Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding

Kyle HundmanValentino ConstantinouChristopher LaporteIan ColwellTom Soderstrom

article2018KDD1,963 citations

Demonstrates an automated spacecraft anomaly detection framework that pairs Long Short-Term Memory networks with nonparametric dynamic thresholding to reliably flag telemetry issues and mitigate false alarms using real NASA mission data.

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Modern spacecraft generate massive streams of performance data, creating an operational challenge for human engineers who must monitor thousands of telemetry channels for unexpected behavior. Traditional monitoring relies heavily on fixed, out-of-limits thresholds and manual chart reviews. These legacy systems require costly expert maintenance, struggle to scale with growing data volumes, and routinely fail to detect subtle anomalies that depend on time or operating context. To address these operational risks and reduce monitoring workloads, the article evaluated an automated anomaly detection framework designed to handle large-scale, complex telemetry data.

The evaluated approach uses Long Short-Term Memory neural networks, a form of recurrent neural network specialized for sequence data, to predict normal channel values one step ahead based on past readings and spacecraft command inputs. Prediction discrepancies are smoothed, and the framework applies a newly developed unsupervised, non-parametric dynamic thresholding technique to identify anomalous deviations without making flawed assumptions about standard data distributions. An anomaly pruning procedure was also introduced to filter out minor, noisy spikes and suppress false alarms. The authors validated this pipeline using historical, expert-labeled incident reports across 82 telemetry channels from two distinct missions: the Soil Moisture Active Passive satellite and the Mars Science Laboratory Curiosity rover.

The findings demonstrate that this combined framework significantly outperforms conventional statistical thresholding methods. The proposed dynamic thresholding with pruning achieved an overall precision of 87.5% and a recall of 80.0%, yielding the highest overall accuracy score across all tested methods. Pruning proved critical, boosting precision by nearly 39 percentage points with only a minimal 4.8 percentage point drop in recall. In contrast, standard Gaussian thresholding struggled because real-world prediction errors violated normal distribution assumptions. Furthermore, the approach successfully identified complex contextual anomalies—which represented 41% of all evaluated anomalies and are typically missed by traditional limit checks—achieving a 69.0% recall on contextual events and a 90.3% recall on point anomalies.

These results show that neural network forecasting paired with dynamic thresholding can reliably capture complex temporal failures while maintaining channel-level interpretability for engineering teams. However, performance varied by mission type; the routine operations of the satellite yielded higher accuracy (85.5% precision and recall) than the highly diverse, irregular activity sequences of the Mars rover (92.6% precision and 69.4% recall). An initial pilot deployment monitoring over 700 satellite channels confirmed several real-world anomalies, but it also underscored that suppressing false positives is essential to gain operational trust when screening hundreds of thousands of daily data points.

To move toward full operational adoption, mission teams should refine feature engineering by integrating detailed command context and event logs rather than relying solely on high-level command indicators. Operations should also incorporate human feedback loops to establish baseline alert scores for noisy channels and explore automated correlation tools to track inter-channel dependencies. While the experimental setup evaluated focused five-day spans around known incidents rather than multi-year continuous operations, the evidence provides strong confidence that this unsupervised framework offers a viable, scalable alternative to manual limit-setting in mission-critical environments.

California Institute of Technology Jet Propulsion Laboratory anomaly detection systems engineers expert knowledge spacecraft anomaly detection nonparametric dynamic thresholding real-time anomaly detection

arXiv: 1802.04431 khundman/telemanom

Paper: Long Short-Term Memory, Sepp Hochreiter et al. (1997). Introduces the Long Short-Term Memory architecture that forms the core sequence modeling and telemetry prediction engine used by the source paper.
Paper: A Critical Review of Recurrent Neural Networks for Sequence Learning, Zachary C. Lipton et al. (2015). Provides a comprehensive foundational review of recurrent architectures, gated memory units, and sequence-learning dynamics essential for understanding recurrent time-series modeling.
Paper: Isolation-Based Anomaly Detection, Fei Tony Liu et al. (2012). Establishes standard principles and baselines of unsupervised anomaly detection in complex, high-dimensional operational datasets.
Paper: Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling, Junyoung Chung et al. (2014). Compares gated recurrent architectures to guide design choices in modeling temporal dependencies within sequential engineering data.
Paper: Recurrent Neural Network Regularization, Wojciech Zaremba et al. (2014). Presents regularization and dropout strategies for recurrent neural networks that prevent overfitting during sequence training.

Paper: Model Assertions for Monitoring and Improving ML Models, Daniel Kang et al. (2020). Extends continuous telemetry monitoring by using domain-specific assertions and runtime quality assurance to detect high-confidence operational errors.
Paper: Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift, Stephan Rabanser et al. (2019). Explores how to identify and characterize distribution and dataset shifts in production systems to mitigate silent failures.
Paper: Data Validation for Machine Learning, Eric Breck et al. (2019). Generalizes runtime telemetry checks into full production data validation pipelines that monitor schema drift and batch anomalies.
Paper: Deep Anomaly Detection with Outlier Exposure, Dan Hendrycks et al. (2019). Advances deep anomaly detection by leveraging outlier exposure during training to improve out-of-distribution detection reliability.
Paper: Energy-based Out-of-distribution Detection, Weitang Liu et al. (2020). Proposes energy-based scoring frameworks for detecting out-of-distribution inputs as an alternative to thresholding predictive errors.
Paper: Deep learning for time series classification: a review, Hassan Ismail Fawaz et al. (2018). Systematically reviews modern deep neural network architectures for time series classification and sequence representation.

Cover for Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding

Abstract

As spacecraft send back increasing amounts of telemetry data, improved anomaly detection systems are needed to lessen the monitoring burden placed on operations engineers and reduce operational risk. Current spacecraft monitoring systems only target a subset of anomaly types and often require costly expert knowledge to develop and maintain due to challenges involving scale and complexity. We demonstrate the effectiveness of Long Short-Term Memory (LSTMs) networks, a type of Recurrent Neural Network (RNN), in overcoming these issues using expert-labeled telemetry anomaly data from the Soil Moisture Active Passive (SMAP) satellite and the Mars Science Laboratory (MSL) rover, Curiosity. We also propose a complementary unsupervised and nonparametric anomaly thresholding approach developed during a pilot implementation of an anomaly detection system for SMAP, and offer false positive mitigation strategies along with other key improvements and lessons learned during development.

Topics

anomaly detection systems engineers expert knowledge recurrent neural networks low earth orbits thresholding techniques anomalous behavior anomaly detection methods long short term memory neural networks detection algorithm

Keywords

spacecraft anomaly detection nonparametric dynamic thresholding real-time anomaly detection spacecraft telemetry LSTM models Local Outlier Probabilities contextual anomalies telemetry monitoring recurrent neural networks

1 Introduction
2 Background and Related Work
2.1 Anomaly Detection in Aerospace
2.2 Anomaly Detection using LSTMs
3 Methods
3.1 Telemetry Value Prediction with LSTMs
3.2 Dynamic Error Thresholds
3.3 Mitigating False Positives
4 Experiments
4.1 Setup
4.2 Model Parameters and Evaluation
4.3 Results and Discussion
5 Deployment
6 Conclusion
References

Knowls

Knowl 1 — Nonparametric Dynamic Thresholding for Time-Series Prediction Residuals
algorithm
To identify anomalous intervals in a time series without making parametric distributional assumptions or relying on labeled training data, prediction errors from a forecasting model are smoothed and evaluated against candidate standard-deviation offsets to find a cutoff that maximizes relative variance and mean reduction while penalizing excessive anomaly detections.

Given scalar telemetry predictions $\hat{y}^{(t)}$ and true values $y^{(t)}$ , the absolute prediction error is $e^{(t)} = |y^{(t)} - \hat{y}^{(t)}|$ . An exponentially-weighted moving average (EWMA) is applied over a historical evaluation window of length $h$ to produce smoothed errors $\mathbf{e}_s = [e_s^{(t-h)}, \dots, e_s^{(t)}]$ .

A candidate threshold $\epsilon$ is defined as $\epsilon(z) = \mu(\mathbf{e}_s) + z \sigma(\mathbf{e}_s)$ , where $\mu(\mathbf{e}_s)$ and $\sigma(\mathbf{e}_s)$ are the mean and standard deviation of $\mathbf{e}_s$ , and $z$ is drawn from a discrete ordered set of positive values $\mathbf{z}$ (typically $z \in \{2.5, 3.0, \dots, 10.0\}$ ).

The selected threshold $\epsilon^*$ maximizes the objective function:

$\epsilon^* = \arg\max_{\epsilon(z)} \frac{\frac{\Delta \mu(\mathbf{e}_s)}{\mu(\mathbf{e}_s)} + \frac{\Delta \sigma(\mathbf{e}_s)}{\sigma(\mathbf{e}_s)}}{|e_a| + |E_{seq}|^2}$

where the quantities are defined as:
- $e_a = \{e_s \in \mathbf{e}_s \mid e_s > \epsilon\}$ is the set of smoothed errors exceeding threshold $\epsilon$ .
- $E_{seq}$ is the set of continuous sequences of error values in $e_a$ .
- $\Delta \mu(\mathbf{e}_s) = \mu(\mathbf{e}_s) - \mu(\{e_s \in \mathbf{e}_s \mid e_s \le \epsilon\})$ represents the reduction in mean smoothed error when anomalous points are excluded.
- $\Delta \sigma(\mathbf{e}_s) = \sigma(\mathbf{e}_s) - \sigma(\{e_s \in \mathbf{e}_s \mid e_s \le \epsilon\})$ represents the reduction in standard deviation when anomalous points are excluded.
For each resulting anomalous sequence $e_{seq}^{(i)} \in E_{seq}$ , an anomaly severity score $s^{(i)}$ is computed based on its maximum error relative to the threshold:

$s^{(i)} = \frac{\max(e_{seq}^{(i)}) - \epsilon^*}{\mu(\mathbf{e}_s) + \sigma(\mathbf{e}_s)}$
Knowl 2 — Anomaly Sequence Pruning Procedure for False Positive Reduction
algorithm
To prevent normal background noise spikes from triggering false alarms after dynamic thresholding, candidate anomalous sequences are evaluated by comparing the relative drop between successive sequence maximum errors.
Input: Set of anomalous sequences E_seq, smoothed error vector e_s, threshold eps_star, minimum percentage drop parameter p (e.g., p = 0.13)
Output: Filtered set of confirmed anomalous sequences E_pruned
1. For each sequence e_seq in E_seq, find its maximum value max(e_seq).
2. Let e_max_non_anom = max({e_s_val in e_s such that e_s_val <= eps_star}).
3. Construct ordered list e_max containing all sequence maximums sorted in descending order, appending e_max_non_anom as the final element.
   Let e_max = [e_max^(0), e_max^(1), ..., e_max^(|E_seq|)].
4. Initialize keep_idx = 0.
5. For i = 1 to |E_seq|:
       Compute relative decrease: d^(i) = (e_max^(i-1) - e_max^(i)) / e_max^(i-1)
       If d^(i) > p:
           keep_idx = i
6. E_pruned = all sequences corresponding to e_max^(j) for j < keep_idx.
7. Return E_pruned
If the relative decrease $d^{(i)}$ fails to exceed threshold $p$ at step $i$ and all subsequent steps down to the baseline non-anomalous error, those candidate sequences are reclassified as nominal. This effectively prunes borderline error sequences whose magnitudes do not sufficiently detach from the underlying noise floor.
Knowl 3 — Single-Channel LSTM Telemetry Forecasting Architecture
model/method
Spacecraft telemetry streams are modeled by training an independent Long Short-Term Memory (LSTM) network per channel to predict the single next telemetry value ( $d=1, l_p=1$ ). Training separate models per channel preserves granular traceability for subsystem diagnosis and allows channel-specific early stopping and regularization.

For a channel at time step $t$ , the input feature vector $\mathbf{x}^{(t)} \in \mathbb{R}^m$ consists of:
1. Historical scalar telemetry values for that specific channel over a lookback window of sequence length $l_s = 250$ .
2. Encoded command inputs sent to the spacecraft, formatted as a one-hot vector indicating the target command module combined with binary indicators denoting whether a command was sent or received at step $t$ .
The neural network architecture uses 2 hidden LSTM layers with 80 units each, a dropout rate of 0.3, a batch size of 64, and the Adam optimizer. Models are trained with early stopping over a maximum of 35 epochs based on validation error.

Knowl 4 — Comparative Performance of Nonparametric and Parametric Error Thresholding

data/table

Using identical LSTM prediction errors across Soil Moisture Active Passive (SMAP) satellite and Mars Science Laboratory (MSL) rover telemetry, the non-parametric dynamic thresholding approach combined with sequence pruning substantially outperforms parametric Gaussian tail thresholding and unpruned baselines.

Thresholding Approach	Precision	Recall	$F_{0.5}$ score
Non-Parametric w/ Pruning ( $p = 0.13$ )
MSL	92.6%	69.4%	0.69
SMAP	85.5%	85.5%	0.71
Total	87.5%	80.0%	0.71
Non-Parametric w/out Pruning ( $p = 0$ )
MSL	75.8%	69.4%	0.61
SMAP	43.0%	92.8%	0.44
Total	48.9%	84.8%	0.47
Gaussian Tail ( $\epsilon_{norm} = 0.0001$ )
MSL	84.2%	44.4%	0.54
SMAP	88.5%	78.3%	0.71
Total	87.5%	66.7%	0.66
Gaussian Tail ( $\epsilon_{norm} = 0.01$ )
MSL	61.3%	52.8%	0.48
SMAP	82.4%	81.2%	0.68
Total	75.8%	71.4%	0.62
Gaussian Tail w/ Pruning ( $\epsilon_{norm} = 0.01, p = 0.13$ )
MSL	88.2%	41.7%	0.54
SMAP	92.7%	73.9%	0.71
Total	91.7%	62.9%	0.66

Pruning candidate sequences with $p = 0.13$ increases overall precision by 38.6 percentage points (from 48.9% to 87.5%) while reducing recall by only 4.8 percentage points (from 84.8% to 80.0%), raising the overall $F_{0.5}$ score from 0.47 to 0.71. Across all single-step predictions, the LSTM models achieved an average normalized absolute error of 5.9% (5.5% on SMAP and 6.8% on MSL).

Knowl 5 — Overlap-Based Sequence Anomaly Evaluation Protocol
experimental setup
Anomaly detection performance on continuous time-series data is evaluated on a per-sequence basis using temporal overlap rules:
1. True Positive (TP): Recorded when any point of a predicted anomalous sequence $e_{seq} \in E_{seq}$ overlaps with a ground-truth labeled anomalous sequence $x_a \in \mathbf{x}_a$ . If multiple predicted sequences fall within a single labeled sequence interval, only one true positive is credited.
2. False Negative (FN): Recorded when a ground-truth labeled anomalous sequence $x_a$ contains no overlapping predicted anomalous sequences.
3. False Positive (FP): Recorded for every predicted anomalous sequence that does not overlap any ground-truth labeled anomalous interval.
Evaluation is conducted by aggregating telemetry values into 1-minute averages and evaluating in batches of 70 minutes (matching downlink batch schedules). Dynamic error threshold calculation uses a rolling historical error buffer of length $h = 2100$ steps (35 hours).

Knowl 6 — SMAP and MSL Expert-Labeled Telemetry Anomaly Dataset

data/table

The benchmark dataset consists of telemetry channels extracted from real spacecraft Incident Surprise, Anomaly (ISA) operational reports for the Soil Moisture Active Passive (SMAP) satellite and the Mars Science Laboratory (MSL) rover, Curiosity.

Metric	SMAP	MSL	Total
Total anomaly sequences	69	36	105
Point anomalies (% tot.)	43 (62%)	19 (53%)	62 (59%)
Contextual anomalies (% tot.)	26 (38%)	17 (47%)	43 (41%)
Unique telemetry channels	55	27	82
Unique ISAs	28	19	47
Telemetry values evaluated	429,735	66,709	496,444

Point anomalies represent out-of-limits or low-density values detectable without temporal context, whereas contextual anomalies (representing 41% of total sequences) represent unexpected behavior dependent on local context or sequence history that cannot be identified using standard limit-checking approaches.

Knowl 7 — Recall Disparity Across Anomaly Types and Spacecraft Operational Profiles

empirical result

Using LSTM predictions with nonparametric thresholding and pruning ( $p = 0.13$ ), anomaly detection recall varies significantly depending on anomaly classification and mission operational complexity:

Point anomalies achieved 90.3% total recall compared to 69.0% for contextual anomalies. Overall performance was higher on SMAP (85.5% precision, 85.5% recall, 5.5% mean prediction error) than on MSL (92.6% precision, 69.4% recall, 6.8% mean prediction error). This disparity is driven by SMAP's regular, routine operational cycles versus MSL's diverse, non-stationary surface activity profiles, which were often absent from limited training timeframes.

Knowl 8 — Violation of Gaussian Error Assumptions in Telemetry Residuals
empirical result
Parametric thresholding techniques that assume prediction errors follow a normal distribution fail because smoothed forecasting residuals in spacecraft telemetry strongly violate Gaussian assumptions.

Applying D'Agostino and Pearson's normality test to the sets of smoothed prediction errors $\mathbf{e}_s$ across all evaluated channels rejects the null hypothesis of normality at significance level $\alpha = 0.005$ for every channel. Consequently, modeling historical errors via normal tail probabilities $L = 1 - Q\left(\frac{\mu_s - \mu_W}{\sigma_W^2}\right)$ produces degraded thresholds that yield inferior precision-recall trade-offs compared to direct non-parametric search.
Knowl 9 — Channel-Specific Minimum Severity Thresholding via User Feedback
model/method
To suppress recurring false alarms on channels with regular, infrequent non-anomalous fluctuations, a channel-specific minimum anomaly score $s_{min}$ is established.

Under this rule, any candidate anomaly sequence whose normalized severity score satisfies $s < s_{min}$ is reclassified as nominal. When domain experts review telemetry alarms and provide feedback identifying confirmed false positives, $s_{min}$ for that channel is adjusted to match or exceed the upper bound of the anomaly scores associated with those false positive events.
Knowl 10 — Operational Deployment Limitations and Feature Granularity Constraints
limitation
Pilot deployment of automated telemetry anomaly detection across over 700 SMAP channels revealed key operational and modeling limitations:
1. High False Positive Sensitivity: In an operations environment processing over $10^6$ values per day, false positives risk eroding operator trust, as engineers are hesitant to divert attention to non-critical alarms.
2. Coarse Command Features: Encoding commands solely as one-hot module destinations with binary sent/received flags omits semantic command parameters and execution arguments, degrading prediction accuracy for dynamic missions like planetary rovers.
3. Absence of Cross-Channel Dependency Modeling: Predicting channels strictly independently prevents automated detection of inter-channel correlations and subsystem-level anomalous interactions.

Coverage note — None was omitted; all contributed methodologies, algorithms, experimental results, empirical comparisons, and deployment lessons from the paper are represented.

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Citation

MLA

Hundman, K., et al. “Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding”. Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 2018, pp. 387–95, https://doi.org/10.1145/3219819.3219845.

APA

Hundman, K., Constantinou, V., Laporte, C., Colwell, I., & Soderstrom, T. (2018). Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding. Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 387–395. https://doi.org/10.1145/3219819.3219845

Chicago

Hundman, K., V. Constantinou, C. Laporte, I. Colwell, and T. Soderstrom. 2018. “Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding”. Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 387–95. https://doi.org/10.1145/3219819.3219845.

Harvard

Hundman, K. et al. (2018) “Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding”, Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. ACM, pp. 387–395. Available at: https://doi.org/10.1145/3219819.3219845.

Vancouver

1. Hundman K, Constantinou V, Laporte C, Colwell I, Soderstrom T (2018) Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding. In: Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. ACM, pp 387–395

BibTeX

@inproceedings{Hundman_2018, series={KDD ’18}, title={Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding}, url={http://dx.doi.org/10.1145/3219819.3219845}, DOI={10.1145/3219819.3219845}, booktitle={Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery &amp; Data Mining}, publisher={ACM}, author={Hundman, Kyle and Constantinou, Valentino and Laporte, Christopher and Colwell, Ian and Soderstrom, Tom}, year={2018}, month=July, pages={387–395}, collection={KDD ’18} }

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Dataset	Recall - Point Anomalies	Recall - Contextual Anomalies
MSL	78.9%	58.8%
SMAP	95.3%	76.0%
Total	90.3%	69.0%

Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Nonparametric Dynamic Thresholding for Time-Series Prediction Residuals

Knowl 2 — Anomaly Sequence Pruning Procedure for False Positive Reduction

Knowl 3 — Single-Channel LSTM Telemetry Forecasting Architecture

Knowl 4 — Comparative Performance of Nonparametric and Parametric Error Thresholding

Knowl 5 — Overlap-Based Sequence Anomaly Evaluation Protocol