Polynomial filtering of discrete-time stochastic linear systems with multiplicative state noise

Abstract

In this paper, the problem of finding an optimal polynomial state estimate for the class of stochastic linear models with a multiplicative state noise term is studied. For such models, a technique of state augmentation is used, leading to the definition of a general polynomial filter. The theory is developed for time-varying systems with nonstationary and non-Gaussian noises. Moreover, the steady-state polynomial filter for stationary systems is also studied. Numerical simulations show the high performances of the proposed method with respect to the classical linear filtering techniques.

Frisch scheme identification for dynamic diagonal bilinear models

“…With reference to the existing linear case, the assumptions postulated here are in common with the welldocumented EIV framework (So¨derstro¨m 2007). It is to be noted that the whiteness property of the input stated in Assumption A3 is also frequently imposed, especially when considering bilinear systems (Carravetta et al 1997;Favoreel, De Moor, and Overschee 1999;Tsoulkas, Koukoulas, and Kalouptsidis 1999;Verdult and Verhaegen 2000). Indeed, due to Assumption A3 and considering the case of diagonal bilinear systems, it is implied that E [y 0 k ] ¼ 0 (Pearson 1999).…”

“…When the inputs are random signals, as opposed to deterministic sequences, bilinear systems can be found in the literature under different names, such as: bilinear stochastic systems, e.g. Carravetta, Germani, and Raimondi (1997), or linear systems whose dynamic matrices comprise random processes, e.g. De Koning (1984).…”

Multi-sensor information fusion estimators for stochastic uncertain systems with correlated noises

“…its variance matrix (15), the innovation (10), the noise predictor (11) and its gain matrix (12) can follow from [22], so, their derivations are omitted here. The different equations from [22] are mainly derived as follows to read the whole paper conveniently.…”

“…The systems with missing measurements, quantization effects and randomly occurring sensor saturations can be converted into the model with multiplicative noises [10,11]. Nonlinear polynomial filters are presented for systems with multiplicative noises [12]. However, it is not suitable for real-time applications since the algorithm has an expensive computational cost.…”

Direct fusion of Dirac mixture densities using an efficient approximation in joint state space

“…Unfortunately, the resulting Gaussian densities are not capable of representing arbitrary density functions that may appear in estimation problems of arbitrary nonlinear systems. Other density representations include Gaussian mixture densities [7], gridbased approaches [8], simple moments of probability density functions [9], exponential densities [3], fourier series [10], [11], the representation by means of sample sets [12], or Dirac mixture densities [13], which are capable of representing more general densities.…”