Fig 1.
Pulse emission and reflective echo patterns of the simulation.
(A) Typical time–frequency structure of the echolocation pulse emitted by Rhinolophus ferrumequinum Nippon. (B) Schematic diagram of amplitude modulation of CF2 component in the simulated echo caused by virtual pinnae motions. In this example simulation, the left and right ear movements were assumed to exhibit anti-phase motions in pitch angle over ±15°. The hearing axis in the right ear rotates down-forward and then up-backward, while that in the left ear rotates in the inverse direction. The amplitude-modulated echo was simulated by assuming the object has an elevation angle of 30°.
Fig 2.
Schematic diagram of model setup.
(A) Direction of the target (green ball) expressed by azimuth angle θ and elevation angle φ. (B) Positions of the two directional ears with spacing d. Each red dot indicates the position of an omni-directional microphone. Each ear consists of four omni-directional microphones, where δy and δz are the horizontal and vertical spacings of each microphone. (C) Hearing directivity pattern of the virtual ear. (D) Three axes (roll, pitch, yaw) fixed to the directional ear and corresponding orthonormal basis [nroll, npitch, nyaw].
Fig 3.
Schematic diagram of the supervised learning approach for obtaining the inverse map of M.
The ILD signal is calculated for all directions (θ, φ)∈X fixing the ear motions. It is discretized at time intervals of 1 ms and passed to the input layer of the neural network. In the neural network, the ReLU activation function is used in hidden layers 1, 2, and 3, and the mean squared error is the error function in the output layer.
Table 1.
Pairing types of left and right angle functions ,
.
Fig 4.
Examples of direction detection performance with and without ear motions.
(A1, B1): Combination of angle functions. (A2, B2): Colormaps of evaluation function UM(θ, φ) and the degree of injection I[M]. (A3, B3): Results of machine learning. Blue ‘x’ markers indicate test data (θ, φ) and red ‘+’ markers indicate output data (θguess, φguess). Black lines are the error lines connecting points (θ, φ) and (θguess, φguess). The detection error E[M] is also given.
Fig 5.
Examples of direction detection performance with appropriate ear motions.
The formation of Fig 5 is same as Fig 4. Blue color map and less-visible error lines mean the good performance of direction detection.
Fig 6.
Colormaps of UM(θ, φ) and the degrees of injection for various ear motion patterns.
The pitch angle functions are fixed to
according to actual bat behavior. Blue and orange lines indicate the angle functions of the left and right ears, respectively. The left and top array panels display the roll angle functions
and the yaw angle functions
, respectively.
Fig 7.
Five types of dimension pairs of the convex hull and each ear’s orbit.
The blue lines indicate the left ear’s orbit and the orange lines indicate the right ear’s orbit
. When both orbits coincide, only the orange line is displayed. The convex hull of the union of both ears’ orbits is displayed in each case.
Fig 8.
Dimension pairs and direction detection errors for various motion patterns.
In each box, the dimension pair of the convex hull and each ear’s orbit is given in the upper part, the degree of injection is given in the middle, and the detection error is given at the bottom. Here, we adopt E[M]<5° as the criterion for precise direction detection. The colored boxes indicate that the corresponding motion patterns give precise direction detection. The boxes bounded by red lines correspond to the motion patterns with large degrees of injection (I[M]>1).
Fig 9.
Relationship between I[M] and E[M] under various degradation levels of ILD resolution.
(A) Relationship between the degree of injection and the detection error for the 36 ear motions without the degradation of the ILD resolution. (B) Example of change in the sinusoidal signal for each degradation level. (C) Relationship between the degree of injection and the detection error for each ear motion under the degraded ILD resolutions. Note that these evaluations were conducted for ear motions with relatively small detection errors (E[M]<20°) in the no degradation condition (A). The length of the vertical black line corresponds to the increase in the detection error when the ILD discretization level changes from 0 dB to 3 dB.
Fig 10.
Colormaps of degree of injection I[M] of all combinations of ψe-φe-θe angle functions.
The fixation of the pitch angle functions to
is removed, so that the degrees of injection were evaluated for 63 = 216 motion patterns.
Fig 11.
Effect of phase difference of ear motions on direction detection performance.
In the upper panels, blue line indicates the left ear’s orbit given by , and orange line does the right ear’s orbit
, respectively. Black straight lines connect simultaneous points of the left and right ears’ orbits with the phase difference ΔΦ. In particular, the ear motion with ΔΦ = 180° is [
,
,
] and the ear motion with ΔΦ = 0° is [
, COS, SIN]. For motions with ΔΦ between 45° and 180°, good-quality direction detection performance is achieved.