Kalman Filtered Compressed Sensing

KF-CS: Compressive Sensing on Kalman Filtered Residual

We consider the problem of recursively reconstructing time sequences of sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear incoherent measurements with additive noise. The idea of our proposed solution, KF CS-residual (KF-CS) is to replace compressed sensing (CS) on the observation by CS on the Kalman filtered (KF) observation residual computed using the previous estimate of the support. KF-CS error stability over time is studied. Simulation comparisons with CS and LS-CS are shown.

A Bayesian Compressed Sensing Kalman Filter for Direction of Arrival Estimation

In this paper, we look to address the problem of estimating the dynamic direction of arrival (DOA) of a narrowband signal impinging on a sensor array from the far field. The initial estimate is made using a Bayesian compressive sensing (BCS) framework and then tracked using a Bayesian compressed sensing Kalman filter (BCSKF). The BCS framework splits the angular region into N potential DOAs and enforces a belief that only a few of the DOAs will have a non-zero valued signal present. A BCSKF can then be used to track the change in the DOA using the same framework. There can be an issue when the…

Analyzing Least Squares and Kalman Filtered Compressed Sensing

In recent work, we studied the problem of causally reconstructing time sequences of spatially sparse signals, with unknown and slow time-varying sparsity patterns, from a limited number of linear "incoherent" measurements. We proposed a solution called Kalman Filtered Compressed Sensing (KF-CS). The key idea is to run a reduced order KF only for the current signal's estimated nonzero coefficients' set, while performing CS on the Kalman filtering error to estimate new additions, if any, to the set. KF may be replaced by Least Squares (LS) estimation and we call the resulting algorithm LS-CS. In…

Stochastic Parameterization using Compressed Sensing: Application to the Lorenz-96 Atmospheric Model

Growing set of optimization and regression techniques, based upon sparse representations of signals, to build models from data sets has received widespread attention recently with the advent of compressed sensing. This paper deals with the parameterization of the Lorenz-96 model with two time-scales that mimics mid-latitude atmospheric dynamics with microscopic convective processes. Compressed sensing is used to build models (vector fields) to emulate the behavior of the fine-scale process, so that explicit simulations become an online benchmark for parameterization. We apply compressed sensin…

基于卡尔曼滤波的时钟异步通信系统中的感知

Kalman Filter-based Sensing in Communication Systems with Clock Asynchronism

针对时钟异步导致上行感知误差大的问题，提出基于卡尔曼滤波的JCAS方案，无需UE先验位置，通过空间滤波与KF增强抑制TO，显著降低定位误差，较基准低约20 dB。