Kinematic Single Vehicle Trajectory Prediction Baselines and Applications with the NGSIM Dataset

Dominique Beauvois; Guillaume Sandou; Guillermo Pita Gil; Jean Mercat; Nicole El Zoghby

REVIEW 2 major objections 4 minor 12 references

Kinematic Single Vehicle Trajectory Prediction Baselines and Applications with the NGSIM Dataset

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A constant-velocity Kalman filter with learned noise outperforms published uncertainty estimates on the NGSIM dataset, reaching 0.75 m RMSE at 1 s and a mean NLL of 0.80.

desk verdict Useful reproducible constant-velocity baseline on NGSIM, but the headline NLL comparison to prior published values is not yet supported. read the letter →

arxiv 1908.11472 v4 pith:ZOC3C7GB submitted 2019-08-29 cs.RO cs.CVcs.LG

Jean Mercat , Nicole El Zoghby , Guillaume Sandou , Dominique Beauvois , Guillermo Pita Gil This is my paper · ORCID

classification cs.ROcs.CVcs.LG

keywords trajectorypredictionKalmanfilterNGSIMbaselinemodelsnegativelog-likelihoodLSTMconstantvelocitymodelmulti-modal

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a constant-velocity Kalman filter, with its noise parameters learned by minimizing negative log-likelihood, is a strong and reproducible baseline for freeway vehicle-trajectory prediction. On the NGSIM dataset it reports RMSE 0.75 m at 1 s and 6.70 m at 5 s, with a mean NLL of 0.80 at 1 s, lower than published values for the same model. It further claims that a multi-modal version of the filter cuts the 5 s miss rate to 30 percent, and that replacing the constant-velocity assumption with an LSTM command predictor improves both accuracy and uncertainty estimates over a retrained LSTM baseline. A careful reader would care because the paper supplies a transparent reference point for judging more complex trajectory models and their claimed covariances.

What carries the argument

The carrying object is a linear Kalman filter with state $(x, v_x, y, v_y)$, transition $A = \mathrm{blkdiag}(A_x, A_y)$ with $A_x = A_y = \begin{pmatrix}1 & dt \\ 0 & 1\end{pmatrix}$, and acceleration noise entering through $Q = E Q_a E^T$, where $Q_a$ is a learned factorized matrix. The paper learns $Q_a$, the observation noise $R$, and the initial state by minimizing the time-averaged negative log-likelihood $\mathrm{MNLL}(k) = \frac{1}{N}\sum_i \mathrm{NLL}((x^i_k-\hat{x}^i_k, y^i_k-\hat{y}^i_k), P_k)$, with the NLL written explicitly as a bivariate Gaussian log-density. This same scaffold is extended in two ways: sampling a quantized exploration distribution over initial velocity to produce Gaussian-mixture modes, and replacing the constant-velocity step with an LSTM cell that outputs a jerk command and its variance at each prediction step.

What would settle it

Compute the empirical residuals between constant-velocity predictions and observed positions on a held-out NGSIM subset, and compare their distribution and autocorrelation with the fitted Gaussian and with white noise. If the residuals show heavy tails, time-varying variance, or significant autocorrelation at short lags, the learned covariance and NLL baseline are misspecified.

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Extended reading notes

Core claim

The paper's central claim is that a properly fitted kinematic model is a serious baseline, not a toy. On the NGSIM US-101 and I-80 datasets, using only relative positions, the constant-velocity Kalman filter with learned process and observation noise reaches RMSE 0.75 m at 1 s and 6.70 m at 5 s, and a mean negative log-likelihood of 0.80 at 1 s, much lower than values reported in earlier work for the same model. The paper attributes the discrepancy to inconsistent NLL definitions and shows that the average predicted error covariance matches the empirical error covariance well. It also shows that a six-mode multi-modal extension reaches a 5 s miss rate of 30 percent, and that an LSTM-commanded Kalman filter, which keeps the state interpretable as position, velocity, and acceleration, improves RMSE, FDE, and MNLL over a retrained LSTM encoder-decoder baseline.

Load-bearing premise

The model assumes that, after fitting, future acceleration is zero-mean white Gaussian noise with fixed covariance, so the reported negative log-likelihood and covariance estimates are only meaningful if NGSIM trajectory variations are Gaussian and stationary.

Editorial extensions

If this is right

Any future trajectory-prediction method that reports NLL should compare against a fitted constant-velocity Kalman filter with an explicit NLL definition; otherwise lower RMSE alone does not demonstrate better uncertainty modeling.
Reported covariance matrices from more complex models can be assessed by the same ellipse-matching procedure; if their mean predicted covariance exceeds the empirical error covariance, the model is overconfident or underconfident in a quantifiable way.
Multi-modal baselines can be built without training by quantizing the initial-velocity exploration distribution; the resulting 30 percent miss rate at 5 s undercuts the need for hand-defined maneuver modes.
The LSTM-commanded Kalman filter shows that interpretable kinematic structure can be retained in a learned predictor, giving a route to constrain predictions by physical limits such as maximum acceleration.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the NLL baseline is adopted as standard, several published trajectory models may need re-benchmarking: their reported uncertainties may be substantially worse than a constant-velocity filter's, not better.
The learned noise parameters are likely dataset-specific; a testable extension would fit the same filter on urban or intersection data and check whether MNLL and covariance matching degrade, indicating non-stationary driving dynamics.
The command-prediction architecture could be ablated to separate the contribution of the kinematic prior from the LSTM: replacing the Kalman prediction step with a pure LSTM output while keeping the same training loss would quantify how much inertia and state structure buy.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's what you should know: this paper gives the trajectory prediction community a workable, reproducible constant-velocity Kalman baseline on NGSIM, with code and a clear NLL definition. That's genuinely useful. The headline claim that its MNLL beats published values for the same model, however, rests on a comparison the authors themselves say may be invalid. Fix that and it's a solid contribution.

What's actually new: not the Kalman filter itself—that's textbook. The multi-modal extension adapts Schoeller et al.'s pedestrian work to vehicles, and the LSTM-Kalman command predictor is a variant of earlier hybrids. The most original pieces are the harmonized NLL metric and the way the LSTM is slotted into the Kalman prediction step to emit jerk commands. The internal comparison against a retrained V-LSTM is fair and shows modest gains.

The core method looks sound. The filter equations are explicit, parameters are learned on a training set and evaluated on a test set, and the code is linked. The RMSE/FDE values align with prior constant-velocity results, so the baseline itself is credible.

Soft spots: the abstract and Table I claim lower MNLL than Deo & Trivedi [4], but the paper also states the NLL values in [4] are 'unclear' and may be computed differently, in different units, or with a different covariance. Printing 3.72 vs 0.80 as though they are comparable overreaches. The internal V-LSTM comparison avoids this because they recomputed the baseline, but the published-baseline comparison needs either a reproduction of the exact NLL computation or a retraction of the direct comparison. Also, the multi-modal grid search over sigma_theta and sigma_alpha_v should specify the split used; if the test set informed the parameter choice, those results are optimistic. Minor issues: the similarity metric needs a bit more justification, and the paper would benefit from reporting variance across seeds or subsamples given overlapping test sequences.

Overall: this paper is for anyone building or evaluating trajectory prediction models who needs a trustworthy kinematic baseline and a common NLL metric. It deserves serious peer review, conditional on the NLL comparison being fixed and the multi-modal tuning protocol documented.

Recommendation: send it to review with a request for revision on those two points.

Referee Report

2 major / 4 minor

Summary. The paper proposes a reproducible constant-velocity Kalman filter baseline for single-vehicle trajectory prediction on the NGSIM dataset, with explicit equations, a published implementation, and reported RMSE, FDE, MNLL, and miss-rate metrics. The authors learn the Kalman process and observation noise parameters by minimizing NLL on a training set, evaluate on the Deo-Trivedi test split, and compare with published constant-velocity and LSTM baselines. They further propose a multi-modal constant-velocity model obtained by sampling a learned exploration distribution over heading and velocity variations, and an LSTM-command Kalman extension that predicts accelerations as commands. The central claims are that the Kalman baseline matches published RMSE while achieving lower MNLL, that the multi-modal baseline reduces miss rate substantially, and that the LSTM-Kalman model improves accuracy and uncertainty estimation over a harmonized V-LSTM baseline.

Significance. If the claims are properly supported, the paper is a useful reproducibility contribution: it makes the baseline explicit, releases code, uses a standardized preprocessing pipeline, and carefully defines the NLL metric, which is often ambiguous in the trajectory prediction literature. The internal comparison in Table III, where the authors retrain the V-LSTM with a harmonized NLL definition, is a methodological strength. The multi-modal baseline with a miss-rate comparison is also potentially useful as a sanity check for more complex interaction-aware models. However, the external NLL comparison with Deo and Trivedi and the unclear data-split handling in the multi-modal section currently weaken the quantitative claims.

major comments (2)

[Section II.B.1 and Table I] The central claim that the constant-velocity Kalman filter achieves a lower NLL than published results is not established. The authors state in Section II.B.1 that 'The NLL values reported in articles [4], [8], [9] are unclear' and later 'It is unclear what the reported NLL values from [4] mean', yet Table I prints a direct numeric comparison (From [4] MNLL 3.72 vs ours 0.80 at 1s) and the abstract repeats the superiority claim. Because the metric definition, units (metres vs feet), dimensionality (per-axis vs full bivariate), and covariance convention in [4] are not verified, the comparison is not meaningful as presented. Please either reproduce [4]'s exact NLL computation or remove the external NLL superiority claim and present the published values only as unverified references.
[Section III.B and Fig. 2] The multi-modal parameters are selected on a subset of the data, but it is not stated whether this subset overlaps the test set. Section III.B says the exploration distribution is 'computed on a random subset of the NGSIM dataset' and that σθ and σαv were obtained 'with a simple grid search over σθ, and σαv using a fixed number of samples k = 6', with no indication that the subset and grid search are restricted to a training or validation split. If the test set is used for distribution estimation or parameter selection, the Table II results, including the miss-rate comparison with [4], are optimistically biased. Specify the exact split used for the exploration distribution and the grid search, and re-evaluate the chosen parameters on a held-out test set if needed.

minor comments (4)

[Section II.A] The parameterization of the learned noise is not fully specified: equation (2) writes Q = E Q_a Q_a^T E^T, but the mapping from the listed arguments (ρ, σa, R, init) to Q_a and R is not given. Since reproducibility is a stated contribution, please make this mapping explicit.
[Section II.B.2 and Fig. 1] The covariance assessment relies on a qualitative 'good match' between the empirical and predicted covariance ellipses. Consider adding a numerical agreement measure, such as the average ratio or Frobenius distance between the two covariance estimates, to make the evaluation less visual.
[Table II and Section III.B] The multi-modal NLL (5.39 at 5s) is higher than the uni-modal NLL (4.44 at 5s) even though the multi-modal model is a strictly more expressive Gaussian mixture. The paper notes this and attributes it to the covariance coefficients, but a short discussion of why the likelihood does not improve would help readers interpret the baseline.
[General] There are several small presentation issues: 'Therefor' should be 'Therefore' in the introduction, 'assessement' should be 'assessment' in Section II.B.2, and 'Pytorch' should be 'PyTorch'. In the provided manuscript text, the square-root symbol in equation (5) renders as 'vuu√' and should be corrected in the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the Kalman parameters are trained on a training split and evaluated on a held-out test set, so the headline baseline results are genuine out-of-sample predictions; the published-NLL caveat concerns metric compatibility rather than circular reasoning.

full rationale

The core derivation is self-contained and non-circular. In Section II, the Kalman noise parameters are learned by minimizing NLL over a training set, via argmin over args of loss(Kalmanpred(Zh,args), Zf), and are then evaluated on a test set built with Deo & Trivedi's preprocessing code; the RMSE, MNLL, FDE, and MR numbers are therefore out-of-sample. The Section IV LSTM-Kalman extension likewise trains its weights by NLL minimization and reports results on a test split, with the V-LSTM baseline retrained under the same NLL definition for Table III. The one flagged weakness is Section II.B.1's admission that published MNLL values from [4] are of unclear meaning ('It is unclear what the reported NLL values from [4] mean'); this is a limitation of the comparison, not an input feeding the paper's own derivation. The paper also states that the multi-modal exploration parameters were obtained by a grid search rather than by a learned fit; while the manuscript would be clearer if it specified a validation split for that search, no equation-level circularity is shown. There is no load-bearing self-citation and no fitted quantity is renamed as a prediction, so the circularity score is 0.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The models rely on standard Kalman filter equations, motion and observation noise assumptions fit to NGSIM, the adoption of [4]'s preprocessing, and hand-selected multi-modal parameters. No new physical or theoretical entities are introduced.

free parameters (7)

Kalman process noise Q_a (acceleration noise) = not reported numerically
Fitted by Adam on the NGSIM training set by minimizing mean NLL (Section II.A).
Observation noise covariance R = not reported numerically
Fitted jointly with Q_a in the same optimization (Section II.A).
Initial state and covariance init = not reported
Included in the optimization arguments args = (rho, sigma_a, R, init) in Section II.A.
Multi-modal standard deviations sigma_theta, sigma_alpha_v = sigma_theta = 0 deg, sigma_alpha_v = 10%
Selected by grid search with k=6 in Section III.B; no separate validation set is described.
Number of modes k = 6
Fixed by hand in Section III.B.
LSTM weights = not reported
Learned on the training set during NLL minimization (Section IV).
Learned jerk variance sigma_hat_u_k = not reported
Output by the RNNCell and used in the covariance update in Eq. (16).

assumptions (5)

domain assumption State evolution follows a linear Kalman filter with zero-mean white Gaussian acceleration noise.
Section II.A defines X_{k+1} = A X_k + E a_k with a_k zero-mean Gaussian; this underpins the NLL and covariance claims.
domain assumption Observations are noisy positions with additive Gaussian noise R.
The innovation step in Eq. (3) assumes observation noise covariance R, which is learned.
domain assumption The NGSIM preprocessing and train/test split from [4] are valid and comparable.
The paper adopts the preprocessing code from [4] without independent validation; comparisons with [4] depend on this.
ad hoc to paper The multi-modal exploration distribution estimated from a subset of NGSIM is representative and does not leak into the test set.
Section III estimates the distribution of velocity and heading variations from a subset of NGSIM, but the paper does not state that this subset excludes the test set.
domain assumption An LSTM cell can serve as a learned command predictor inside a Kalman filter without degrading calibration.
Section IV, Eq. (16)-(17), assumes the RNNCell output (u_k, q_u_k) is a valid command and variance for the Kalman update.

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Cite this review

Pith. "Pith review of Kinematic Single Vehicle Trajectory Prediction Baselines and Applications with the NGSIM Dataset." pith.science (2026). https://pith.science/paper/ZOC3C7GB

@misc{pith2026190811472,
  author       = {Pith},
  title        = {Pith review of: Kinematic Single Vehicle Trajectory Prediction Baselines and Applications with the NGSIM Dataset},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZOC3C7GB}},
  note         = {Machine review of arXiv:1908.11472}
}

read the original abstract

In the recent vehicle trajectory prediction literature, the most common baselines are briefly introduced without the necessary information to reproduce it. In this article we produce reproducible vehicle prediction results from simple models. For that purpose, the process is explicit, and the code is available. Those baseline models are a constant velocity model and a single-vehicle prediction model. They are applied on the NGSIM US-101 and I-80 datasets using only relative positions. Thus, the process can be reproduced with any database containing tracking of vehicle positions. The evaluation reports Root Mean Squared Error (RMSE), Final Displacement Error (FDE), Negative Log-Likelihood (NLL), and Miss Rate (MR). The NLL estimation needs a careful definition because several formulations that differ from the mathematical definition are used in other works. This article is meant to be used along with the published code to establish baselines for further work. An extension is proposed to replace the constant velocity assumption with a learned model using a recurrent neural network. This brings good improvements in accuracy and uncertainty estimation and opens possibilities for both complex and interpretable models.

Figures

Figures reproduced from arXiv: 1908.11472 by the authors.

**Figure 1.** In blue (FDEx(t), FDEy(t)) parametric curve as a function of the prediction time. Covariance ellipses at 1s, 3s, and 5s of the predicted sequences. Green ellipses represent the prediction error covariance computed over the test examples. Red ellipses represent the estimated error covariance of each prediction averaged over the test examples. TABLE I: Comparison of RMSE, MNLL and FDE results for constant velocity mod… view at source ↗

**Figure 2.** Distribution of velocity and heading angle variation from the estimated values on a random subset of NGSIM. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Graph of two Gaussian probability density functions [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

12 extracted references · 11 canonical work pages

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [4]

N. Deo, M. Trivedi, Convolutional Social Pooling for Vehicle Tra- jectory Prediction, IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pp. 1549-1555, 2018

work page 2018

[2] [8]

C. Ju, Z. Wang, C. Long, X. Zhang, G. Cong, and D. E. Chang, Interaction-aware Kalman Neural Networks for Trajectory Prediction, arXiv, 2019

work page 2019

[3] [9]

Massaoud, I

K. Massaoud, I. Yahiaoui, A. Verroust-blondet, and F. Nashashibi, Non-local Social Pooling for Vehicle Trajectory Prediction, in pro- ceedings of the IEEE Intelligent Vehicles Symposium (IV), Jun 2019

work page 2019

[4] [1]

R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Transactions of the ASME, Journal of Basic Engineering 1960, vol. 82 pp. 35-45

work page 1960

[5] [2]

Sch ¨oller, V

C. Sch ¨oller, V . Aravantinos, F. Lay and, A. Knoll, The Simpler the Better: Constant Velocity for Pedestrian Motion Prediction, ArXiv 2019

work page 2019

[6] [3]

Hochreiter, and J

S. Hochreiter, and J. Schmidhuber, Long short-term memory, Neural computation 9(8), 1997, pp. 1735-1780

work page 1997

[7] [5]

Y . Xu, T. Zhao C. Baker, Y . Zhao, and Y . Wu, Learning Trajectory Prediction with Continuous Inverse Optimal Control via Langevin Sampling of Energy-Based Models, in Proc. of the 18th Interna- tional Conference on Autonomous Agents and Multiagent Systems (AAMAS), May 2019

work page 2019

[8] [6]

L. Liu, H. Jiang, P. He, W. Chen, X. Liu, J. Gao, and J. Han, On the Variance of the Adaptive Learning Rate and Beyond, arXiv:1908.03265v1, 2019

arXiv 1908