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Method on Laser Ranging Residual Estimation Based on Interactive Multiple Model Kalman Filtering
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DOI：10.3788/LOP251286.png)
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Abstract
En 中文
Objective Satellite laser ranging (SLR) is a fundamental technique in modern space geodesy, high-precision orbit determination, and Earth system science. It enables the millimetre-level measurement of satellite positions by analyzing the travel time of laser pulses between ground stations and retroreflectors mounted on satellites. However, the SLR echo signal is inherently affected by a combination of noise sources, such as atmospheric turbulence, instrumental delay fluctuations, and satellite attitude perturbations. These uncertainties lead to significant challenges in achieving real-time, high-precision prediction or correction of the measured observed-minus-computed (O-C) residuals. To improve the reliability of echo signal interpretation, this work investigates an adaptive preprocessing strategy based on interacting multiple model Kalman filtering (IMM-KF). Our aim is not to predict deterministic outcomes in a strict sense but rather to provide an accurate and consistent real-time estimation of the evolving signal behavior, especially in the presence of nonlinearity and abrupt changes. By modeling the echo residuals as a dynamic stochastic process, the proposed approach enhances robustness against noise and enables effective filtering and trajectory tracking. Methods The core methodology involves constructing an IMM framework that integrates two distinct filtering mechanisms: the adaptive Kalman filter (AKF) and the unscented Kalman filter (UKF). The AKF is capable of self-adjusting its noise covariance matrix in response to system changes, while the UKF is well-suited for handling nonlinearity by propagating sigma points through the nonlinear transformation. The IMM mechanism allows these models to interact and exchange likelihood-based weights at each time step, thereby improving the tracking performance by dynamically adjusting to the underlying signal behavior. In our implementation, real-world SLR O-C residual datasets from three satellite missions are used. Each dataset is first analyzed for its statistical properties, such as mean drift and the ratio of positive deviations, which are then used to initialize the filter parameters. We compare the proposed IMM-KF model against a conventional standard Kalman filter (KF) as a baseline. For each dataset, both filtering methods are applied, and their predictive performance is evaluated using multiple statistical metrics. Specifically, we define and use the following: root mean square error (E-RMSE), which measures the overall prediction deviation; mean error (E-ME), which indicates the bias in predictions; Nash-sutcliffe efficiency (E-NSE), which quantifies the consistency between predictions and actual measurements. Moreover, we introduce outlier detection by filtering extreme prediction points that exceed the original data bounds, ensuring that the visualization reflects only statistically meaningful trends. For each scenario, three subplots are generated: the original signal, the predicted signal, and the prediction error. Results and Discussions The experimental outcomes strongly support the effectiveness of the IMM-KF framework. Across all datasets, the IMM-KF achieves substantial improvements over the standard KF in terms of accuracy, stability, and adaptability. Specifically, the E-RMSE is reduced by over 80 % on average, and the standard deviation of prediction errors shows a greater than 90 % reduction. The E-NSE metric consistently exceeds 0. 999, indicating that the IMM-KF output aligns extremely well with the actual data. In Fig. 2, which displays the results of the standard KF, noticeable lag and larger fluctuations in prediction errors can be observed. These deviations highlight the model's limitations in capturing nonlinear transitions and adapting to changes in the signal's behavior. In contrast, Fig. 3 illustrates the results of the IMM-KF, where the residuals are smoother, and the response is more prompt during periods of dynamic change. The IMM-KF not only follows the signal trajectory closely but also significantly suppresses noise-induced spikes, especially during transitions. It is worth emphasizing that the IMM-KF does not eliminate randomness from the signal but instead provides a statistically consistent estimate based on the latest observation history. The apparent determinism in certain plots reflects the high alignment of the filtered estimates with actual measurements, not the prediction of deterministic trends. This distinction is crucial in understanding the value of IMM-KF: it excels in real-time estimation under uncertainty, not future state extrapolation for long-term forecasting. Further simulation tests (not shown) were conducted using synthetic datasets with injected noise and abrupt trend changes. These additional tests confirm that the IMM-KF framework is resilient to measurement spikes and remains effective even when data quality deteriorates. Such robustness is highly desirable in operational space geodesy systems where data integrity cannot always be guaranteed. Conclusions This study proposes a hybrid filtering architecture based on interacting multiple model Kalman filtering to improve the estimation of satellite laser ranging echo signals. By leveraging the strengths of both adaptive and unscented Kalman filtering and embedding them into a dynamically weighted framework, the IMM-KF demonstrates strong performance in noisy and nonlinear environments. The algorithm effectively suppresses outliers, enhances prediction accuracy, and adapts to sudden trend changes, making it a promising tool for future laser ranging and space geodetic applications. Our results suggest that such signal processing frameworks can be extended to other dynamic measurement systems requiring real-time estimation with noise suppression. Potential applications include spacecraft tracking, satellite attitude control, and even terrestrial dynamic system modeling. In summary, the proposed IMM-KF model offers a flexible, robust, and high-precision approach for signal preprocessing in satellite laser ranging systems.
Keywords:
satellite laser ranging
distance measurement residual estimation
Kalman filter
interactive multiple model filter
signal processing
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