Optimum Linear Estimation of Stochastic Signals in the Presence of Multiplicative Noise

Rajasekaran, P.; Satyanarayana, N.; Srinath, M

doi:10.1109/taes.1971.310288

Cited by 102 publications

(49 citation statements)

References 5 publications

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“…Optimal linear predictor design is considered by Nahi (1969) and Hadidi and Schwartz (1979) for scalar binary-valued multiplicative noise appearing in the measurement equation. A continuous-valued noise version of similar results was reported by Rajasekaran et al (1971) and Tugnait (1981); the former paper derives the predictor, the latter proves uniform asymptotic stability in the large. Recently, De Koning (1984) assumed a more general model involving matrices of stochastic parameters and derived the optimal one-step predictor.…”

supporting

confidence: 65%

Observer design for stochastic-parameter systems

Yaz

1987

International Journal of Control

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ENGIN YAZtConstant-gain linear observer design is utilized to reconstruct the state vector of stochastic systems with both multiplicative and additive noises. It is shown that if the system model is mean square stable, then it is very easy to design an effective estimation scheme. I. IntroductionDiscrete-time systems with observation equations containing multiplicative as well as additive noise have been important to communication engineers because such modelling corresponds to physical phenomena that may involve reflection of a transmitted signal at an ionospheric layer, amplitude modulation or random sampling of some kind. Optimal linear predictor design is considered by Nahi (1969) and Hadidi and Schwartz (1979) for scalar binary-valued multiplicative noise appearing in the measurement equation. A continuous-valued noise version of similar results was reported by Rajasekaran et al. (1971) and Tugnait (1981); the former paper derives the predictor, the latter proves uniform asymptotic stability in the large. Recently, De Koning (1984) assumed a more general model involving matrices of stochastic parameters and derived the optimal one-step predictor. He showed that mean square stability of the system is sufficient for the existence, uniqueness and stability of the time-invariant estimator.In this work we shall assume the more general stochastic model considered in De Koning (1984), but our approach is not from the optimization point of view; instead, it is shown that any constant-gain linear observer, whether optimal in some sense or not, will result in a stable observation scheme if the gain used does not destabilize the open-loop stable system.

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supporting

confidence: 65%

Observer design for stochastic-parameter systems

Yaz

1987

International Journal of Control

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“…In 1971, Rajasekaran et al derived the optimal linear filter for systems with unknown continuous observation gain [7], but did not consider non-linear strategies. This optimal linear filter was further analyzed by Tugnait [8], who noted that error turns out to be stable only in situations when the system is stable.…”

Section: Introductionmentioning

confidence: 99%

Non-coherence in estimation and control

Ranade

Sahai

2013

2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-Control strategies for systems with information bottlenecks often follow an estimate-then-control paradigm. This paper presents a "non-coherent" system where this strategy cannot work and provides an alternative.The paper considers the estimation and control of a discretetime linear system with continuous random observation gain, i.e. through a non-coherent channel. It is shown that such an unstable system is not mean-squared observable regardless of the density of the random observation gain: the mean-squared estimation error for any estimator must go to infinity. This is surprising in the context of threshold results for rate-limited estimation.In contrast to other results with rate-limited feedback, the paper shows that the system can be closed-loop mean-square stabilized in a certain parameter regime even though its open-loop counterpart is not mean-square observable. Finally, carry-free models (generalized deterministic models) provide an intuitive interpretation for the results.

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“…Combining the image generation model in (12) and the observation model in (14) would yield a complete block dynamic model with uncertain observation [26], [27] due to the presence of the multiplicative noise. This 2-D block state-space dynamic model is (15) to be BIBO stable, it is necessary that all the eigenvalues of matrices A o .…”

Section: Equationsmentioning

confidence: 99%

Two-dimensional adaptive block Kalman filtering of SAR imagery

Azimi-Sadjadi

Bannour

1991

IEEE Trans. Geosci. Remote Sensing

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Abstract-Speckle effects are commonly observed in synthetic aperture radar (SAR) imagery. In airborne SAR systems the effect of this degradation reduces the accuracy of detection substantially. Thus, the elimination of this noise is an important task in SAR imaging systems. In this paper a new method for speckle noise removal is mtroduced using 2-D adaptive block Kalman filtering (ABKF). The image process is represented by an autoregressive (AR) model with nonsymmetric half-plane (NSHP) region of support. New 2-D Kalman filtering equations are derived which take into account not only the effect of speckles as a multiplicative noise but also those of the additive receiver thermal noise and the blur. This method assumes local stationarity within a processing window, whereas the image can be assumed to be globally nonstationary. A recursive identification process using the stochastic Newton approach is also proposed which can be used on-line to estimate the filter parameters based upon the information within each new block of the image. Simulation results on several images are provided to indicate the effectiveness of the proposed method when used to remove the effects of speckle noise as well as that of the additive noise.

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Optimum Linear Estimation of Stochastic Signals in the Presence of Multiplicative Noise

Cited by 102 publications

References 5 publications

Observer design for stochastic-parameter systems

Observer design for stochastic-parameter systems

Non-coherence in estimation and control

Two-dimensional adaptive block Kalman filtering of SAR imagery

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