Perfect and almost perfect pulse compression codes for range spread radar targets
Markku Lehtinen Baylie Damtie Petteri Piiroinen Mikko Orispää
Inverse Problems & Imaging 2009, 3(3): 465-486 doi: 10.3934/ipi.2009.3.465
It is well known that a matched filter gives the maximum possible output signal-to-noise ratio (SNR) when the input is a scattering signal from a point like radar target in the presence of white noise. However, a matched filter produces unwanted sidelobes that can mask vital information. Several researchers have presented various methods of dealing with this problem. They have employed different kinds of less optimal filters in terms of the output SNR from a point-like target than that of the matched filter. In this paper we present a method of designing codes, called perfect and almost perfect pulse compression codes, that do not create unwanted sidelobes when they are convolved with the corresponding matched filter. We present a method of deriving these types of codes from any binary phase radar codes that do not contain zeros in the frequency domain. Also, we introduce a heuristic algorithm that can be used to design almost perfect codes, which are more suitable for practical implementation in a radar system. The method is demonstrated by deriving some perfect and almost perfect pulse compression codes from some binary codes. A rigorous method of comparing the performance of almost perfect codes (truncated) with that of perfect codes is presented.
keywords: comparison of experiments Radar waveform Ambiguity function.
Fortran linear inverse problem solver
Mikko Orispää Markku Lehtinen
Inverse Problems & Imaging 2010, 4(3): 485-503 doi: 10.3934/ipi.2010.4.485
FLIPS (Fortran Linear Inverse Problem Solver) is a Fortran 95 module for solving large-scale statistical linear systems. Instead of inverting large matrices, FLIPS transforms the system into a simpler one by using Givens rotations. This simplified system is then solved by FLIPS quickly and efficiently. FLIPS is also capable of calculating the full a posteriori covariance matrix. It is also possible to add or delete measurements and unknowns making it useful in time-dependent problems of the Kalman-filter type. The FLIPS implementation is explained and the advantages of using FLIPS, especially for overdetermined systems, are shown. Plans for future developments are discussed.
keywords: linear solver Statistical inverse problems Givens rotations. matrix inverse
Correlation priors
Lassi Roininen Markku S. Lehtinen Sari Lasanen Mikko Orispää Markku Markkanen
Inverse Problems & Imaging 2011, 5(1): 167-184 doi: 10.3934/ipi.2011.5.167
We propose a new class of Gaussian priors, correlation priors. In contrast to some well-known smoothness priors, they have stationary covariances. The correlation priors are given in a parametric form with two parameters: correlation power and correlation length. The first parameter is connected with our prior information on the variance of the unknown. The second parameter is our prior belief on how fast the correlation of the unknown approaches zero. Roughly speaking, the correlation length is the distance beyond which two points of the unknown may be considered independent.
   The prior distribution is constructed to be essentially independent of the discretization so that the a posteriori distribution will be essentially independent of the discretization grid. The covariance of a discrete correlation prior may be formed by combining the Fisher information of a discrete white noise and different-order difference priors. This is interpreted as a combination of virtual measurements of the unknown. Closed-form expressions for the continuous limits are calculated. Also, boundary correction terms for correlation priors on finite intervals are given.
   A numerical example, deconvolution with a Gaussian kernel and a correlation prior, is computed.
keywords: a priori distributions discretization-invariance. Statistical inversion

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