Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Fuzzy interacting multiple model H∞ particle filter algorithm based on current statistical model

In this paper, fuzzy theory and interacting multiple model are introduced into H∞ filter-based particle filter to propose a new fuzzy interacting multiple model H∞ particle filter based on current statistical model. Each model uses H∞ particle filter algorithm for filtering, in which the current statistical model can describe the maneuver of target accurately and H∞ filter can deal with the nonlinear system effectively. Aiming at the problem of large amount of probability calculation in interacting multiple model by using combination calculation method, our approach calculates each model matching probability through the fuzzy theory, which can not only reduce the calculation amount, but also improve the state estimation accuracy to some extent. The simulation results show that the proposed algorithm can be more accurate and robust to track maneuvering target

Performance Analysis of Bearings-only Tracking Problems for Maneuvering Target and Heterogeneous Sensor Applications

State estimation, i.e. determining the trajectory, of a maneuvering target from noisy measurements collected by a single or multiple passive sensors (e.g. passive sonar and radar) has wide civil and military applications, for example underwater surveillance, air defence, wireless communications, and self-protection of military vehicles. These passive sensors are listening to target emitted signals without emitting signals themselves which give them concealing properties. Tactical scenarios exists where the own position shall not be revealed, e.g. for tracking submarines with passive sonar or tracking an aerial target by means of electro-optic image sensors like infrared sensors. This estimation process is widely known as bearings-only tracking. On the one hand, a challenge is the high degree of nonlinearity in the estimation process caused by the nonlinear relation of angular measurements to the Cartesian state. On the other hand, passive sensors cannot provide direct target location measurements, so bearings-only tracking suffers from poor target trajectory estimation accuracy due to marginal observability from sensor measurements. In order to achieve observability, that means to be able to estimate the complete target state, multiple passive sensor measurements must be fused. The measurements can be recorded spatially distributed by multiple dislocated sensor platforms or temporally distributed by a single, moving sensor platform. Furthermore, an extended case of bearings-only tracking is given if heterogeneous measurements from targets emitting different types of signals, are involved. With this, observability can also be achieved on a single, not necessarily moving platform. In this work, a performance bound for complex motion models, i.e. piecewisely maneuvering targets with unknown maneuver change times, by means of bearings-only measurements from a single, moving sensor platform is derived and an efficient estimator is implemented and analyzed. Furthermore, an observability analysis is carried out for targets emitting acoustic and electromagnetic signals. Here, the different signal propagation velocities can be exploited to ensure observability on a single, not necessarily moving platform. Based on the theoretical performance and observability analyses a distributed fusion system has been realized by means of heterogeneous sensors, which shall detect an event and localize a threat. This is performed by a microphone array to detect sound waves emitted by the threat as well as a radar detector that detects electromagnetic emissions from the threat. Since multiple platforms are involved to provide increased observability and also redundancy against possible breakdowns, a WiFi mobile ad hoc network is used for communications. In order to keep up the network in a breakdown OLSR (optimized link state routing) routing approach is employed

Situation awareness for UAV operating in terminal areas using bearing-only observations and circuit flight rules

Situation awareness is required for an Unmanned Aerial Vehicle (UAV) when it makes an arrival at an uncontrolled airfield. Since no air traffic control service is available, the UAV needs to detect and track other traffic aircraft by using its onboard sensors. General aviation pilots obtain enough situation awareness to operate in these environments, only using their vision and radio messages heard from other traffic aircraft. To improve the target tracking performance of a UAV, the circuit flight rules and standard radio messages are incorporated to provide extra knowledge about the target behaviour. This is achieved by using the multiple models to describe the target motions in different flight phases and characterising the phase transition in a stochastic manner. Consequently, an interacting multiple model particle filter with state-dependent transition probabilities is developed to perform Bayesian filtering with bearing-only observations from a vision sensor

Simultaneous intent prediction and state estimation using an intent-driven intrinsic coordinate model

The motion of an object (e.g. ship, jet, pedestrian, bird, drone, etc.) is usually governed by premeditated actions as per an underlying intent, for instance reaching a destination. In this paper, we introduce a novel intent-driven dynamical model based on a continuous-time intrinsic coordinate model. By combining this model with particle filtering, a seamless approach for jointly predicting the destination and estimating the state of a highly manoeuvrable object is developed. We examine the proposed inference technique using real data with different measurement models to demonstrate its efficacy. In particular, we show that the introduced approach can be a flexible and competitive alternative, in terms of prediction and estimation performance, to other existing methods for various measurement models including nonlinear ones