Dual-Branch INS/GNSS Fusion with Inequality and Equality Constraints

Mor Levenhar; Itzik Klein

cs.ROFeb 24, 2026

Dual-Branch INS/GNSS Fusion with Inequality and Equality Constraints

Authors: Mor Levenhar, Itzik Klein

Organizations: I. Klein and M. Levenhar are with the Autonomous Navigation and Sensor Fusion Lab, Hatter Department of Marine Technologies, University of Haifa, Israel.

Abstract

Reliable vehicle navigation in urban environments remains a challenging problem due to frequent satellite signal blockages caused by tall buildings and complex infrastructure. While fusing inertial reading with satellite positioning in an extended Kalman filter provides short-term navigation continuity, low-cost inertial sensors suffer from rapid error accumulation during prolonged outages. Existing information aiding approaches, such as the non-holonomic constraint, impose rigid equality assumptions on vehicle motion that may be violated under dynamic urban driving conditions, limiting their robustness precisely when aiding is most needed. In this paper, we propose a dual-branch information aiding framework that fuses equality and inequality motion constraints through a variance-weighted scheme, requiring only a software modification to an existing navigation filter with no additional sensors or hardware. The proposed method is evaluated on four publicly available urban datasets featuring various inertial sensors, road conditions, and dynamics, covering a total duration of 4.3 hours of recorded data. Under Full GNSS availability, the method reduces vertical position error by 16.7% and improves altitude accuracy by 50.1% over the standard non-holonomic constraint. Under GNSS-denied conditions, vertical drift is reduced by 24.2% and altitude accuracy improves by 20.2%. These results demonstrate that replacing hard motion equality assumptions with physically motivated inequality bounds is a practical and cost-free strategy for improving navigation resilience, continuity, and drift robustness without relying on additional sensors, map data, or learned models.

Figures & tables

Abbreviation	Description
ARMSE	Altitude RMSE
ECEF	Earth-Centered Earth-Fixed
EKF	Extended Kalman Filter
es-EKF	Error-State Extended Kalman Filter
GNSS	Global Navigation Satellite System
GPS	Global Positioning System

TABLE I : Abbreviations and Descriptions.

Fig. 1 : Proposed dual-branch EKF architecture. Inertial readings are always available and feed both branches continuously. GNSS input is switchable, allowing both branches to operate with or without satellite positioning.

DATASET	Number of Trajectories	TOTAL DISTANCE (km)	TOTAL TIME (min)	AVG. HEIGHT RANGE (m)	IMU Rate (Hz)
Hongkong	3	11.20	77.4	8.73	100
Odyssey	12	43.05	82.2	29.96	250
Tokyo	2	14.28	55.6	11.59	50
Kitti	12	24.69	45.4	20.63	100

TABLE II : Main Dataset Parameters.

PRMSE [m]
Dataset	EKF	NHCEKF	INQEKF	Dual-Branch
			(ours)	(ours)
Hongkong	6.80	6.48	6.22	6.17
	(9.3%)	(4.8%)	(0.9%)
Odyssey	6.86	6.48	6.38	6.30
	(8.2%)	(2.8%)	(1.3%)

TABLE III : RMSE under full GNSS availability. Percentages in parentheses indicate the improvement of our dual-branch approach over the other methods.

Horizontal Position RMSE [m]
Dataset	EKF	NHCEKF	INQEKF	Dual-Branch
			(ours)	(ours)
Hongkong	5.61	5.52	5.59	5.53
	(1.3%)	(-0.2%)	(1.1%)
Odyssey	5.71	5.73	5.71	5.61
	(1.6%)	(2.1%)	(1.7%)

TABLE IV : Position RMSE under full GNSS availability. Percentages in parentheses indicate the improvement of our dual-branch approach over other methods.

Metric	EKF	NHCEKF	INQEKF	Dual-Branch
			(ours)	(ours)
Horizontal	10.21	10.25	10.25	10.10
	(1.1%)	(1.4%)	(1.5%)
Position [m]
Vertical	7.66	6.74	5.52	5.52
	(28.0%)	(18.1%)

TABLE V : 95th Percentile Error under full GNSS availability. Percentages in parentheses indicate the improvement ofour dual-branch approach over other methods.

Fig. 2 : Vertical position over time for the Theater sequence 2 (Odyssey dataset).

Fig. 3 : 2D trajectory comparison for the residential sequence 27 at 10/03/2011 (KITTI dataset).

PRMSE [m]
Dataset	EKF	NHCEKF	INQEKF	Dual-Branch
			(ours)	(ours)
Hongkong	93.71	30.24	136.33	33.01
	(64.8%)	(-9.1%)	(75.8%)
Odyssey	139.58	79.46	132.71	77.94
	(44.2%)	(1.9%)	(41.3%)

TABLE VI : RMSE under GNSS-denied scenarios. Percentages in parentheses indicate the improvement of our dual-branch approach over other methods.

Horizontal Position RMSE [m]
Dataset	EKF	NHCEKF	INQEKF	Dual-Branch
			(ours)	(ours)
Hongkong	91.93	30.01	136.30	32.88
	(64.2%)	(-9.6%)	(75.9%)
Odyssey	137.74	79.30	132.66	77.81
	(43.5%)	(1.9%)	(41.3%)

TABLE VII : Position RMSE under GNSS-denied scenarios. Percentages in parentheses indicate the improvement of our dual-branch approach over other methods.

Metric	EKF	NHCEKF	INQEKF	Dual-Branch
			(ours)	(ours)
Horizontal	279.06	196.58	279.16	182.10
Position [m]	(34.7%)	(7.4%)	(34.8%)
Vertical	61.96	10.83	7.58	6.22
Position [m]	(90.0%)	(42.5%)	(17.9%)
3D Velocity	18.78	19.26	19.06	16.88

TABLE VIII : 95th Percentile Error under GNSS-denied scenarios. Percentages in parentheses indicate the improvement of our dual-branch approach over other methods.

Fig. 4 : Vertical position error during run of the Shinjuku route (Tokyo dataset).

Fig. 5 : 2D trajectory during run 1 of the Theater route (Odyssey dataset) under GNSS outage conditions.

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Abstract

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