This article formulates a multi-rate linear minimum mean squared error (LMMSE) state estimation problem, which includes four rates as follows: the state updating rate in the model, the measurement sampling rate, the estimate updating rate and the estimate output rate. This formulation is unique in two ways. First, the rate ratio between state measurement and state estimate is more general (a rational number), instead of just an integer or its reciprocal as considered in the existing literature. Second, state estimates are produced in blocks, which have never been considered before in the multi-rate estimator design. The multi-rate LMMSE estimation problem is solved by examining several distinctive cases for single-rate state estimation, obtained through the lifting technique. Also, sufficient conditions are given for asymptotic stability of the proposed multi-rate LMMSE estimators. An example in tracking a manoeuvering target is given to illustrate the proposed multi-rate state estimators.

In transportation networks, the majority of moving vehicles are route-based or trajectory-scheduled. Taking advantage of such predictive information generally produces more accurate dynamic models and better surveillance performance. This paper is concerned with the route-based dynamic modeling along with the route-aided tracking. First, the evolution of the positions across the route is formulated as a stationary Markov process from the characteristics of the route-based dynamics, which follows that the second- and third-order models of the straight-line route-based motions are constructed. This novel modeling strategy is in reverse to the conventional ones starting from the acceleration and its resultant dynamic models are easy to implement due to the linearity with respect to the system states. Second, an optimal initialization technique for route-aided tracking is proposed by utilizing the stationary process information sufficiently. Furthermore, an extension to the circular route-based dynamic modeling and a combinational modeling structure are also presented. Finally, in the context of aerial surveillance, numerical simulations are provided to show the effectiveness of the proposed dynamic modeling and to verify the theoretical results given in the paper.

Motivated by tracking a manoeuvring target in electronic counter environments, the authors present the problem of joint estimation and identification of a class of discrete‐time stochastic systems with unknown inputs in both the plant and sensors. Based on the expectation‐maximum criterion, the joint optimisation scheme of state estimation, parameter identification and iteration terminate decision were derived. A numerical example of tracking a manoeuvring target accompanied range gate pull‐off is utilised to verify the proposed scheme.

Goal-guided behavior and destination-directed motion appear in a wide range of human activities and physical processes. Taking advantage of such predictive information can produce better system models and state estimates. This paper focuses on modeling and filtering issues of linear dynamic systems with linear destination constraints. We examine deficiencies of the existing destination constrained (DC) estimation methods. Basically, they resort to post-treatment by imposing destination constraints on updated states only. Viewing destination constraints as an attribute implicit of the state evolution, we propose to incorporate the destination constraints accordingly, particularly on the predictive distribution of the whole state sequence. We construct a congruous DC dynamic model by sufficiently refining the relaxed dynamics with the destination constraint using the state augmentation technique, and analyze its characterization and properties. Next, for the proposed DC model, we develop an optimal DC state estimator and describe its properties. Finally, in the context of aerial surveillance, the superiority of the proposed estimator to existing DC estimators is verified by simulation results, and the effectiveness of the proposed DC dynamic model is demonstrated using real data.

Over-the-horizon radar (OTHR) target tracking in the presence of complicated ionospheric environment mainly faces three challenges, i.e., discrete uncertainty of multipath data association, continuous uncertainty of ionospheric heights, and coupling of target state estimation and ionospheric parameters identification. The existing OTHR target tracking algorithms demanded that the ionospheric heights should be exactly known or statistical properties known. However, the ionospheric heights is inaccurate due to the inherent variability of ionosphere, especially when the deployment of ionosondes is unavailable in the sea area or hostile zone. This paper introduces a joint optimization scheme called distributed expectation-conditional maximization (DECM), which solves the target state estimation, multipath data association, and ionospheric heights identification simultaneously. The proposed DECM algorithm consists of a local estimation level and a global fusion level whereas information is exchanged within these two levels until iteration terminates. This dual-level processing framework transforms the high-dimensional estimation problems into several low-dimensional parallel path-dependent estimation problems, which improves the computational efficiency of expectation maximization under high-dimensional latent variables case. In addition, the closed-loop structure is beneficial to the coupling problem. The simulation indicates the effectiveness of the proposed scheme.

The optimality of Bayesian filtering relies on the completeness of prior models, while deep learning holds a distinct advantage in learning models from offline data. Nevertheless, the current fusion of these two methodologies remains largely ad hoc, lacking a theoretical foundation. This paper presents a novel solution, namely an explainable gated Bayesian recurrent neural network specifically designed to state estimation under model mismatches. Firstly, we transform the non-Markov state-space model into an equivalent first-order Markov model with memory. It is a generalized transformation that overcomes the limitations of the first-order Markov property and enables recursive filtering. Secondly, by deriving a data-assisted joint state-memory-mismatch Bayesian filtering, we design a Bayesian gated framework that includes a memory update gate for capturing the temporal regularities in state evolution, a state prediction gate with the evolution mismatch compensation, and a state update gate with the observation mismatch compensation. The Gaussian approximation implementation of the filtering process within the gated framework is derived, taking into account the computational efficiency. Finally, the corresponding internal neural network structures and end-to-end training methods are designed. The Bayesian filtering theory enhances the interpretability of the proposed gated network, enabling the effective integration of offline data and prior models within functionally explicit gated units. In comprehensive experiments, including simulations and real-world datasets, the proposed gated network demonstrates superior estimation performance compared to benchmark filters and state-of-the-art deep learning filtering methods.