DocumentCode :
2255614
Title :
Cauchy estimation for linear scalar systems
Author :
Idan, Moshe ; Speyer, Jason L.
Author_Institution :
Mech. & Aerosp. Eng., Univ. of California, Los Angeles, CA, USA
fYear :
2008
fDate :
9-11 Dec. 2008
Firstpage :
658
Lastpage :
665
Abstract :
An estimation paradigm is presented for scalar discrete linear systems entailing additive process and measurement noises that have Cauchy probability density functions (pdf). For systems with Gaussian noises, the Kalman filter has been the main estimation paradigm. However, many practical system uncertainties that have impulsive character, such as radar glint, are better described by stable non-Gaussian densities, for example, the Cauchy pdf. Although the Cauchy pdf does not have a defined mean and does have an infinite second moment, the conditional density of a Cauchy random variable, given its linear measurements with an additive Cauchy noise, has a conditional mean and a finite conditional variance, both being functions of the measurement. For a single measurement, simple expressions are obtained for the conditional mean and variance, by deriving closed form expressions for the infinite integrals associated with the minimum variance estimation problem. To alleviate the complexity of the multi-stage estimator, the conditional pdf is represented in a special factored form. A recursion scheme is then developed based on this factored form and closed form integrations, allowing for the propagation of the conditional mean and variance over an arbitrary number of time stages. In simulations, the performance of a newly developed scalar discrete-time Cauchy estimator is significantly superior to a Kalman filter in the presence of Cauchy noise, whereas the Cauchy estimator deteriorates only slightly compared to the Kalman filter in the presence of Gaussian noise. Remarkably, this new recursive Cauchy conditional mean estimator has parameters that are generated by linear difference equations with stochastic coefficients, providing computational efficiency.
Keywords :
Gaussian noise; Kalman filters; discrete systems; estimation theory; linear differential equations; linear systems; stochastic systems; Cauchy estimation; Cauchy probability density functions; Gaussian noises; Kalman filter; linear difference equations; linear scalar systems; multistage estimator; scalar discrete linear systems; stochastic coefficients; Additive noise; Density measurement; Gaussian noise; Linear systems; Noise measurement; Parameter estimation; Probability density function; Radar; Random variables; Recursive estimation;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on
Conference_Location :
Cancun
ISSN :
0191-2216
Print_ISBN :
978-1-4244-3123-6
Electronic_ISBN :
0191-2216
Type :
conf
DOI :
10.1109/CDC.2008.4739421
Filename :
4739421
Link To Document :
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