Three-dimensional location estimation using multiplicative processing of sensor measurements

A non-transitory computer storage medium encoded with computer program instructions that, when executed by one or more computers, cause the one or more computers to perform operations comprising:

• receiving, from an analog to digital converter, a series of measurements representing frequency samples and spatial samples corresponding to signals obtained from a sensor array, the signals associated with one or more objects in motion that are detected by the sensor array;
• generating a plurality of factors by projecting the series of measurements over a plurality of steering vectors corresponding to a range of values of a characteristic associated with the one or more objects, wherein each factor of the plurality of factors corresponds to a measurement of the series of measurements and is weighted by a complex weight corresponding to a factorized polynomial;
• combining the plurality of factors to obtain a plurality of values;
• and
• identifying the characteristic associated with the one or more objects detected by the sensor array based on the plurality of values.

A system comprising:

• one or more computers and one or more storage devices storing instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform operations comprising:
• receiving, from an analog to digital converter, a series of measurements representing frequency samples and spatial samples corresponding to signals obtained from a sensor array, the signals associated with one or more objects in motion that are detected by the sensor array;
• generating a plurality of factors by projecting the series of measurements over a plurality of steering vectors corresponding to a range of values of a characteristic associated with the one or more objects, wherein each factor of the plurality of factors corresponds to a measurement of the series of measurements and is weighted by a complex weight corresponding to based on a factorized polynomial;
• combining the plurality of factors to obtain a plurality of values;
• and
• identifying the characteristic associated with the one or more objects detected by the sensor array based on the plurality of values.