Continuous-discrete Filtering Research Articles

Efficient extended cubature Kalman filtering for nonlinear target tracking

For states estimation problem of continuous–discrete systems, the numerical approximation methods with high order of accuracy are commonly used to build the continuous–discrete filtering algorithms. However, there is a common contradiction between the computational efficiency and the accuracy. In order to improve the efficiency of state estimation in the continuous–discrete filtering method, continuous–discrete extended cubature Kalman filtering based on Adams–Bashforth–Moulton (ABM) numerical approximation is proposed. ABM is the linear multi-step numerical method, which can achieve the fourth-order accuracy for solving the differential state equation, and its ‘predictor–corrector’ mathematic structure is relatively simple. The performances of ABM method are theoretically analysed; the mixed-type filtering method for continuous–discrete nonlinear states estimation is proposed to integrate the best features of extended Kalman filtering and cubature Kalman filtering. More precisely, the time updates are deduced by extended Kalman filtering whereas the measurement updates are conducted by the third-degree spherical-radial cubature rule. The superior performances of proposed method are illustrated in the simulations under the conditions of different step-sizes and sampling periods.

Third-Order Continuous-Discrete Filtering for a Nonlinear Dynamical System

Approximate higher-order filters are more attractive and popular in control and signal processing literature in contrast to the exact filter, since the analytical and numerical solutions of the nonlinear exact filter are not possible. The filtering model of this paper involves stochastic differential equation (SDE) formalism in combination with a nonlinear discrete observation equation. The theory of this paper is developed by adopting a unified systematic approach involving celebrated results of stochastic calculus. The Kolmogorov–Fokker–Planck equation in combination with the Kolmogorov backward equation plays the pivotal role to construct the theory of this paper “between the observations.” The conditional characteristic function is exploited to develop “filtering” at the observation instant. Subsequently, the efficacy of the filtering method of this paper is examined on the basis of its comparison with extended Kalman filtering and true state trajectories. This paper will be of interest to applied mathematicians and research communities in systems and control looking for stochastic filtering methods in theoretical studies as well as their application to real physical systems.

Universal Nonlinear Filtering using Feynman Path Integrals I: The Continuous-Discrete Model with Additive Noise

The continuous-discrete filtering problem requires the solution of a partial differential equation known as the Fokker-Planck-Kolmogorov forward equation (FPKfe). The path integral formula for the fundamental solution of the FPKfe is derived and verified for the general additive noise case (i.e., explicitly time-dependent state model and with state-independent rectangular diffusion vielbein). The solution is universal in the sense that the initial distribution may be arbitrary. The practical utility is demonstrated via some examples.

Track-before-Detect Using Swerling 0, 1, and 3 Target Models for Small Manoeuvring Maritime Targets

Real-radar data containing a small manoeuvring boat in sea clutter is processed using a finite difference (FD) implementation of continuous-discrete filtering with a four-dimensional constant velocity model. Measurement data is modelled assuming a Rayleigh sea clutter model with embedded Swerling 0, 1, or 3 target signal models. The results are examined to obtain a qualitative understanding of the effects of using the different target models. The Swerling 0 model is observed to exhibit a heightened sensitivity to changes in measured signal strength and provides enhanced detection of the maritime target examined at the cost of more peaked or multimodal posterior density in comparison with Swerling 1 and 3 targets.

Adaptive nonlinear continuous-discrete filtering

The mean square optimal adaptive filtering problem for wide class of the nonlinear continuous-discrete stochastic systems is solved. The state vector of a system is determined by the Ito stochastic differential equation and the observation described by stochastic difference equations depend on unknown vector parameters. Equations for conditional densities, optimal estimates of state vector and covariance matrices are given. In particular case of linear continuous-discrete systems with unknown parameters the optimal adaptive filtering equations are derived. The examples are considered.

Continuous-discrete filtering for presmoothed observations

Data filtering with presmoothed measurements is a useful technique for data compression in high data rate, noisy measurement systems. A sequential filtering algorithm is derived for processing integrated measurements, and the algorithm is applied to data filtering with discrete presmoothed measurements. Prefilter trade studies with a two dimension system show that the algorithm may provide a large reduction in filter computations with only a small increase in rms error.

A square-root data array solution of the continuous-discrete filtering problem

The Dyer-McReynolds [1] discrete square-root filtering algorithm is extended to accommodate continuous dynamics. Differential equations are given to represent the time evolution of the filter data array. These equations are nonlinear, but it is shown that the nonlinearities act to enhance the stability of the solution.