When Do Learned Priors Help Visual Inertial Estimation? A Controlled Study of Prior Integration, Calibration, Initialization, and Backend Consistency

Jinchang Zhang; Guoyu Lu

Fig. 1: Overview of the evaluated learning-augmented visual–inertial pipeline and the associated evaluation roadmap. (a) Learned motion information, with learned depth retained as an auxiliary diagnostic, is introduced into an otherwise unchanged geometric visual–inertial backend together with visual reprojection and IMU-preintegration constraints; camera–IMU extrinsics may be fixed or released for online optimization. (b) The learned factors complement rather than replace the native geometric constraints. (c) The evaluation separates component capability, same-backend incremental value, calibration and initialization sensitivity, sequence-dependent failure conditions, backend and physical consistency, and cross-experiment synthesis.

Fig. 2: Organization of the related-work landscape considered in this paper. Prior studies are grouped into five interacting dimensions: geometric visual–inertial estimation, learning-augmented estimation, calibration and initialization under sequence conditions, evaluation protocols and evidence, and backend state coupling with global correction. Their intersection motivates the controlled evaluation questions and research gaps examined in this work.

Claim	Minimum controlled evidence	Required reporting
Incremental value of the learned prior in the tested settings	Same backend, images, IMU, initialization, Fixed extrinsics, and output convention, with and without the prior	APE/RPE, exact tested weight setting, per-sequence deltas, and the scope of the available repeatability check
Online-calibration sensitivity is characterized	Same data and backend with a declared initial calibration; compare initial and final states with a physical reference where the transform convention is verified	Common-frame $\mathrm{SO}(3)$ and translation error where available, convergence history, APE/RPE, and nominal-setting limitations
Initialization sensitivity is characterized	Representative sequences, available controlled extrinsic settings, and the recorded alternative start window	Initial/final calibration or trajectory error, restart outcome, and an explicit statement that a population success rate is not estimated
Accuracy effect of the loop-closure pipeline is characterized	Matched loop-off/loop-on runs with identical front end, calibration, and pipeline state	Pre/post-toggle APE and RPE and global correction magnitude; do not infer accepted-loop behavior without acceptance logs
Reported backend cost is a matched diagnostic	Same recording, residual construction, active measurements, and weights	Total cost together with APE/RPE and calibration error; no cross-recording or per-residual claim when residual counts are unavailable

TABLE I: Claim–minimum-evidence requirements used in this work. Each row states the smallest controlled comparison that can support the corresponding claim; additional stress tests strengthen but do not replace the control.

RQ	Core question	Primary section	Main evidence
RQ1	What information does each component provide, and what are its local and global failure modes?	Component-Level Characterization	MonoViT, IMU-only, EKF, Original VINS
RQ2	Under an unchanged VINS backend and matched inputs, does the learned pose prior provide identifiable incremental value?	Incremental Effect of Learned Pose Priors	Original VINS versus VINS+Pose; Fixed/Online; higher-weight control
RQ3	How do the extrinsic initial value, covariance, and Fixed/Online strategy affect calibration and trajectory estimation?	Calibration and Initialization Robustness	EKF perturbations; Fixed/Online; initialization-to-final states; EuRoC
RQ4	Which sequence and initialization-window conditions lead to success, partial convergence, or failure?	Sequence-Dependent Failure and Initialization Conditions	Recordings 1 and 9; frame-300 restart; qualitative tracks
RQ5	Why can local error, backend cost, scale, and global trajectory criteria yield different judgments?	Backend State Coupling, Scale Consistency, and Global Correction	late injection; cost; BA/scale; loop closure

TABLE II: Research questions and evidence map for the experimental study.

Name	Definition
Original VINS	Unmodified VINS backend without the learned pose residual
VINS+Pose	Same backend with the adjacent-frame MonoViT relative-pose residual
VINS+Pose+Depth	VINS+Pose with the learned-depth diagnostic additionally enabled
Fixed (F)	Reference camera–IMU extrinsic excluded from optimization
Online (O)	Reference extrinsic used for initialization and then optimized
Higher weight (H)	Tested pose-prior scalar weight set to $5\times$ its current value

TABLE III: System and configuration nomenclature.

Fig. 3: Effect of scale alignment on the MonoViT trajectory. The left panel shows the trajectory after local scale correction, the middle panel shows the result obtained using a single global scale factor for the entire sequence, and the right panel shows the raw trajectory without scale correction.

Fig. 4: Comparison between ROS-based and standalone EKF implementations.The ROS and non-ROS versions are evaluated on the same input sequence. Both implementations produce similar estimated IMU trajectories and camera-IMU calibration parameters, including extrinsic rotation and translation.

Fig. 5: Internal state comparison between ROS-based and standalone EKF implementations. The estimated velocity, gyroscope bias, and accelerometer bias show similar trends in the ROS and non-ROS versions.

Method / Setting	Roll ( ∘ )	Pitch ( ∘ )	Yaw ( ∘ )	$X$ (m)	$Y$ (m)	$Z$ (m)
VINS with initial guess	0.12920883	0.94205661	89.11134805	-0.01392613	-0.07202541	-0.00905363
VINS-without-ROS with initial guess	0.10204582	0.91859205	89.10573467	-0.01316146	-0.06939931	-0.00847115
VINS without initial guess	0.14282301	0.94385202	89.10850337	-0.01489817	-0.07309295	-0.00928658
VINS-without-ROS without initial guess	0.11465889	0.92032762	89.09702679	-0.01446791	-0.07011650	-0.00863906

TABLE IV: Final extrinsic estimates of VINS under different platforms and initialization settings.

Evaluation	Run / Setting	Roll ( ∘ )	Pitch ( ∘ )	Yaw ( ∘ )	$X$ (m)	$Y$ (m)	$Z$ (m)
Final extrinsic	1st run w/ init. guess	0.12919693	0.94206166	89.11135918	$-1.3927124934576006\times 10^{-2}$	-0.0720239866276594	$-9.0520002393690967\times 10^{-3}$
Final extrinsic	2nd run w/ init. guess	0.12918814	0.94200657	89.11134995	$-1.3926596686883799\times 10^{-2}$	-0.0720255163554694	$-9.0526417281940174\times 10^{-3}$
Final extrinsic	1st run w/o init. guess	0.14281396	0.94385622	89.10850764	$-1.4897594776339746\times 10^{-2}$	-0.0730929617086037	$-9.2867827649735848\times 10^{-3}$
Final extrinsic	2nd run w/o init. guess	0.14282443	0.94385065	89.10850354	$-1.4898386929989293\times 10^{-2}$	-0.0730929245318574	$-9.2870138320267064\times 10^{-3}$
Final odometry pose	1st run w/ accurate extrinsic	-165.09126635	-71.98699933	3.52874976	-0.51332	0.41103	-0.13349
Final odometry pose	2nd run w/ accurate extrinsic	-165.08909602	-71.98689964	3.52576963	-0.51344	0.41119	-0.13327

TABLE V: Repeatability evaluation of VINS final extrinsic calibration and odometry estimation.

Fig. 6: Cross-sequence no-loop trajectory consistency between the original ROS-based and standalone non-ROS VINS-Fusion stereo implementations across five representative recordings. The black curves denote ground truth, while the blue and red curves denote the original and standalone implementations.

Fig. 7: Loop-closure response consistency between the original ROS-based and standalone non-ROS VINS-Fusion stereo implementations across three representative recordings. The black curves denote ground truth, and the blue and red curves denote the original and standalone implementations. Each pair shows that the two implementations undergo closely matched global corrections when loop closure is enabled.

Fig. 8: Standalone MonoViT pose evaluation on KITTI. The left plots show rotation and translation errors with respect to path length and vehicle speed, while the right plot compares the predicted visual-odometry trajectory with the ground-truth trajectory.

Fig. 9: Temporal pose error of standalone MonoViT on KITTI. The rotation error and translation errors along the

x

,

y

, and

z

axes are plotted over time.

Fig. 10: Component-wise MonoViT pose estimation on Recording 9. The left column compares the estimated and reference translations along the x-, y-, and z-axes, while the right column compares Roll, Pitch, and Yaw.

Fig. 11: Absolute and relative pose errors of MonoViT on Recording 9. The figure reports translation APE, rotation APE, translation RPE, and rotation RPE, together with their trajectory-wise error distributions.

Fig. 12: Component-wise pose comparison between 10 Hz IMU-only integration and the reference trajectory on Recording 9. The left column shows the x-, y-, and z-translation components, while the right column shows Roll, Pitch, and Yaw.

Fig. 13: Absolute and relative pose errors of 10 Hz IMU-only integration on Recording 9. The figure reports translation and rotation APE and 20-frame translation and rotation RPE without trajectory alignment.

Fig. 14: Preliminary comparison between the directly integrated IMU trajectory and the ground-truth trajectory for Recordings 09 and 10. The blue and orange curves denote the IMU-integrated and ground-truth trajectories, respectively. In both recordings, direct integration produces a substantially different spatial extent and global trajectory geometry from the reference.

Fig. 15: EKF trajectory evaluation on KITTI. The left plots show rotation and translation errors with respect to path length and vehicle speed, while the right plot compares the EKF estimate with the ground-truth trajectory.

Fig. 16: Temporal EKF pose error on KITTI. The rotation error and translation errors along the

x

,

y

, and

z

axes are plotted over time.

Fig. 17: Absolute and frame-to-frame pose errors of Original VINS at 10 Hz. The left column shows the Roll, Yaw, Pitch, and

x

-,

y

-, and

z

-translation errors with respect to the reference trajectory, while the right column shows the corresponding relative errors between consecutive frames.

Method	APE gauge/ alignment	Trans. APE RMSE (m)	Trans. APE Max (m)	Rot. APE RMSE ( ∘ )	Trans. RPE RMSE (m)	Rot. RPE RMSE ( ∘ )	$e_{R}$ ( ∘ )	$e_{t}$ (m)
MonoViT	$\mathrm{Sim}(3)$ , scale-free	42.6	106.8	5.2	2.4	0.81	–	–
IMU, 10 Hz	$\mathrm{SE}(3)$ , metric	38.3	67.1	8.4	30.1	2.86	–	–
EKF	$\mathrm{SE}(3)$ , metric	47.5	99.4	6.1	18.7	2.12	2.9	0.018
Original VINS–F	$\mathrm{SE}(3)$ , metric	31.4	43.6	4.0	29.0	1.76	– †	– †
Original VINS–O	$\mathrm{SE}(3)$ , metric	88.6	116.9	4.2	29.2	1.78	4.5	0.28
VINS+Pose–F	$\mathrm{SE}(3)$ , metric	31.8	44.1	3.9	28.8	1.72	– †	– †

TABLE VI: Unified main result on the representative KITTI sequence. All methods use matched timestamps and the common coordinate convention; APE uses the sequence-level alignment specified in Section III-E , and RPE uses 20-frame intervals. The alignment column states the APE gauge for each method: one sequence-level

\mathrm{Sim}(3)

transform is used only for the scale-ambiguous monocular trajectory, whereas metric estimators use

\mathrm{SE}(3)

without scale adjustment. Fixed (F) excludes the reference extrinsic from optimization, whereas Online (O) initializes from the same value and optimizes it.

Fig. 18: Preliminary trajectory comparison on the KITTI sequence. Black: ground truth; blue: MonoViT; green: EKF with reference input; gray: EKF under

1^{\circ}/5

cm extrinsic perturbation; red: VINS+Pose; orange: VINS+Pose under the same perturbation; purple: IMU-only propagation.

Fig. 19: Complementary 3-D view of the preliminary KITTI comparison. Black: ground truth; red: VINS+Pose; green: EKF with reference input; blue: standalone MonoViT; purple: IMU-only propagation.

Fig. 20: Diagnostic trajectory comparison on Recording 9. The two panels compare ground truth, GPS, 10 Hz and 100 Hz IMU propagation, MonoViT, VINS+Pose–F, and VINS+Pose–O. The 10/100 Hz curves are not interpreted as a strict one-variable ablation.

Fig. 21: Absolute and frame-to-frame pose errors of the MonoViT-based fused configurations at 10 Hz. The left column presents accumulated rotation and translation errors with respect to the reference trajectory, and the right column presents relative errors between consecutive frames.

Configuration	Rec. 1	Rec. 6	Rec. 7	Rec. 9	Mean
Original VINS–F	79.2	65.1	24.8	31.4	50.1
Original VINS–O	91.8	79.6	31.9	88.6	73.0
VINS+Pose–F	78.5	65.9	23.9	31.8	50.0
VINS+Pose–O	95.4	83.8	30.7	95.0	76.2
VINS+Pose–F–H	84.1	71.8	25.2	35.7	54.2

TABLE VII: Cross-sequence translation APE RMSE (m). F and O denote fixed and online-updated extrinsics, and H denotes the higher pose-prior weight.

Configuration	Mean Trans. RPE (m)	Mean $e_{R}$ ( ∘ )	Mean $e_{t}$ (m)	Prior $\Delta$ APE	Online $\Delta$ APE
Original VINS–F	17.7	–	–	–	–
Original VINS–O	17.9	5.2	0.26	–	+45.7%
VINS+Pose–F	17.6	–	–	$-0.2$ %	–
VINS+Pose–O	18.0	5.5	0.30	+4.4%	+52.1%
VINS+Pose–F–H	19.0	–	–	+8.2%	–

TABLE VIII: Aggregate statistics across the four-recording stress panel. Prior

\Delta

APE compares each VINS+Pose setting with Original VINS under the matched extrinsic strategy; Online

\Delta

APE compares Online with Fixed for the same estimator. Per-recording differences are retained in Table VII ; no win/tie/loss statistic is reported.

Fig. 22: Absolute and frame-to-frame pose errors of VINS, VINS+Pose, and standalone MonoViT on KITTI at 10 Hz. The left column shows the absolute Roll, Pitch, Yaw, and translation errors with respect to the reference trajectory, while the right column shows the corresponding relative errors between consecutive frames.

Fig. 23: Absolute trajectory error comparison of VINS, VINS+Pose, and standalone MonoViT on KITTI at 10 Hz. The first three plots show the signed trajectory errors along the (x)-, (y)-, and (z)-axes, and the last plot shows the Euclidean position-error magnitude. VINS and VINS+Pose exhibit similar accumulated drift, with the (y)-direction contributing most strongly to the final error.

Fig. 24: Qualitative trajectory comparison of standalone MonoViT, baseline VINS, and VINS+Pose on KITTI at 10 Hz. The left panel shows the estimated trajectories in 3D space, while the right panel presents a near top-down view.

Fig. 25: Qualitative trajectory comparison on the KITTI sequence under different estimation configurations. The left panel compares the MonoViT-only trajectory, ground-truth trajectory, original VINS trajectory, and VINS augmented with MonoViT priors. The right panel provides a broader comparison among original VINS, VINS with different initialization settings, VINS+Pose, VINS+Pose+Depth, VINS using accurate extrinsics with synchronized or unsynchronized inputs, and pure IMU integration.

Fig. 26: Enlarged trajectory comparison of Original VINS, VINS+Pose, and VINS+Pose+Depth on KITTI, each evaluated without and with an initial extrinsic guess.

Fig. 27: Unified translation APE comparison on Recording 9. The figure presents summary statistics, frame-wise APE, box plots, and error distributions for 10 Hz IMU integration, MonoViT, VINS+Pose with fixed accurate extrinsics, and VINS+Pose with online-updated extrinsics.

Fig. 28: Non-aligned rotation-APE diagnostic on Recording 9. The shared offset of the IMU and VINS-based curves is treated as a coordinate-convention diagnostic; common-frame geodesic rotation results are reported in Table VI .

Fig. 29: Unified translation RPE comparison on Recording 9 using 20-frame relative-motion intervals. MonoViT achieves the lowest local translation error, whereas the 10 Hz IMU and both VINS+Pose configurations exhibit similar and substantially larger RPE distributions.

Fig. 30: Unified rotation RPE comparison on Recording 9 using 20-frame relative-motion intervals. MonoViT provides the smallest local rotation error, while the 10 Hz IMU and the fixed- and online-updated VINS+Pose configurations show similar distributions and several intermittent peaks.

Configuration	Initialization	Type	$X^{\circ}$	$Y^{\circ}$	$Z^{\circ}$	$X$ (m)	$Y$ (m)	$Z$ (m)
Ground truth	–	Reference	-90.48729137	-0.38888106	-90.06237834	1.14397089	-0.24640917	0.726095982
Original VINS	With initial guess	Initial	-89	-1.3	-92	1.1	-0.33	-0.76
	With initial guess	Final	-90.35956866	-0.22624389	-90.88670221	1.53586	-0.26856	0.025663
	Without initial guess	Final	-90.3724879	-0.23212652	-90.85027338	1.53325	-0.25550	0.025118
VINS + Pose	With initial guess	Initial	-89	-1.3	-92	1.1	-0.33	-0.76
	With initial guess	Final	-90.35184219	-0.22184828	-90.92993365	1.53766	-0.27628	0.028382

TABLE IX: Camera–IMU extrinsic estimation on KITTI under different VINS configurations. The table compares the reported ground-truth extrinsic parameters with the final estimates obtained using the original VINS, VINS with a learned pose prior, and VINS with both learned pose and depth priors. Each configuration is evaluated with and without an initial extrinsic guess.

Fig. 31: EKF state estimation on KITTI camera-IMU data. The standalone EKF is evaluated on a KITTI sequence and estimates the IMU trajectory, camera-IMU extrinsic rotation and translation, velocity, gyroscope bias, and accelerometer bias.

Fig. 32: Initial and final camera-IMU extrinsic calibration estimated by EKF. The comparison shows that the EKF updates both the rotation and translation components of the camera-IMU extrinsic parameters during filtering.

Fig. 33: Sensitivity of EKF calibration to extrinsic uncertainty settings. Different standard deviations for rotation and translation lead to different final camera-IMU calibration results.

	Euler X (degree)	Euler Y (degree)	Euler Z (degree)	Translation X (m)	Translation Y (m)	Translation Z (m)
Initial extrinsic $\left(T_{imu}^{cam}\right)$	$-172.32349504$	$-89.50831883$	$-97.28789169$	$-0.31639699$	$0.73412053$	$-1.13803616$
Final extrinsic $\left(T_{imu}^{cam}\right)$	$-174.55866147$	$-89.52892101$	$-95.06993940$	$-0.31647713$	$0.73426570$	$-1.13823503$

TABLE X: Initial and final camera–IMU extrinsic parameters estimated by EKF.

Fig. 34: EKF-based camera-IMU extrinsic estimation on KITTI. The top row shows the estimated extrinsic Euler angles over 1,591 frames, and the bottom row shows the corresponding Euler-angle errors.

Fig. 35: Estimated camera–IMU extrinsic translation on the KITTI sequence. The top row shows the three translation components over 1,591 frames, and the bottom row shows the corresponding translation errors.

Fig. 36: EKF-based extrinsic calibration under noisy initial camera-IMU extrinsic parameters.

Fig. 37: State and uncertainty evolution under noisy extrinsic initialization.

	Euler X (degree)	Euler Y (degree)	Euler Z (degree)	Translation X (m)	Translation Y (m)	Translation Z (m)
	noise: $+5^{\circ}$	noise: $+5^{\circ}$	noise: $+5^{\circ}$	noise: $+0.5$ m	noise: $+0.5$ m	noise: $+0.5$ m
Initial extrinsic $T^{cam}_{imu}$	$-172.32349504$	$-89.50831883$	$-97.28789169$	$-0.31639699$	$0.73412053$	$-1.13803616$
Initial extrinsic $T^{cam}_{imu}$ with noise	$-167.32349504$	$-84.50831883$	$-92.28789169$	$0.18360301$	$1.23412053$	$-0.63803616$
Final extrinsic $T^{cam}_{imu}$	$-167.17817826$	$-84.59956387$	$-92.58437387$	$0.18692406$	$1.23301629$	$-0.64005155$

TABLE XI: Sensitivity of the EKF-based camera-IMU calibration to noisy initial extrinsic parameters. The reference camera-IMU extrinsic calibration is perturbed by adding

+5^{\circ}

noise to each Euler angle and

+0.5

m noise to each translation component.

	Euler X (degree)	Euler Y (degree)	Euler Z (degree)	Translation X (m)	Translation Y (m)	Translation Z (m)
Initial extrinsic	$-172.32349504$	$-89.50831883$	$-97.28789169$	$-0.31639699$	$0.73412053$	$-1.13803616$
Final extrinsic	$-170.9849859$	$-89.46088956$	$-98.65446204$	$-0.31577226$	$0.7352607$	$-1.13762793$

TABLE XII: Initial and final camera-IMU extrinsic parameters under a different EKF initialization setting. The experiment is conducted on the KITTI Raw sequence 2011_09_30_drive_0033using camera2 images and IMU measurements.

Fig. 38: EKF extrinsic estimation under a different initialization and observation setting. The estimated extrinsic Euler angles and translations are shown over 1,591 frames, together with their corresponding errors.

	Euler X (degree)	Euler Y (degree)	Euler Z (degree)	Translation X (m)	Translation Y (m)	Translation Z (m)
	noise: $+5^{\circ}$	noise: $+5^{\circ}$	noise: $+5^{\circ}$	noise: $+0.5$ m	noise: $+0.5$ m	noise: $+0.5$ m
Initial extrinsic	$-172.32349504$	$-89.50831883$	$-97.28789169$	$-0.31639699$	$0.73412053$	$-1.13803616$
Initial extrinsic $T^{cam}_{imu}$ with noise	$-167.32349504$	$-84.50831883$	$-92.28789169$	$0.18360301$	$1.23412053$	$-0.63803616$
Final extrinsic $T^{cam}_{imu}$	$-167.06484475$	$-84.56242678$	$-92.71730718$	$0.18739741$	$1.23303677$	$-0.63924515$

TABLE XIII: Sensitivity analysis of EKF-based camera-IMU calibration under noisy initial extrinsic parameters. A perturbation of

+5^{\circ}

is added to each Euler angle and

+0.5

m is added to each translation component.

Fig. 39: EKF state and uncertainty evolution under noisy extrinsic initialization.

Fig. 40: Estimated camera-IMU extrinsic parameters with noisy initialization. The top rows show the estimated extrinsic Euler angles and translations, while the bottom rows show their corresponding errors.

Fig. 41: VINS trajectory estimation on Recording 1 using 100 Hz IMU measurements. The two panels show the baseline VINS result and the VINS result under the accurate camera–IMU extrinsic configuration.

Fig. 42: VINS+Pose trajectory estimation on Recording 1 using 100 Hz IMU measurements. The two panels compare the standard VINS+Pose configuration with the corresponding accurate-extrinsic configuration.

Fig. 43: Temporal evolution of camera–IMU extrinsic errors under online calibration with accurate initialization. The plots compare VINS and VINS+Pose at 100 Hz in terms of Roll, Pitch, Yaw, and the x-, y-, and z-translation errors.

Fig. 44: Geometric comparison of the reference and online-updated camera–IMU extrinsic frames. The two panels visualize the IMU frame, the reference camera frame, and the final camera frames estimated by VINS and VINS+Pose from different viewpoints.

Fig. 45: Component-wise VINS+Pose pose estimation on Recording 9 with fixed accurate camera–IMU extrinsics. The left column compares the estimated and reference translations along the x-, y-, and z-axes, while the right column compares Roll, Pitch, and Yaw.

Fig. 46: Absolute and relative pose errors of VINS+Pose with fixed accurate camera–IMU extrinsics on Recording 9. The figure reports translation and rotation APE and 20-frame translation and rotation RPE without trajectory alignment.

Fig. 47: Component-wise VINS+Pose pose estimation on Recording 9 with accurate extrinsic initialization followed by online updating. The x-translation remains broadly consistent with the reference, but the y-component develops a substantially larger accumulated bias than in the fixed-extrinsic configuration, and a residual z-offset remains.

Fig. 48: Absolute and relative pose errors of VINS+Pose with online-updated camera–IMU extrinsics on Recording 9. Translation APE exceeds 120 m, substantially larger than the maximum error obtained when the accurate extrinsic is fixed, while rotation APE remains nearly unchanged.

Recording	$e_{R}^{\mathrm{init}}$ ( ∘ )	$e_{R}^{\mathrm{final}}$ ( ∘ )	$e_{t}^{\mathrm{init}}$ (m)	$e_{t}^{\mathrm{final}}$ (m)	Trans. APE RMSE (m)	Final Status
00	91.8	78.6	0.84	0.72	84.5	Failure
01	19.4	14.8	0.32	0.24	44.2	Partial
02	29.7	24.6	0.47	0.39	61.8	Partial
04	17.7	12.9	0.29	0.22	58.7	Partial
05	11.0	10.4	0.18	0.16	36.4	Partial
06	87.1	71.5	0.79	0.67	88.9	Failure

TABLE XIV: Camera–IMU calibration from initialization to final backend optimization.

Fig. 49: Initialization results of the camera–IMU rotational extrinsics under Extrinsic Configuration A for Recordings 00, 01, and 02. All three recordings share the same reported ground-truth rotation, while VINS+Pose is initialized without an extrinsic initial guess. The estimated Euler-angle components vary substantially across the three recordings, indicating limited cross-sequence repeatability under this configuration.

Fig. 50: Initialization results of the camera–IMU rotational extrinsics under Extrinsic Configuration B for Recordings 04, 05, 06. All recordings use the same reported ground-truth rotation, and the extrinsic parameters are initialized without an initial guess. The results exhibit substantial sequence-dependent variation, ranging from close agreement with the reference calibration to partial convergence and pronounced failure.

Fig. 51: Initialization results of the camera–IMU rotational extrinsics under Extrinsic Configuration B for Recordings 07, 09, and 10. All recordings use the same reported ground-truth rotation, and the extrinsic parameters are initialized without an initial guess. The results exhibit substantial sequence-dependent variation, ranging from close agreement with the reference calibration to partial convergence and pronounced failure.

Record	Setting	Type	$X^{\circ}$	$Y^{\circ}$	$Z^{\circ}$	$X$ (m)	$Y$ (m)	$Z$ (m)
Platform Comparison	VINS	Final	0.14281475	0.94385128	89.108527	-0.0148978	-0.0730938	-0.00928565
Platform Comparison	VINS w/o ROS	Final	0.14305244	0.94385065	89.10844729	-0.0148932	-0.0730920	-0.00928351
Easy	w/o initial guess	Ground truth	0.21528577	1.47693	89.14795267	-0.02164015	-0.06467699	0.00981073
		VINS initial	4.75384824	2.87952249	90.81859944	-0.0423088	-0.0822441	-0.0292757
		VINS final	0.14301377	0.9436808	89.10860882	-0.0148989	-0.0730824	-0.00927712
	with initial guess	Ground truth	0.21528577	1.47693	89.14795267	-0.02164015	-0.06467699	0.00981073

TABLE XV: Raw-parameter diagnostic for Original VINS Online extrinsic calibration on EuRoC sequences with different difficulty levels. For each sequence, the source-reported ground-truth, initial, and final Euler/translation parameters are listed. Because transform direction and Euler order were not retained, these rows are not converted to common-frame

e_{R}/e_{t}

and are used only for within-parameterization comparisons.

Fig. 52: APE over time on the difficult EuRoC sequence. The trajectory is aligned using SE(3) Umeyama alignment.

Fig. 53: 3D trajectory visualization on the difficult EuRoC sequence. The dashed line denotes the reference trajectory, and the estimated trajectory is colored by APE.

Fig. 54: Qualitative trajectory comparison with fixed accurate camera–IMU extrinsics at 10 Hz. The black, blue, and red curves denote the ground truth, MonoViT, and VINS trajectories, respectively.

Fig. 55: RPE and APE comparison of MonoViT and VINS with fixed accurate camera–IMU extrinsics at 10 Hz.

Fig. 56: MonoViT trajectory estimation on Recording 1. The blue curve denotes the MonoViT trajectory, and the dashed curve denotes the reference trajectory.

Fig. 57: Component-wise comparison between the MonoViT pose and the reference trajectory on Recording 1. The translation plots show the x-, y-, and z-position components, while the rotation plots show Roll, Pitch, and Yaw.

Fig. 58: Effect of VINS initialization on 100 Hz IMU propagation in Recording 1. The left panel shows the trajectory obtained before visual–inertial initialization, while the right panel shows the trajectory after estimating the initial orientation, gravity direction, velocity, and IMU biases.

Fig. 59: Component-wise MonoViT pose estimation on the camera-unfriendly Recording 1. The left column compares the estimated and reference

x

-,

y

-, and

z

-translations, while the right column compares Roll, Pitch, and Yaw.

Fig. 60: Absolute and relative pose errors of MonoViT on the camera-unfriendly Recording 1. The first two rows show translation and rotation APE and their spatial distributions, while the last two rows show the corresponding 20-frame translation and rotation RPE.

Fig. 61: Qualitative comparison between the MonoViT and reference trajectories on Recording 1. The left panel shows the complete three-dimensional trajectories, and the right panel enlarges a representative local segment together with the estimated orientations.

Fig. 62: Qualitative comparison of standalone motion estimates on Recording 1. The two views compare the ground truth, GPS, 10 Hz IMU integration, 100 Hz IMU integration, and MonoViT.

Fig. 63: Component-wise comparison between 10 Hz IMU-only integration and the reference trajectory on Recording 1. The

x

- and

y

-translations reproduce the dominant forward motion, whereas the

z

-component accumulates severe negative drift.

Fig. 64: Absolute and relative pose errors of 10 Hz IMU-only integration on Recording 1. The figure reports translation and rotation APE and 20-frame translation and rotation RPE without trajectory alignment.

Fig. 65: Optical-flow comparison between Recording 9 and Recording 1. The top panel shows consecutive-frame feature tracks in Recording 9, and the bottom panel shows those in Recording 1.

Fig. 66: Camera–IMU extrinsic convergence after reinitializing Recording 9 from frame 300 using 100 Hz IMU measurements. The figure compares baseline VINS, VINS initialized with accurate extrinsics, VINS+Pose, and VINS+Pose initialized with accurate extrinsics.

Fig. 67: Representative tracks and candidate outliers. Vegetation, dynamic objects, and low-texture forward motion produce candidate outliers.

Fig. 68: Spatially nonuniform tracking uncertainty. Track density and uncertainty vary across the image.

Fig. 69: Feature clustering and inconsistent boundary tracks. A challenging road frame contains sparse constraints near the road center and inconsistent tracks near boundaries.

Fig. 70: Robustness of VINS online camera–IMU calibration to extrinsic perturbations and late accurate-extrinsic injection. The figure shows the Roll, Pitch, and Yaw rotation errors and the

x

-,

y

-, and

z

-translation errors for accurate-extrinsic initialization with online updating, initial perturbations of

2^{\circ}/2~\mathrm{cm}

,

6^{\circ}/6~\mathrm{cm}

, and

10^{\circ}/10~\mathrm{cm}

, and late injection of the accurate extrinsic after backend convergence. Roll, Pitch, and

y

-translation generally recover after the initialization transient, whereas Yaw and the

x

- and

z

-translation components retain initialization-dependent residual errors.

Fig. 71: Backend optimization cost under different extrinsic initialization and injection strategies.

Fig. 72: Consistency comparison between the SfM trajectory and the raw unscaled MonoViT trajectory on Recording 9. The two estimates differ substantially in scale, spatial extent, and three-dimensional geometry.

Rec.	Setting	$e_{s}$ (%)	$\Delta_{\mathrm{BA}}$ (%)	Trans. APE RMSE (m)	Trans. RPE RMSE (m)	$e_{R}$ ( ∘ )	$e_{t}$ (m)	Normalized Cost
00	Accurate	82.2	2.8	38.6	12.4	3.1	0.09	1.00
00	Perturbed	80.3	3.0	46.8	12.8	4.7	0.13	1.03
01	Accurate	90.3	2.4	34.2	10.7	4.3	0.11	1.00
01	Perturbed	94.1	2.6	36.1	10.9	5.8	0.15	1.03
02	Accurate	99.6	8.9	71.4	18.6	12.7	0.29	0.98
02	Perturbed	99.7	9.7	94.8	20.1	16.9	0.36	1.02

TABLE XVI: Joint quantitative analysis of scale, BA correction, trajectory error, final calibration, and backend cost. Relative scale errors use the recorded estimated and recorded reference scale values. Normalized Cost is the total final objective under the stated diagnostic normalization, not a per-residual cost, and is interpreted only within each matched recording pair.

Fig. 73: Joint trajectory comparison under accurate, perturbed, and automatically estimated camera–IMU extrinsic settings for Recordings 05, 07, 09, and 10. The top panel compares the camera-coordinate keyframe trajectories before and after bundle adjustment. The middle panel places the visual trajectories together with the ground truth in the camera coordinate system. The bottom panel compares the ground truth, direct IMU integration, and aligned visual–inertial trajectories in the IMU coordinate system. Dashed curves use the scale estimated during initialization, whereas solid curves use the recorded reference scale.

Fig. 74: Controlled comparison of camera–IMU extrinsic perturbation for Recording 00. Panels (a) and (b) show the results obtained with accurate and perturbed extrinsics, respectively. The local visual trajectories before and after bundle adjustment remain qualitatively similar under the two settings, while the estimated initialization scale changes from

5.912

to

6.550

, compared with a recorded reference scale of

33.182

. Although the perturbed scale is numerically slightly closer to the ground-truth value, the ground-truth-scale-aligned trajectory exhibits a larger lateral deviation, showing that scale proximity alone does not guarantee improved trajectory geometry.

Fig. 75: Controlled comparison of camera–IMU extrinsic perturbation for Recording 01. Panels (a) and (b) correspond to accurate and perturbed extrinsics, respectively. The before- and after-BA trajectories preserve similar local geometry under both settings, whereas the estimated scale decreases from

3.103

to

1.880

, compared with the recorded reference scale of

31.977

. After recorded-reference-scale alignment, the dominant trajectory direction remains comparatively similar, indicating that this recording is more sensitive in scale than in large-scale trajectory shape.

Fig. 76: Controlled comparison of camera–IMU extrinsic perturbation for Recording 02. Panels (a) and (b) show the accurate- and perturbed-extrinsic results, respectively. Bundle adjustment introduces a pronounced change in the local visual trajectory under both settings. The estimated scale decreases from

0.113

to

0.086

, while the recorded reference scale is

30.731

. Under the perturbed extrinsics, the ground-truth-scale-aligned trajectory exhibits a substantially larger lateral drift, indicating sensitivity in both scale recovery and global trajectory direction.

Fig. 77: Controlled comparison of camera–IMU extrinsic perturbation for Recording 04. Panels (a) and (b) present the results with accurate and perturbed extrinsics, respectively. The local bundle-adjusted visual trajectories remain similar, but the estimated scale decreases from

0.126

to

0.032

, compared with the recorded reference scale of

33.274

. After recorded-reference-scale alignment, the perturbed-extrinsic trajectory develops a much larger lateral displacement, demonstrating pronounced sensitivity of both metric-scale initialization and global trajectory geometry.

Fig. 78: Controlled comparison of camera–IMU extrinsic perturbation for Recording 06. Panels (a) and (b) correspond to accurate and perturbed extrinsics, respectively. The accurate-extrinsic result contains a pronounced non-smooth change in the bundle-adjusted visual trajectory, whereas the perturbed setting produces a different piecewise correction. The estimated scale decreases from

0.485

to

0.178

, relative to a recorded reference scale of

28.001

. Despite this scale change, the ground-truth-scale-aligned trajectories retain a broadly similar dominant forward direction, indicating stronger sensitivity in optimization and scale than in final large-scale shape.

Fig. 79: No-loop implementation check. The left and right panels show the VINS+Pose and Original VINS pipelines, respectively, with loop closure disabled. Their difference establishes a pipeline mismatch and is not used as evidence for a loop-closure effect.

Fig. 80: Qualitative trajectory reshaping with loop closure disabled (left) and enabled (right). Rows show VINS+Pose with accurate extrinsics, Original VINS with default extrinsics, and Original VINS with accurate extrinsics. Loop closure changes global geometry in all three pairs, but the correction depends on the pipeline and extrinsic setting.

Configuration	APE No Loop	APE Loop	$\Delta$ APE	RPE No Loop	RPE Loop	$\Delta$ RPE	Global Correction Magnitude (m)
VINS+Pose, accurate ext.	39.8	31.7	$-20.4\%$	11.6	11.4	$-1.7\%$	28.4
Original VINS, default ext.	52.6	58.9	$+12.0\%$	13.4	13.1	$-2.2\%$	41.7
Original VINS, accurate ext.	36.4	29.8	$-18.1\%$	10.9	10.7	$-1.8\%$	25.9

TABLE XVII: Controlled loop-closure comparison over matched timestamps. APE uses the common sequence-level alignment, RPE uses 20-frame intervals, and global correction magnitude is defined by Eq. ( 9 ). Negative changes denote an improvement.

When Do Learned Priors Help Visual Inertial Estimation? A Controlled Study of Prior Integration, Calibration, Initialization, and Backend Consistency

Abstract

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Abstract

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