Autonomous State Space Models for Recursive Signal Estimation Beyond Least Squares
| Autor: | Nour Zalmai, Hans-Andrea Loeliger, Reto A. Wildhaber |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematical optimization
Polynomial State-space representation Mean squared error 020208 electrical & electronic engineering 020206 networking & telecommunications 02 engineering and technology Function (mathematics) Kalman filter Least squares Window function 0202 electrical engineering electronic engineering information engineering State space Algorithm Mathematics |
| Zdroj: | EUSIPCO |
| DOI: | 10.5281/zenodo.1159258 |
| Popis: | The paper addresses the problem of fitting, at any given time, a parameterized signal generated by an autonomous linear state space model (LSSM) to discrete-time observations. When the cost function is the squared error, the fitting can be accomplished based on efficient recursions. In this paper, the squared error cost is generalized to more advanced cost functions while preserving recursive computations: first, the standard sample-wise squared error is augmented with a sample-dependent polynomial error; second, the sample-wise errors are localized by a window function that is itself described by an autonomous LSSM. It is further demonstrated how such a signal estimation can be extended to handle unknown additive and/or multiplicative interference. All these results rely on two facts: first, the correlation function between a given discrete-time signal and a LSSM signal can be computed by efficient recursions; second, the set of LSSM signals is a ring. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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