Analyzing Non Stationary Processes in Radiometers

The lack of well-developed techniques for modeling changing statistical moments in our observations has stymied the application of stochastic process theory for many scientific and engineering applications. Non linear effects of the observation methodology is one of the most perplexing aspects to modeling non stationary processes. This perplexing problem was encountered when modeling the effect of non stationary receiver fluctuations on the performance of radiometer calibration architectures. Existing modeling approaches were found not applicable; particularly problematic is modeling processes across scales over which they begin to exhibit non stationary behavior within the time interval of the calibration algorithm. Alternatively, the radiometer output is modeled as samples from a sequence random variables; the random variables are treated using a conditional probability distribution function conditioned on the use of the variable in the calibration algorithm. This approach of treating a process as a sequence of random variables with non stationary stochastic moments produce sensible predictions of temporal effects of calibration algorithms. To test these model predictions, an experiment using the Millimeter wave Imaging Radiometer (MIR) was conducted. The MIR with its two black body calibration references was configured in a laboratory setting to observe a third ultra-stable reference (CryoTarget). The MIR was programmed to sequentially sample each of the three references in approximately a 1 second cycle. Data were collected over a six-hour interval. The sequence of reference measurements form an ensemble sample set comprised of a series of three reference measurements. Two references are required to estimate the receiver response. A third reference is used to estimate the uncertainty in the estimate. Typically, calibration algorithms are designed to suppress the non stationary effects of receiver fluctuations. By treating the data sequence as an ensemble collection, it is possible to apply temporal algorithms which exacerbate the non stationary effects. By varying the algorithm, information about the properties of the non stationary receiver fluctuations is obtained. Comparisons of analytical calculations and statistical analysis of data demonstrate impressive agreement

Device and Method for Gathering Ensemble Data Sets

An ensemble detector uses calibrated noise references to produce ensemble sets of data from which properties of non-stationary processes may be extracted. The ensemble detector comprising: a receiver; a switching device coupled to the receiver, the switching device configured to selectively connect each of a plurality of reference noise signals to the receiver; and a gain modulation circuit coupled to the receiver and configured to vary a gain of the receiver based on a forcing signal; whereby the switching device selectively connects each of the plurality of reference noise signals to the receiver to produce an output signal derived from the plurality of reference noise signals and the forcing signal

A Preliminary Study of Three-Point Onboard External Calibration for Tracking Radiometric Stability and Accuracy

Absolute calibration of radiometers is usually implemented onboard using one hot and one cold external calibration targets. However, two-point calibration methods are unable to differentiate calibration drifts and associated errors from fluctuations in receiver gain and offset. Furthermore, they are inadequate to characterize temporal calibration stability of radiometers. In this paper, a preliminary study with linear radiometer systems has been presented to show that onboard external three-point calibration offers the means to quantify calibration drifts in the radiometer systems, and characterize associated errors as well as temporal stability in Earth and space measurements. Radiometers with three external calibration reference targets operating two data processing paths: i.e., (1) measurement path and (2) calibration validation path have been introduced. In the calibration validation data processing path, measurements of one known calibration target is calibrated using the other two calibration references, and temporal calibration stability and possible calibration temperature drifts are analyzed. In the measurement data processing path, the impact of the calibration drifts on Earth and space measurements is quantified and bounded by an upper limit. This two-path analysis is performed through calibration error analysis (CEA) diagrams introduced in this paper

Tracking Radiometer Calibration Stability Using Three-Point Onboard Calibration

Absolute calibration of radiometers is implemented onboard using one hot and one cold external calibration targets. However, two-point calibration methods are unable to differentiate calibration drifts and associated errors from fluctuations in receiver gain and offset. This paper investigates the use of onboard three-point calibration algorithm for microwave radiometers to track calibration drifts and characterize associated errors in Earth and Space measurements of the radiometer

CubeSat Measures World's First Ice Cloud Map to Support Climate Research

Virginia Diodes, Inc. received NASA SBIR Awards to fund research and development for a lesser developed region of the electromagnetic spectrumterahertz waves. Their work led to funding from NASA ESTO, and the resulting CubeSat (named IceCube) captured the worlds first ice cloud map, which will contribute to our understanding of Earths climat

Tri-Frequency Synthetic Aperture Radar for the Measurements of Snow Water Equivalent

A new airborne synthetic aperture radar (SAR) system was recently developed for the estimation of snow water equivalent (SWE). The radar is part of the SWESARR (Snow Water Equivalent Synthetic Aperture Radar and Radiometer) instrument, an active passive microwave system specifically designed for the accurate estimation of SWE. The dual polarization (VV, VH) radar operates at three frequency bands (9.65 GHz, 13.6 GHz, and 17.25 GHz), with bandwidths of up to 200 MHz. The radar flew its first flight campaign in November 2019, along with SWESARRs - already operational radiometer. The radar collected comprehensive data sets over various terrains that show a successful system performance. The inst slated to participate in future SnowEx campaigns

Receiver Gain Modulation Circuit

A receiver gain modulation circuit (RGMC) was developed that modulates the power gain of the output of a radiometer receiver with a test signal. As the radiometer receiver switches between calibration noise references, the test signal is mixed with the calibrated noise and thus produces an ensemble set of measurements from which ensemble statistical analysis can be used to extract statistical information about the test signal. The RGMC is an enabling technology of the ensemble detector. As a key component for achieving ensemble detection and analysis, the RGMC has broad aeronautical and space applications. The RGMC can be used to test and develop new calibration algorithms, for example, to detect gain anomalies, and/or correct for slow drifts that affect climate-quality measurements over an accelerated time scale. A generalized approach to analyzing radiometer system designs yields a mathematical treatment of noise reference measurements in calibration algorithms. By treating the measurements from the different noise references as ensemble samples of the receiver state, i.e. receiver gain, a quantitative description of the non-stationary properties of the underlying receiver fluctuations can be derived. Excellent agreement has been obtained between model calculations and radiometric measurements. The mathematical formulation is equivalent to modulating the gain of a stable receiver with an externally generated signal and is the basis for ensemble detection and analysis (EDA). The concept of generating ensemble data sets using an ensemble detector is similar to the ensemble data sets generated as part of ensemble empirical mode decomposition (EEMD) with exception of a key distinguishing factor. EEMD adds noise to the signal under study whereas EDA mixes the signal with calibrated noise. It is mixing with calibrated noise that permits the measurement of temporal-functional variability of uncertainty in the underlying process. The RGMC permits the evaluation of EDA by modulating the receiver gain using an external signal. Without the RGMC, samples of calibrated references from radiometers form an ensemble data set of the natural occurring fluctuations within a receiver. By driving the gain of an otherwise stable receiver with an external signal, the conceptual framework and generalization of the mathematics of EDA can be tested. A series of measurements was conducted to evaluate and characterize the performance of the RGMC. Test signals stepped the RGMC across its dynamic range of performance using a radiometer that sampled four noise references; analysis indicates that the RGMC successfully modulated the receiver gain with an external signal. Calibration algorithms applied to four noise references demonstrate the RGMC produced ensemble data sets of the external signal

Tri-Frequency Synthetic Aperture Radar for the Measurements of Snow Water Equivalent

SWESARR (Snow Water Equivalent Synthetic Aperture Radar and Radiometer) is an airborne instrument developed at the NASA Goddard Space Flight Center for the retrieval of Snow Water Equivalent. SWESARR was specifically designed to measure co-located active and passive signals using a high resolution and multi-frequency Synthetic Aperture Radar (SAR) and a multifrequency radiometer. SWESARRs Synthetic Aperture Radar (SAR) system is made up of three independent radar units that operate in the X, Ku-Low, and Ku-High bands with bandwidths up to 200 MHz, and acquires data in two polarizations (dual-polarization radar). The difference in sensitivity of the backscatter signals to snow microstructure, in conjunctions with radiometer measurements, permits an accurate estimation of the snow water equivalent (SWE)

Calibrated Noise Measurements with Induced Receiver Gain Fluctuations

The lack of well-developed techniques for modeling changing statistical moments in our observations has stymied the application of stochastic process theory in science and engineering. These limitations were encountered when modeling the performance of radiometer calibration architectures and algorithms in the presence of non stationary receiver fluctuations. Analyses of measured signals have traditionally been limited to a single measurement series. Whereas in a radiometer that samples a set of noise references, the data collection can be treated as an ensemble set of measurements of the receiver state. Noise Assisted Data Analysis is a growing field of study with significant potential for aiding the understanding and modeling of non stationary processes. Typically, NADA entails adding noise to a signal to produce an ensemble set on which statistical analysis is performed. Alternatively as in radiometric measurements, mixing a signal with calibrated noise provides, through the calibration process, the means to detect deviations from the stationary assumption and thereby a measurement tool to characterize the signal's non stationary properties. Data sets comprised of calibrated noise measurements have been limited to those collected with naturally occurring fluctuations in the radiometer receiver. To examine the application of NADA using calibrated noise, a Receiver Gain Modulation Circuit (RGMC) was designed and built to modulate the gain of a radiometer receiver using an external signal. In 2010, an RGMC was installed and operated at the National Institute of Standards and Techniques (NIST) using their Noise Figure Radiometer (NFRad) and national standard noise references. The data collected is the first known set of calibrated noise measurements from a receiver with an externally modulated gain. As an initial step, sinusoidal and step-function signals were used to modulate the receiver gain, to evaluate the circuit characteristics and to study the performance of a variety of calibration algorithms. The receiver noise temperature and time-bandwidth product of the NFRad are calculated from the data. Statistical analysis using temporal-dependent calibration algorithms reveals that the natural occurring fluctuations in the receiver are stationary over long intervals (100s of seconds); however the receiver exhibits local non stationarity over the interval over which one set of reference measurements are collected. A variety of calibration algorithms have been applied to the data to assess algorithms' performance with the gain fluctuation signals. This presentation will describe the RGMC, experiment design and a comparative analysis of calibration algorithms

WISM - A Wideband Instrument for Snow Measurement: Past Accomplishments, Current Status, and Path Forward

Presented are the prior accomplishments, current status and path forward for GSFC's Wideband Instrument for Snow Measurement (WISM). This work is a high level overview of the project, presented via Webinar to the IEEE young professionals