Table 1. Default parameter values for the synthesized trajectories, spherical camera model, and module model.

Some simulations have changed parameter values and we denoted this explicitly.

Description of parameter	Identifier and value
Synthesized trajectories inside a cube
Number of samples	n Sample = 50,000
Sampling frequency	f Sample = 20 Hz
Duration of the simulated time	T = 41.67 min
Peak location β v of the Rayleigh distribution	β v ≈ 13 cm/sec
Mean of the normal distribution	μ ω ≈ 0 deg/sec
Standard deviation of the normal distribution	σ ω ≈ 340 deg/sec
Width and length of the square environment	w Cube = l Cube = 150 cm
Height of walls	h Cube = 50 cm
Eye-height above ground	d = 2.5 cm
Number of visual features on ground, walls, and ceiling	n Features = 54
Number of samples on the ground	n Ground = 9
Spherical camera model
Horizontal field of view	h FoV = 360 deg
Vertical field of view	v FoV = 120 deg
Focal length	f Sphere = 1 cm
Module model
Initial head direction	φ 0 = 0 deg
Initial location	(x 0, y 0) = (0 cm, 0 cm)
Regularization parameter	α = 10−4
Velocity controlled oscillator model
Oscillation of theta rhythm	f = 7.38 Hz
Parameter for grid spacing–moving feature system	β 1 = 0.004
Parameter for grid spacing–static feature system	β 2 = 0.003
Threshold for spikes	ϴ = 1.8
Attractor model
Horizontal cells	n x = 9
Vertical cells	n y = 10
Synaptic peak strength	I = 0.3
Inhibition for weights	T = 0.05
Input gain (grid spacing)–moving feature system	α 1 = 1.4×10−3
Input gain (grid spacing)–static feature system	α 2 = 0.9×10−3
Gaussian standard deviation	σ = 0.24 meters
Grid orientation	γ = 0°
Threshold for firing	η = 0.1
Simulations
Standard deviation of velocity noise	σ v in units of deg/sec
Standard deviation of location noise	σ l in units of deg/sec
Mean of velocity noise	μ v in units of deg/sec
Mean of location noise	μ l in units of deg/sec