IPI
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.
IPI
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
IPI
Constructing continuous stationary covariances as limits of the second-order stochastic difference equations
Lassi Roininen Petteri Piiroinen Markku Lehtinen
Inverse Problems & Imaging 2013, 7(2): 611-647 doi: 10.3934/ipi.2013.7.611
In Bayesian statistical inverse problems the a priori probability distributions are often given as stochastic difference equations. We derive a certain class of stochastic partial difference equations by starting from second-order stochastic partial differential equations in one and two dimensions. We discuss discretisation schemes on uniform lattices of these stationary continuous-time stochastic processes and convergence of the discrete-time processes to the continuous-time processes. A special emphasis is given to an analytical calculation of the covariance kernels of the processes. We find a representation for the covariance kernels in a simple parametric form with controllable parameters: correlation length and variance. In the discrete-time processes the discretisation step is also given as a parameter. Therefore, the discrete-time covariances can be considered as discretisation-invariant. In the two-dimensional cases we find rotation-invariant and anisotropic representations of the difference equations and the corresponding continuous-time covariance kernels.
keywords: covariance convergence Stochastic difference equation statistical inversion.

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