaxations, which is done here. We demonstrate in simulations that, in contrast with some other approaches, our algorithm produces very accurate and statistically meaningful outputs. Pseudocode, specific to the IMU measurements is also provided. [ABSTRACT FROM AUTHOR]

This article presents a novel algorithm for adaptive explicit nonlinear model predictive control (eNMPC) with applications to fault tolerance. In order to account for plant-model mismatch, under which fault tolerance applies, the controller's explicit solution is designed with multiple dynamic models representing various operating modes as opposed to a single system model. Each model is weighted by a parameter variable to be evaluated online as mode probabilities produced by an interacting multiple model (IMM). Weighting each potential system model allows the controller to use a dynamic model that best matches the current operating mode, thus mitigating the degrading performance brought on by plant-model mismatch. The developed strategy is validated on attitude maneuvers for a nonlinear spacecraft system in the presence of disturbances and two actuator faults, which are indicative of the system mode. Average root mean squared values on the tracking error and control effort over Monte Carlo simulations are used to evaluate the effectiveness of the proposed techniques. Results indicate eNMPC benefits from access to weighted system models and manages similar levels of tracking error to standard spacecraft controllers at the same or minimal control effort. [ABSTRACT FROM AUTHOR]

This article proposes a method to decentralize the navigation burden and improve the fault tolerance for a spacecraft constellation. The constellation body reference system is introduced, which is the perifocal frame of one satellite in the constellation. The structure of the proposed navigation method is constructed to enable each spacecraft to estimate its own orbit in this body reference system. This step is essentially the relative orbit determination (OD) based on inter-satellite range measurements. Thereafter, the approach to transfer an orbit from the constellation body reference system to an inertial reference system is developed. The essential requirements on absolute measurements to realize the coordinate transfer are presented. By dividing the absolute OD into relative OD and coordinate transfer, each navigation subsystem operated in a spacecraft can be independent with others, and the absolute measurements collected by any spacecraft can contribute to the absolute OD of the whole constellation. The proposed method applies to constellations in any geometric configuration. A Walker constellation is taken as an example for numerical simulations. The results show that the proposed method has a lower computation burden compared to an integrated navigation system. With the same type of absolute measurements, the proposed method has higher accuracy and convergence velocity than conventional decentralized algorithms. When a spacecraft occurs with fault, the orbit results of other spacecraft are not affected using the proposed method, which is beyond the ability of conventional methods. [ABSTRACT FROM AUTHOR]

This article presents an optimization-based formulation for privacy-utility tradeoff in the ensemble and unscented Kalman filtering framework, focusing on the space situational awareness. Privacy and utility are defined in terms of lower and upper bound on the state estimation error covariance. The synthetic sensor noise is used to satisfy these bounds and is determined by solving an optimization problem. Given privacy and utility bounds, this article present optimization problem formulations to determine the maximum noise for which the utility is satisfied or the estimation errors are upper bounded, the minimum noise for which the privacy is satisfied or the estimation errors are lower bounded, the optimal noise that satisfies utility constraints and maximizes privacy, and the optimal noise that satisfies privacy constraints and minimizes the uncertainty. We demonstrate the application of these formulations to the tracking of the International Space Station and highlight the optimal privacy versus utility tradeoff for this dynamical system. [ABSTRACT FROM AUTHOR]

The actual article presents the modeling and control of a multilink unmanned aerial system whose dynamics is computed by means of the Euler–Lagrange approach. The aforementioned system is subjected to lumped disturbances, which comprise external disturbances and parametric uncertainties. An augmented-state extended Kalman filter intended to estimate endogenous and exogenous uncertainties is conceived and a trajectory-tracking controller fulfilling Lyapunov asymptotic stability is synthesized. A simulation stage is conducted to validate the effectiveness of the proposal. [ABSTRACT FROM AUTHOR]

Filters relying on the Gaussian approximation typically incorporate the measurement linearly, i.e., the value of the measurement is premultiplied by a matrix-valued gain in the state update. Nonlinear filters that relax the Gaussian assumption, on the other hand, typically approximate the distribution of the state with a finite sum of point masses or Gaussian distributions. In this work, the distribution of the state is approximated by a polynomial transformation of a Gaussian distribution, allowing for all moments, central and raw, to be rapidly computed in a closed form. Knowledge of the higher order moments is then employed to perform a polynomial measurement update, i.e., the value of the measurement enters the update function as a polynomial of arbitrary order. A filter employing a Gaussian approximation with linear update is, therefore, a special case of the proposed algorithm when both the order of the series and the order of the update are set to one: it reduces to the extended Kalman filter. At the cost of more computations, the new methodology guarantees performance better than the linear/Gaussian approach for nonlinear systems. This work employs monomial basis functions and Taylor series, developed in the differential algebra framework, but it is readily extendable to an orthogonal polynomial basis. [ABSTRACT FROM AUTHOR]

Kalman filter-based retrodiction plays an indispensable role in modern multitarget tracking and retrodiction (MTTR) algorithms. To this end, the Rauch–Tung–Striebel (RTS) smoother is a widely used Kalman filter-based target state smoother. With a large number of targets, MTTR algorithms, particularly with large window sizes, become very computationally intensive. If not addressed, these algorithms will not meet the requirements for tracking a large number of targets in real time. A natural approach is to parallelize these algorithms to render them useful, particularly in the context of emerging multicore platforms. However, this is nontrivial, as the governing mathematical framework of the RTS smoother, namely the dependencies between complex computations, prevents any form of parallelization. Although the MTTR component can naively be parallelized ignoring the smoothing component, the overall benefit, as we demonstrate in this article, is a fraction of the best possible benefits. In this article, by carefully reformulating the underlying mathematical framework that is necessary for retrodiction, we propose a novel, easily parallelizable RTS smoother. The proposed parallelized RTS smoother we outline in this article has best data reuse and enables the overall MTTR problem to be parallelized more efficiently. We demonstrate this on a state-of-the-art multicore processor platform using the shared-memory parallelism. Our results show that the parallel MTTR solution, which includes gating, assignment, tracking, and retrodiction, can offer nearly 150 times speed up against a fully sequential version. With excellent computational performance, our proposed RTS smoother enables very large window sizes with little or no impact on the overall performance. [ABSTRACT FROM AUTHOR]

Land vehicle navigation based on the inertial navigation system (INS) and odometers (ODs) is a classical autonomous navigation application and has been extensively studied over the past several decades. In this article, we seriously analyze the error characteristics of the OD pulses and investigate three types of OD measurement models in the INS/OD integrated system. Specifically, in the pulse velocity model, a preliminary Kalman filter is designed to obtain an accurate vehicle velocity from the accumulated pulses; the pulse increment model is accordingly obtained by integrating the pulse velocity; a new pulse accumulation model is proposed by augmenting the traveled distance into the system state. The three types of measurements, along with the nonholonomic constraint, are implemented in the standard extended Kalman filter. In view of the motion-related pulse error characteristics, the multiple model adaptive estimation (MMAE) approach is exploited to further enhance the performance. Simulations and long-distance experiments are conducted to verify the feasibility and effectiveness of the proposed methods. It is shown that the standard pulse velocity measurement achieves superior performance, whereas the accumulated pulse measurement is most favorable with the MMAE enhancement. [ABSTRACT FROM AUTHOR]

The use of frequency division duplex (FDD) communication in a multihop wireless network partitions the nodes in two operating modes. Since the FDD nodes of the same mode cannot communicate with each other, it can limit the node connectivity and also lead to network partitioning. In this article, a novel, distributed, low-complexity mode reassignment (MR) scheme is designed for maintaining connectivity among the mobile FDD nodes in a decentralized, multihop wireless (airborne) network. Since it is not practical to know the complete topology of such a network in real time, the proposed scheme is fully distributed, relies only on the local node information, and applied only on those nodes whose connectivity drops below a threshold. Besides maintaining a desired value of connectivity degree for each node while it is moving around, the proposed MR scheme also minimizes the impact of mode change on the existing links and ongoing data transmissions. A Kalman filter based node mobility prediction and link failure prediction scheme is designed to select the best candidate nodes for mode change. The optimality and error control bounds of the proposed MR scheme show that it consistently achieves optimal connectivity for most nodes, while requiring a low number of nodes undergoing the mode change during each MR round. [ABSTRACT FROM AUTHOR]

The lifespan of a satellite is primarily dependent on its battery performance. Thus, proper management and monitoring of the battery is important. Most miniaturized satellites of cubeSat and nanosatellite primarily rely on battery voltage readings for monitoring and seldom provide battery health status in a satellite. As the voltage readings can be affected by satellite operating conditions such as temperature and battery lifespan, it can give unreliable readings that might jeopardize satellite operation. The availability of the battery health status can prevent unexpected battery failures and provide useful insights into the planning of satellite operations. In this article, the battery management system of a satellite with state-of-charge (SOC) and state-of-health (SOH) monitoring is presented. For SOC estimation, a scaled unscented Kalman filter (UKF) is proposed. When compared to the existing UKF approach, it requires fewer sigma points and the positive weights used in the scaled unscented transform ensure the positive semidefiniteness of the covariance matrix leading to the improved numerical stability of the filter. Conversely, SOH monitoring is achieved by taking advantage of the opportunity arising from the satellite operations. The battery parameters are extracted without artificially injecting charge and discharge pulses. To validate the performance of the BMS, the experimental prelaunch tests and the actual in-flight data of the VELOX-II satellite is used as an example. From the results, the SOC estimation error is approximately 1% and the SOH estimation is consistent with the manufacturer's datasheet. [ABSTRACT FROM AUTHOR]

Accurate carrier-phase integer ambiguity resolution is fundamental to high-precision global navigation satellite systems (GNSSs). Real-time GNSSs typically resolve the ambiguities by a combination of recursive estimators and integer least-squares solvers, which need to be reset when satellites are added or cycle slip occurs. In this article, we propose a mixture Kalman filter solution to integer ambiguity resolution. By marginalizing out the set of ambiguities and exploiting a likelihood proposal for generating the ambiguities, we can bound the possible values to a tight and dense set of integers. Thus, we extract the state and integer estimates from a mixture Kalman filter. The proposed approach yields an integrated method to detect cycle slip and initialize new satellites. Numerical analysis and experimental results indicate that the proposed method achieves reliable position estimates, repeatedly finds the correct integers in cases when other methods may fail, and is more robust to cycle slip. [ABSTRACT FROM AUTHOR]

This correspondence is concerned with the problem of distributed Kalman filtering for cooperative localization with absolute and relative measurements. Each target state is estimated by using locally available absolute measurements and relative measurements with other targets in the neighborhood. Two distributed Kalman filters are developed by enforcing each target to transmit its local estimates to the neighbors in a directed graph. A sufficient condition is established to guarantee the stability of the error dynamics. Numerical simulations are provided to verify the effectiveness of the proposed filters. [ABSTRACT FROM AUTHOR]

This article presents a Kalman-type recursive estimator for discrete-time systems with a measurement noise modeled by a Gaussian-uniform mixture. The objective is to deal with data containing outliers that degrade the performance of the regular Kalman filter. The proposed non-Gaussian noise model takes into account the reliability of the measurement with respect to erroneous data. The Kalman-type estimator is based on Masreliez's formulation which copes with non-Gaussian noise models. Results in different simulated conditions are displayed to evaluate the performance of the newly-presented algorithm and to compare it to state-of-art alternatives. [ABSTRACT FROM AUTHOR]

The problem of multisensor multitarget state estimation in the presence of constant but unknown sensor biases is investigated. The classical approach to this problem is to augment the state vector to include the states of all the targets and the sensor biases, and then implement an augmented state Kalman filter (ASKF). In this article, we propose a novel decoupled Kalman filtering algorithm. The decoupled Kalman filtering first processes each target in a separate branch, namely the single-target Kalman filtering branch, where the single-target states and the sensor biases are estimated. Then the bias estimate is refined by fusing the former bias estimates across all the single-target Kalman filtering branches. Finally, the refined bias estimate is fed back to each single-target Kalman filtering branch to improve the target state estimation. We prove that the proposed decoupled Kalman filtering is exactly equivalent to the ASKF in terms of the estimation results under a usual initial condition. The equivalence is also confirmed via the numerical example. Moreover, we further validate the proposed algorithm using the field experimental data of a multistatic passive radar. [ABSTRACT FROM AUTHOR]

The performance of a partial diffusion Kalman filtering (PDKF) algorithm for the networks with noisy links is studied here. A closed-form expression for the steady-state mean square deviation is then derived and theoretically shown that when the links are noisy, the communication–performance tradeoff, reported for the PDKF algorithm, does not hold. Additionally, optimal selection of combination weights is investigated, and a combination rule along with an adaptive implementation is motivated. The results confirm the theoretical outcome. [ABSTRACT FROM AUTHOR]

A novel robust Rauch–Tung–Striebel smoothing framework is proposed based on a generalized Gaussian scale mixture (GGScM) distribution for a linear state-space model with heavy-tailed and/or skew noises. The state trajectory, mixing parameters, and unknown distribution parameters are jointly inferred using the variational Bayesian approach. As such, a major contribution of this paper is unifying results within the GGScM distribution framework. Simulation and experimental results demonstrate that the proposed smoother has better accuracy than existing smoothers. [ABSTRACT FROM AUTHOR]

In practice, additional knowledge about the target to be tracked, other than its fundamental dynamics, can often be modeled as a set of soft constraints and utilized in a filtering process to improve the tracking performance. This paper develops a general approach to the modeling of soft inequality constraints, and investigates particle filtering (PF) with soft state constraints for target tracking. We develop two PF algorithms with soft inequality constraints, i.e., a sequential-importance-resampling particle filter and an auxiliary sampling mechanism. The latter probabilistically selects the candidate particles from the soft inequality constraints of the state variables so that they are more likely to comply with the soft constraints. The performances of the proposed algorithms are evaluated using Monte Carlo simulations in a target tracking scenario. [ABSTRACT FROM AUTHOR]

This paper considers nonlinear state estimation subject to inequality constraints in the form of linear and linear-matrix inequalities. Rewriting the standard maximum likelihood objective function used to derive the Kalman filter allows the Kalman gain to be found by solving a constrained optimization problem with a linear objective function subject to a linear-matrix-inequality constraint. Additional constraints, such as weighted-norm- or linear-inequality constraints, that the state estimate must satisfy are easily augmented to the constrained optimization problem. The proposed constrained estimation methodology is applied in the extended Kalman filter (EKF) and sigma point Kalman filter (SPKF) frameworks. Motivated by estimation problems involving a vehicle that can rotate and translate in space, multiplicative versions of the constrained EKF and SPKF formulations are discussed. Simulation results for a ground-based mobile robot operating in a constrained three-dimensional terrain are presented and are compared to results that use the traditional multiplicative EKF and SPKF, as well as filters that enforce inequality constraints by simply projecting the state estimate into the constrained domain along the shortest Euclidean distance. [ABSTRACT FROM AUTHOR]

This paper presents a new filter estimating quaternion using inertial and magnetic sensors. Using a reference coordinate system multiplicative quaternion error representation and a constrained structure filter gain, the proposed filter has a separation property, where the magnetic sensor output does not affect pitch and roll angle estimation. Furthermore, the proposed filter gain can be computed just from five scalar equations. Through simulation, the separation property of the proposed filter is verified. [ABSTRACT FROM AUTHOR]

Automatic dependent surveillance-broadcast (ADS-B) is an air traffic control system in which aircraft transmit their own information (identity, position, velocity etc.) to ground sensors for surveillance scope. The tracking of the different sensors’ clocks by the use of time difference of arrival of ADS-B messages is proposed to check the veracity of the position information contained in the ADS-B messages. The method allows detecting possible on-board anomalies or the malicious injection of fake messages (intrusion) without the use of the multilateration (or any other) location algorithm. It follows that it does not need the inversion of the location problem (usually strong nonlinear and ill-posed), and, contrary to the multilateration, it works also with less than four sensors. [ABSTRACT FROM AUTHOR]

We consider the problem of Bayesian tracking of radar cross section. The adopted observation model employs the gamma family, which covers all Swerling cases in a unified framework. State dynamics are modeled using a nonstationary autoregressive gamma process. The principal component of the proposed solution is a nontrivial gamma approximation, applied during the time update recursion. The superior performance of the proposed approach is confirmed using simulations and a real-world dataset. [ABSTRACT FROM AUTHOR]

In this paper, a time-frequency (TF) jammer mitigation algorithm based on a Kalman filter is proposed for global navigation satellite system (GNSS) receivers. A new state-space representation of the received signal is formed considering the rapidly changing characteristics of the jamming signal. Using the instantaneous frequency (IF) and chirp rate estimates obtained by the TF analysis, the proposed algorithm applies a Kalman filter for jamming signal estimation. The estimated jamming signal is then subtracted from the received data to remove the jammer signal. To cope with the time-varying accuracy in the jammer parameter estimates, the methods for adaptively adjusting the process and measurement noise variances using chirp rate estimates are described. Simulations are performed to verify the effectiveness of the proposed method for mitigating various types of jammers. The proposed approach improves the jammer signal removal performance by minimizing the effect of the Kalman filter model mismatch when compared to other techniques reported in the literature. [ABSTRACT FROM AUTHOR]

Interference, such as jamming, is widely encountered in practical applications, such as target tracking. Kalman-based nonlinear filters may not be feasible for nonlinear state estimation with nonlinearly transformed interference. This paper presents an online-based adaptive (oba) filter, which we have named the oba filter (OF), for state filtering and prediction of nonlinear discrete dynamic models with estimate constraints, nonlinearly transformed interference and noise. In the OF, noises and interference are approximated by discrete noises and interference; states are quantized; some undesired state estimates, which are not in near vicinities of the actual state values, are detected by a confidence level, and then state quantization levels are updated at the times when undesired estimates occur by using the measurement model; and states are recursively estimated by a suboptimal implementation of multiple composite hypothesis testing. The OF can prevent some undesired state estimates and outperform the unscented Kalman, regularized, sampling importance resampling (SIR), and auxiliary SIR particle filters for some nonlinear models with noise and interference. It is also suitable for state estimation with either missing observations or estimate constraints. [ABSTRACT FROM AUTHOR]

In this paper, first, two methods of positioning an indoor receiver with transferred global navigation satellite system signals from cellular base stations are proposed. Then, a technique of fusing the position results produced by the two methods through Kalman filter is introduced; thus, the positioning accuracy is improved. To mitigate the near–far problem generated by signals from base stations and satellites, a pulse shaping scheme and the strategy of assigning pulse patterns to base stations are investigated. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive sequential fusion estimation method for the target tracking with nonsynchronous measurements in wireless sensor networks (WSNs). Based on Gaussian assumption and Bayesian inference, a sequential cubature Kalman filtering (SCKF) method, as well as its square root form (SR-SCKF), is presented by applying the cubature rule to approximate the $function \times Gaussian$ integrals. By taking into consideration the time-varying properties of the measurement noise and the linearization errors, some adaptive factors are introduced into the SCKF to compensate for the measurement uncertainties based on Chi-square tests. The convergence analysis of the SCKF is presented. It is proved that the adaptive SCKF (ASCKF) has a better convergence property than the SCKF. Both simulations and experiments of a target tracking example are presented to show the effectiveness and superiority of the proposed ASCKF method. [ABSTRACT FROM AUTHOR]

A new information formulation of the Kalman filter is presented where the information matrix is parameterized as the product of an upper triangular matrix, a diagonal matrix, and the transpose of a triangular matrix (referred as UDU factorization). The UDU factorization of the Kalman filter is known for its numerical stability; this paper extends the technique to the information filter. A distinct characteristic of the new algorithm is that measurements can be processed as vectors, while the classic UDU factorization requires scalar measurement processing, i.e., a diagonal measurement noise covariance matrix. [ABSTRACT FROM AUTHOR]

Tracking with bistatic sonar or radar measurements is challenging due to the fact that the measurements are nonlinear functions of the Cartesian state. The performance of existing approaches, including the extended Kalman filter and sigma point Kalman filters, such as the unscented Kalman filter and cubature Kalman filter, may not be acceptable in terms of mean square error or tracker consistency (i.e., the tracker's state estimation error covariance is not statistically consistent with the actual estimation errors). This paper generalizes the sigma point Kalman filter (SPKF) as a converted measurement SPKF. The resulting converted measurement sigma point Kalman filter is demonstrated to have improved performance over the conventional SPKF when employed in a bistatic tracking scenario. [ABSTRACT FROM AUTHOR]

Asynchronous multisensor systems have been widely equipped on various host platforms to meet the requirements of modern navigation campaigns. However, the existing asynchronous fusion algorithms are not efficient in many challenged environments, due to the limitations of communication condition, out-of-sequence observation, and computation affordance. To solve these problems, this paper proposes a batch state asynchronous fusion algorithm with feedback for distributed architecture systems. It is optimal in the sense of minimum mean-squared estimation and its fusion solution is rigorously derived by fully considering the correlations of sequential/cross channels and one-step prediction information. The final fusion solution is straightforward expressed with the combinations of multiple local Kalman filtering estimates outputs during one fusion period. Moreover, no additional interpolation, extrapolation or synchronization procedures are required. Furthermore, to alleviate the computational burden of our proposed algorithm, its approximation form is also given by replacing the weighting matrix by the weighting scalar. Simulations are carried out to illustrate the efficiency and the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a novel filtering technique to estimate the position of a moving target based on discrete-time direction and velocity measurements. The velocity is assumed to be corrupted by an unknown constant bias, which is explicitly estimated in the process. A nonlinear system is first designed, describing the dynamics and observations associated to the target, followed then by a state augmentation that yields an equivalent linear time-varying system. An observability analysis for the latter is conducted based on necessary and sufficient conditions that are related to the target's motion. The final estimation solution resorts to a Kalman Filter with globally exponentially stable error dynamics. Its performance is assessed via realistic numerical simulations, including Monte Carlo runs and a comparison with both the standard extended Kalman filter and the Bayesian Cramér–Rao bound. A set of experimental results achieved within the scope of a realistic underwater mission scenario is also presented that allows to further assess the proposed technique. [ABSTRACT FROM AUTHOR]

This paper introduces a filter for tracking a ballistic missile during its boost phase. This filter includes a new switching algorithm and a modified interacting multiple model unscented filter (IMMUF), where the Markov transition matrix is time variable. Position, velocity, and all unknown parameters of a medium-range ballistic missile model are reconstructed. Simulations demonstrate that the new filter is able to consistently estimate a missile's trajectory and all unknown parameters and to outperform the previous forms of the IMMUF. [ABSTRACT FROM AUTHOR]

This paper addresses the continuous discrete-time nonlinear filtering problem for stochastic dynamical systems using the feedback particle filter (FPF). The FPF updates each particle using feedback from the measurements, where the gain function that controls the particles is the solution of a Poisson equation. The main difficulty in the FPF is to approximate this solution using the particles that approximate the probability distribution. We develop a novel Galerkin-based method inspired by high-dimensional data-analysis techniques. Based on the time evolution of the particle cloud, we determine basis functions for the gain function and compute values of it for each individual particle. Our method is completely adapted to the recorded history of the particles and the update of the particles do not require further intermediate approximations or assumptions. We provide an extensive numerical evaluation of the proposed approach and show that it compares favorably compared to baseline FPF and particle filters based on the importance-sampling paradigm. [ABSTRACT FROM AUTHOR]