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A Kalman filter has many properties that make it an attractive choice as a technique for combining Earth orientation measurements. It allows the full accuracy of the measurements to be used, whether the measurements are degenerate or are of full rank, are irregularly or regularly spaced in time, or are corrupted by systematic or other errors that can be described by stochastic models.
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The Kalman Earth Orientation Filter (KEOF) is used at JPL to combine independent observations of the Earth's rotation parameters, producing smoothed, interpolated estimates of polar motion (PM) and UT1-TAI, as well as estimates of their excitation functions such as the length-of-day (lod). Prior to their combination, adjustments to the data sets are made in order to place them within a common reference frame. Recently, a number of lod data sets have been determined at JPL by combining the observations summarized in Table 1. The resulting lod data sets, summarized in Table 2, span different time intervals depending upon the particular subset of observations being combined, with the longest series, spanning 1630-1990, being obtained by combining all of the observations. The determination of these lod data sets and their comparison with series of climate indicators such as the Southern Oscillation Index will be discussed.
Universal time (UT1) measurements obtained using VLBI, lunar laser ranging (LLR), and BIH optical astronomy are compared. The JPL Kalman filter for the earth rotation and the polar motion is utilized to smooth one data set or combine data sets for intercomparison. The differences between raw UT1 data and independently smoothed data are employed to assess the accuracy of the measured series and the sufficiency of the error budget. Systematic errors in periodic signatures and length of day estimates are analyzed. The data reveal that the techniques of LLR and VLBI agree to within their formal errors. It is determined that the residual error for the LLR is too large and the residual error estimated for the BIH data is too small.
The ability to predict short-term variations in the Earth's rotation has gained importance in recent years owing to more precise spacecraft tracking requirements. Universal time (UT1), that component of the Earth's orientation corresponding to the rotation angle, can be measured by number of high-precision space geodetic techniques. A Kalman filter developed at the Jet Propulsion Laboratory (JPL) optimally combines these different data sets and generates a smoothed times series and a set of predictions for UT1, as well as for additional Earth orientation components. These UT1 predictions utilize an empirically derived random walk stochastic model for the length of the day (LOD) and require frequent and up-to-date measurements of either UT1 or LOD to keep errors from quickly accumulating. Recent studies have shown that LOD variations are correlated with changes in the Earth's axial atmospheric angular momentum (AAM) over timescales of several years down to as little as 8 days. AAM estimates and forecasts out to 10 days are routinely available from meteorological analysis centers; these data can supplement geodetic measurements to improve the short-term prediction of LOD and have therefore been incorporated as independent data types in the JPL Kalman filter. We find that AAM and, to a lesser extent, AAM forecast data are extremely helpful in generating accurate near-real-time estimates of UT1 and LOD and in improving short-term predictions of these quantities out to about 10 days.
The Artemis Program is NASA’s campaign to explore the Moon and beyond. Artemis-1, the uncrewed exoLEO test flight of the Orion spacecraft, was completed in 2022. There were four navigation Extended Kalman Filters (EKFs) that are part of the Orion navigation system. The Atmospheric Extended Kalman Filter (ATMEKF) estimates the vehicle position, velocity, and attitude (referred to as the vehicle state) during the ascent and entry phases of flight. Once Orion is outside of Earths atmosphere, the Earth Orbit Extended Kalman Filter (EOEKF) and CisLunar Extended Kalman Filter (CLEKF) estimate the translational states, depending on the phase of flight, while the Attitude Extended Kalman Filter (ATTEKF) estimates the rotational state of the vehicle. The Kalman filters propagate the vehicle state forward in time using a combination of dynamics models and the output data from the Inertial Measurement Unit (IMU). The filters update the vehicle states and associated uncertainties, in the form of the covariance matrix, using pseudorange measurements from GPS (in ATMEKF/EOEKF), optical navigation measurements of the Earth or Moon (in CLEKF), and star tracker measurements (in ATTEKF). Simultaneously, the Kalman filters estimate error sources in the sensors, which are included in the state vectors as Exponentially Correlated Random Variables (ECRVs). This paper will summarize the performance of these filters during the Artemis-1 mission.
Universal time measurements taken by the lunar occultation, optical astrometry, lunar laser ranging, and very long baseline interferometry have been combined using a Kalman filter to produce a smoothed length-of-day series, LUNAR97, spanning 1832.5-1997.5 at yearly intervals.
A Kalman filter has been used to combine independent measurements of the Earth's orientation taken by optical astrometry and the space-geodetic techniques of LLR, SLR, VLBI, and GPS.
The Earth's rotation is not constant but exhibits minute changes on all observable time scales ranging from subdaily to secular. This rich spectrum of observed Earth rotation changes reflects the rich variety of astronomical and geophysical phenomena that are causing the Earth's rotation to change, including, but not limited to, ocean and solid body tides, atmospheric wind and pressure changes, oceanic current and sea level height changes, post-glacial rebound, and torques acting at the core-mantle boundary. In particular, the decadal-scale variations of the Earth's rotation are thought to be largely caused by interactions between the Earth's outer core and mantle. Comparing the inferred Earth rotation variations caused by the various core-mantle interactions to observed variations requires Earth rotation observations spanning decades, if not centuries. During the past century many different techniques have been used to observe the Earth's rotation. By combining the individual Earth rotation series determined by each of these techniques, a series of the Earth's rotation can be obtained that is based upon independent measurements spanning the greatest possible time interval. In this study, independent observations of the Earth's rotation are combined to generate a length-of-day series spanning 1832-1997. The observations combined include lunar occultation measurements spanning 1832-1955, optical astrometric measurements spanning 1956-1982, lunar laser ranging measurements spanning 1970-1997, and very long baseline interferometric measurements spanning 1978-1998. These series are combined using a Kalman filter developed at JPL for just this purpose. The resulting combined length-of-day series will be presented and compared with other available length-of-day series of similar duration.
An innovative approach to autonomous attitude, trajectory, and rate estimation is presented for low earth orbit (LEO) satellites which relies on magnetometers and sun sensors. These two sensors are reliable, inexpensive, and are used routinely in LEO missions for attitude determination and control. An extended Kalman filter (EKF) is developed from two existing systems, one which uses an EKF to estimate attitude and trajectory using magnetometer and gyro data and a second pseudo-linear filter which estimates rotation rate using magnetometer and sun sensor data. The theoretical background of the combined system is presented along with test results from noisy, simulated sensor data.