System and method for linear prediction
View Patent ↗In a digital signal processor (DSP), input data is configured as a data matrix comprising data samples collected from an input signal. A weight vector is applied to the matrix, where the weight vector comprises three parts including (a) a rank reduction transformation produced by decomposition of data samples in a multistage Wiener filter having a plurality of stages, each stage comprising projection onto two subspaces. Each subsequent stage comprises projecting data transformed by the preceding second subspace onto each of a first subspace comprising a normalized cross-correlation vector at the previous stage and a second subspace comprising the null space of the normalized cross-correlation vector of the current stage, to form a reduced rank data matrix. Part (b) of the weight vector comprises minimizing mean squared error in the reduced rank data space. The output is a linear estimate of input data.
1. A method for training a linear prediction filter for prediction of information, comprising:
providing reference data;
collecting observed data containing the reference data;
identifying a reduced order Krylov subspace between the observed data and the reference data; and
maximizing mutual data between the observed data and the reference data in the subspace to define at least one autoregressive weight for use in the linear prediction filer; and
wherein the information comprises time of arrival information.
2. A method for linear prediction of information determinable from at least one input signal comprising plurality of data points, the method comprising:
providing plurality of reference data points;
training a filter by collecting p observed data points from the at least one input signal corresponding to p reference data points, wherein p reference data points comprise a portion of the plurality of reference data points, wherein the training further comprises:
processing the p observed data points through the filter to identify a reduced order Krylov subspace between the observed data points and the reference data points; and
defining a weight for minimizing the mean squared error between a predicted p+1 observed data point and a p+1 reference data point; and applying the weight to filter the at least one input signal; and
wherein the information comprises time of arrival information.
3. A method for linear prediction of information determinable from at least one received signal containing a plurality of data points received at a detector, the method comprising:
defining a reference data matrix comprising data points collected from the at least one reference signal;
defining a received data matrix comprising data points collected from the at least one received signal;
calculating a weight vector by:
(a) performing a rank reduction transformation to create a reduced rank data matrix produced by decomposition of the received data matrix in a multi-stage Wiener filter; and
(b) minimizing the mean squared error in the reduced rank data matrix; and applying the weight vector to the received data matrix; and
wherein the information comprises time of arrival information.
4. A system for linear prediction of information determinable from at least one received signal comprising a plurality of data points, the system comprising:
a linear prediction filter for processing the plurality of data points, the linear prediction filter comprising a multi-stage Wiener filter for projecting a full rank data matrix formed from the plurality of data points into a subspace having a reduced rank to form a reduced rank data matrix and minimizing the mean squared prediction error in the reduced rank matrix, and for applying a weight vector to the at least one received signal to generate a predicted signal, and
wherein the information comprises time of arrival information.
5. A computer program product for training a linear prediction filter for prediction of information, the computer program product comprising:
at least one computer readable medium;
a providing module resident on the medium and operable to provide reference data;
a collection module resident on the medium and operable to collect observed data containing the reference data;
an identification module resident on the medium and operable to identify a reduced order Krylov subspace between observed data containing the information and the reference data characteristic of the information; and
a maximization module resident on the medium and operable to maximize mutual data between the observed data and the reference data in the reduced order data space; and
wherein the information comprises time of arrival information.
6. A computer program product for linear prediction of information determinable from at least one input signal comprising a plurality of data points, the computer program product comprising:
at least one computer readable medium;
a providing module resident on the medium and operable to provide a plurality of reference data points;
a training module resident on the medium and operable to train a filter by collecting p observed data points in a snapshot from the at least one input signal corresponding to p reference data points, wherein p reference data points comprise a portion of the plurality of reference data points, wherein the training module further comprises:
a processing module resident on the medium and operable to process the p observed data points through the filter to identify a reduced order Krylov subspace between the observed data points and the reference data points; and
a defining module resident on the medium and operable to define a weight for minimizing the mean squared error between a predicted p+1 observed data point and a p+1 reference data point; and
an applying module resident on the medium and operable to apply the weight to filter the at least one input signal; and
wherein the information comprises time of arrival information.
7. A computer program product for linear prediction of information determinable from at least one signal comprising a plurality of data points, the computer program product comprising:
at least one computer readable medium:
a processing module resident on the medium and operable to process the plurality of data points by using a multi-stage Wiener filter for projecting a full rank data matrix formed from the plurality of data points into a subspace having a reduced rank to form a reduced rank data matrix;
the processing module resident on the medium and operable to minimize the mean squared prediction error in the reduced rank matrix;
the processing module resident on the medium and operable to apply a weight vector to the at least one signal to generate a predicted signal; and
wherein the information comprises time of arrival information.