Robust state estimation for jump Markov linear systems with missing measurements

The conventional interacting multiple models (IMM) approach for a hybrid system under the Gaussian assumption is limited for most real applications due to the noisy measurements often being in the presence of outliers. This paper aims at accommodating the IMM approach to the non‐Gaussian cases where outliers exist. In the proposed IMM algorithm, the Student‐t distribution is used to model the non‐Gaussian measurement noise. At the interaction step, the mixed statistics of the noise parameter under a Bayesian framework are obtained via a Gamma approximation and a recently reported moments matching method. To address the state noise‐coupled intractability in Bayesian filtering, a variational Bayesian method is utilized to approximate the posterior distributions of the noise and state recursively. The proposed algorithm is tested with a maneuvering target tracking example and is shown to be robust to the outliers.

This paper presents a simple yet efficient adaptive Kalman filter for tracking targets expected to perform varying turn maneuvers. The process noise covariance level of a second order Kalman filter is adjusted at each time step according to the calculated turn rate. The turning rate is estimated from the magnitude of the calculated acceleration divided by the estimated speed of the target. At each scan the previous and current velocity estimates are used to calculate the acceleration. The comparison of the performance of the proposed algorithm is made with that of an interacting multiple model (IMM) algorithm, employing three models with different levels of process noise covariance and also to that of a second order Kalman filter. Two different assumptions have been made for selecting the process noise values for the the IMM and Kalman filter algorithms, in the first case it was assumed that there was no prior information about the target motion whereas in the second case it was assumed that the largest turn rate that the target of interest could perform was known. The IMM algorithm utilizing three models gives slightly better estimates during the nonmaneuvering periods, but the proposed algorithm is superior to the IMM algorithm during maneuvering periods in terms of estimation errors. Also the proposed algorithm requires 78% less computation, almost the same number of calculations required by a single fixed process noise Kalman filter, than the IMM algorithm.

This paper presents sensor and data rate control algorithms for tracking maneuvering targets. The manuevering target is modeled as a jump Markov linear system. We present novel extensions of the Interacting Multiple Model (IMM), Particle filter tracker, and Probabilistic Data Association (PDA) algorithms to handle sensor and data rate control. Numerical studies illustrate the performance of these sensor and data rate control algorithms.

For maneuvering target tracking, general interacting multiple model (IMM) algorithms have a fixed structure. It has been overlooked that how the performance of these algorithms depends on the set of models used. The use of too many models is as bad as that of too few models. Therefore, a variable structure IMM (VSIMM) was presented and applied to ground target tracking. This algorithm eliminates the need for carrying all the possible models throughout the entire tracking period as in the standard IMM estimator, significantly improving performance and reducing computational load. But it is difficult to apply the VSIMM to other scenario (for example, aerial target) without auxiliary information such as map for ground target. This paper then presents a model set multiple hypotheses IMM algorithm (MS-MHIMM) which leads to a systematic treatment of model-set adaptation without using any additional auxiliary information. The new approach is illustrated in detail with an aerial complex maneuvering target tracking example.

Correct knowledge of noise statistics is essential for an effective estimator in maneuvering target tracking. In practice, however, the noise statistics are usually unknown or not perfectly known. To deal with the estimation problem in linear discrete-time systems with Markov jump parameters, where the measurement noise covariance is unknown, a novel approach is presented in this paper. This approach is based on the interacting multiple model (IMM) framework. An H ∞ filter is employed to construct a noise statistics estimator to obtain the information which is necessary for the IMM algorithm. In our approach, even the priori knowledge of noise statistics is not needed. The noise statistics loss problem is solved while the merits of IMM algorithm is reserved. The effectiveness of the proposed approach is demonstrated in comparison with single-model H ∞ filter through Monte Carlo simulation for maneuvering target tracking.

An improved Interacting Multiple Model tracking algorithm is presented to solve the maneuvering target tracking problem. The model set including Constant Velocity Model, Constant Acceleration Model and Current Statistical Model is designed, and the Interacting Multiple Model method is used to select model. The improved unscented Kalman filter algorithm is proposed to enhance filtering effect. The simulation and actual tracking experiment results indicate that the algorithm in maneuvering target tracking is valid.

To solve the problem of missing measurements in highly manoeuvring target tracking, an expected‐mode‐augmentation‐based unscented Kalman filter with missing measurements compensation (EMA‐MMCUKF) is designed based on the variable‐structure multiple model method. In the proposed EMA‐MMCUKF, the random missing measurements are described by the Bernoulli distribution, and the one‐step prediction is used as the compensation. Based on the proposed EMA‐MMCUKF, a Bayesian estimation‐based expected‐mode‐augmentation unscented Kalman filter with missing measurements compensation (BE‐EMA‐MMCUKF) is proposed for adaptive estimation of the sensor measurement reception rate, where the unknown measurement reception rate can be estimated by fully utilising prior information. Simulation results demonstrate that the proposed EMA‐MMCUKF can effectively track the manoeuvring target at different measurement reception rates. Moreover, when the sensor prior information differs significantly from the true measurement reception rate, the proposed BE‐EMA‐MMCUKF can effectively estimate the unknown sensor measurement reception rate and improve the accuracy of manoeuvring target tracking compared with non‐estimation of the sensor measurement reception rate.

Bayesian estimation for jump Markov linear systems with non-homogeneous transition probabilities

Today's power system predominantly employing the weighted least squares (WLS) technique for estimating the state of the power system over robust state estimation techniques. The computational inexpensiveness of WLS made it a good choice for the operators compared to the robust state estimators. When the system is completely observable by PMUs, the relationship between measurements and state variables changes from non-linear to linear. This made robust state estimators computationally competitive with the WLS estimator (WLSE). In this paper, quadratic-constant (QC) robust estimator has been improved to make it suitable for linear state estimation. The constant part of the estimator after the break-even point is changed to decaying exponential. The proposed quadratically- decaying exponential criterion (QE) is tested on IEEE 14, 30, 57 and 118- bus systems for two cases. (a) measurement data having only Gaussian noise (b) with corrupt measurement data. It is demonstrated that the proposed estimator is able to suppress the bad data and exhibiting better estimation accuracy and computational performance compared to least absolute value (LAV) and WLSE.

Maneuvering target tracking, as a core task in multi-sensor information fusion, is widely used in unmanned vehicles, missile navigation, and underwater ship localization, where real-time and robust state estimation is critical. Due to the uncertainty of the moving characteristics of maneuvering targets and the low sensor measurement accuracy, trajectory tracking has always been an open research problem and challenging work. This paper proposes a Bayesian-inspired stacked LSTM fusion network (SLSTM) for uncertain motion characteristics. The network consists of two LSTM fusion networks with stacked serial relationships, one of which is used to predict the movement dynamics, and the other is used to update the track's state. Compared with the classical Kalman filter based on the maneuver model, the method proposed here does not need to model the motion characteristics and sensor characteristics. It can achieve high-performance tracking by learning historical data dynamics and sensor characteristics. Experimental results show that this method can effectively improve the trajectory estimation performance when the target motion is unknown and uncertain.

This paper presents a tracking algorithm based on the interacting multiple model (IMM) algorithm and pseudo linear Kalman filter (PKF) in order to improve the performance of traditional methods in maneuvering target tracking. The IMM-PKF algorithm uses the constant velocity (CV) model and coordinated turn (CT) model to form a model set, and the filtering algorithm uses PKF. In target tracking, IMM is used to improve the matching between state prediction and actual motion, therefore improving the accuracy of maneuvering tracking. The performance of extended Kalman filter (EKF), PKF, and IMM-PKF is compared through simulation and experiment. The results show that the IMM-PKF method has the best tracking accuracy among the three methods in helicopter tracking.

In this paper, we investigate the problem of robust state estimation in time-difference-of-arrival (TDOA) localization systems under scenarios involving random measurement loss. Traditional TDOA localization methods typically rely on the extended Kalman filter (EKF), which performs local linearization of the nonlinear system model using a first-order Taylor expansion. However, the EKF relies on a first-order linearization of the system model, which inevitably introduces approximation errors and compromises the accuracy of state estimation. In addition, when the fusion center is subject to Denial-of-Service (DoS) attacks, communication interruptions, or data tampering, measurement data may be lost or corrupted, further compromising the stability and reliability of the state estimation process. To address these challenges, we augment the EKF cost function with a penalty term on the innovation sensitivity to modeling errors, thereby proposing a robust state estimation algorithm with enhanced resilience to disturbances and system uncertainties. Under certain assumptions, it is theoretically established that the proposed robust estimator guarantees bounded estimation error. Numerical simulations indicate that, in three-dimensional TDOA-based localization scenarios, the proposed algorithm achieves improved estimation accuracy compared to the standard EKF.

A Recursive Sparse Learning Method: Application to Jump Markov Linear Systems

In this paper, the joint time-frequency domain channel estimation problem in orthogonal frequency-division multiplexing (OFDM) wireless communication systems is transformed to a set of independent time-domain estimation problems. A robust channel estimation algorithm based on the H/sub /spl infin// filtering approach is proposed to estimate the channel fading in the time domain. The estimation criterion is to minimize the worst possible amplification of the estimation errors in terms of the exogenous input disturbances such as multiplicative and additive noise. The criterion is different from the traditional minimum estimation error variance criterion for the Kalman estimation algorithm, and requires no a priori knowledge of the disturbance statistics. It is shown that the proposed channel estimation algorithm is more robust compared with the Kalman estimation counterpart in terms of model uncertainty, and is more suitable to practical OFDM wireless communication systems.

This article is concerned with the robust distributed state estimation problem for a class of uncertain sensor networks with multiple stochastic communication delays. A sequence of mutually independent random variables obeying the Bernoulli distribution is introduced to account for the randomly occurred communication delays. Both the discrete-time target plant and the sensor model are subject to parameter uncertainties as well as stochastic disturbance. The parameter uncertainties are norm-bounded and enter both the system and the measurement matrices. The external stochastic disturbance is given in the form of a scalar Wiener process. Through available output measurements from not only each individual sensor but also its neighbouring sensors, we aim to design distributed state estimators in order to approximate the state of the target plant. By using the Kronecker product, stochastic analysis is carried out to derive a sufficient criterion ensuring the estimation error systems to be convergent in the mean square sense for all randomly occurred delays, admissible stochastic disturbance and parameter uncertainties. Then, an explicit expression of the individual estimator is given in terms of the solution to a convex optimisation problem that can be easily solved by using the semi-definite programme method. A numerical example is given at the end of this article to demonstrate the usefulness of the developed theoretical results.