Clipped Input RLS Applied to Vehicle Tracking
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Clipped Input RLS Applied to Vehicle Tracking Hadi Sadoghi Yazdi Department of Electrical Engineering, Tarbiat Modarres University, P.O. Box 14115-143, Tehran, Iran Email: sadoghi [email protected]
Mojtaba Lotfizad Department of Electrical Engineering, Tarbiat Modarres University, P.O. Box 14115-143, Tehran, Iran Email: [email protected]
Ehsanollah Kabir Department of Electrical Engineering, Tarbiat Modarres University, P.O. Box 14115-143, Tehran, Iran Email: [email protected]
Mahmood Fathy Faculty of Computer Engineering, Iran University of Science and Technology, Tehran 16844, Iran Email: [email protected] Received 24 July 2004; Revised 27 November 2004; Recommended for Publication by John Homer A new variation to the RLS algorithm is presented. In the clipped RLS algorithm (CRLS), proposed in updating the filter weights and computation of the inverse correlation matrix, the input signal is quantized into three levels. The convergence of the CRLS algorithm to the optimum Wiener weights is proved. The computational complexity and signal estimation error is lower than that of the RLS algorithm. The CRLS algorithm is used in the estimation of a noisy chirp signal and in vehicles tracking. Simulation results in chirp signal detection shows that this algorithm yields considerable error reduction and less computation time in comparison to the conventional RLS algorithm. In the presence of strong noise, also using the proposed algorithm in tracking of 59 vehicles shows an average of 3.06% reduction in prediction error variance relative to conventional RLS algorithm. Keywords and phrases: RLS, clipped input data, noise cancellation, vehicle tracking.
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INTRODUCTION
The subject of adaptive signal processing has been one of the fastest growing fields of research in recent years. The recursive least square (RLS) and the least mean square (LMS) are two adaptive filtering algorithms [1]. The adaptive RLS and LMS are kinds of data-driven algorithms. Fast convergence of the RLS has given rise to the development of the algorithms based on it [2, 3, 4, 5]. The work on reducing the amount of computations and numerical instability of the RLS algorithm is continuing. For example, in [6], the computational complexity of the inverse correlation matrix is reduced by presentation of a pseudoinversion technique. The numerical instability of the RLS algorithm is an issue that has been studied in [7]. Also reduction of computational complexity of the RLS is done by joining LMS to RLS because LMS has better performance in terms of tracking property in noisy environment and is simply realized [8, 9].
The current work is based on borrowing the idea of simplifications performed on the LMS algorithm in order to reduce the RLS algorithm computations while increasing its performance. Reduction of the complexity of the LMS has received attention in the area of adaptive filter [10, 11, 12, 13]. The sign and clipped data algorithms are the most important ones [10, 12, 13, 14, 15]. The works reported in the above references have been done fo
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