The use of fake algebraic riccati equations for co-channel demodulation

Abstract

Abstract-This paper describes a method for nonlinear filtering based on an adaptive observer, which guarantees the local stability of the linearized error system. A fake algebraic Riccati equation is employed in the calculation of the filter gain. The design procedure attempts to produce a stable filter at the expense of optimality. This contrasts with the extended Kalman filter (EKF), which attempts to preserve optimality via its linearization procedure, at the expense of stability. A passivity approach is applied to deduce stability conditions for the filter error system. The performance is compared with an EKF for a co-channel frequency demodulation application.

Adaptive Robust Extended Kalman Filter

“…This conclusion is similar with the traditional perspective that enlarging the covariance matrices may enhance the filter stability (Einicke et al, 2003;Boutayeb & Aubry, 1999). As unknown matrix t β may be rather large in the presence of large unknown inputs, from (16), the condition (19) may be violated and stability of the filter can not be guaranteed.…”

Phase portraits for some symmetric Riccati cubic polynomial differential equations

“…Since then, in the subsequent centuries many contributions appeared regarding these equations. Nowadays it has been shown that Riccati differential equations appear in many applications such as in control, dynamic games, river flow, linear systems with Markovian jumps, invariant embedding, stochastic control theory, econometric models and diffusion problems (see for instance [2,3,4,5,7,8,9,10,11,16,17]). In general, there is no method for solving this differential system because it is a nonhomogeneous differential system of degree two in the variable y and, therefore, a complete analysis of it does not exist.…”

Tracking points within noisy images

“…It follows that the use of a forward and an adjoint extended Kalman predictor can be employed similarly within nonlinear applications such as demodulation and nonlinear equalisation [1], and tracking superimposed signals [2]. Compared to the Rauch-Tung-Striebel smoother [4], the above procedure not require the inversion of…”

“…In [2], fixed solutions for the underlying Riccati equations were assumed which enforce observer stability for superimposed signal problems. This paper contributes the derivation of an optimum fixed interval smoother for the stationary output estimation problem.…”