3D Statistical Resolution Limit of Two Close
Spaced Targets for Active Array in the GLRT
Context
Pei Peng
(&) , Yunlei Zhang, and Jianbin Lu
Electronic Engineering Institute, Navy University of Engineering, Wuhan, China
46190145@qq.com
Abstract. The current research of the statistical resolution limit (SRL), which is
based on the hypothesis test, usually takes Taylor expansion and approximation
to get a linear model of general likelihood rate test (GLRT) and achieves an
analytical expression of the SRL. In the way, one dimension (range, angle) and
two dimensions (range-Doppler, angle-Doppler) SRLs have been explored. In
this paper we dwell on the three-dimension (3D) SRL in range-angle-Doppler
domain and discuss the factors which make effects on 3D SRL. Our theoretical
and simulation results both demonstrate that the 3D SRL is the weighting square
sum of three respective SRLs, which will throw some insights into the systemic
design to improve the resolution ability.
Keywords: Hypothesis test Á Active array Á 3D SRL Á GLRT Á
Taylor expansion and approximation
1 Introduction
Statistical resolution limit (SRL) indicates the minimum separation from the statistical
standpoint, which describes the ability of the system distinguishing two very close
parameters under some given resolution rate and false-alarm rate, and the ability is
related to the signal-noise-rate (SNR) and signal waveforms, etc. Nowadays, there are a
lot of researches about this, and on the one-dimension aspect, the authors in [1] studied
the range SRL in the optics domain, while authors in [2] and [3] made researches on the
passive array, which adopted the approximation general likelihood rate test (GLRT)
and the information entropy criteria, respectively. The DOA and DOD united SRL was
explored in [4]. On the multi-dimension aspect, the range-Doppler SRL was studied in
[5] for the active array, while the angle-Doppler SRL with space-time snaps was
explored in [6]. The authors in [7] had expended the united angle SRL to the Doppler
dimension. However, there is no research on the range-angle-Doppler domain yet.
In the reality for sensors like radar observing two or more very closely targets, their
parameters along with the range, angle and Doppler may be very close, so the research
of 3D SRL is necessary. From the results of the 2D SRL we can see that, the unit SRL
is a function of single SRLs, while for the transmitted the linear frequency modulation
(LFM) signal, the range-Doppler SRL in [5] is the weighting sum of range SRL and
Doppler SRL. In [6] the angle-Doppler SRL is also the function of the angle SRL and
© Springer Nature Singapore Pte Ltd. 2020
Q. Liang et al. (Eds.): Artificial Intelligence in China, LNEE 572, pp. 369–377, 2020.
https://doi.org/10.1007/978-981-15-0187-6_43
Spaced Targets for Active Array in the GLRT
Context
Pei Peng
(&) , Yunlei Zhang, and Jianbin Lu
Electronic Engineering Institute, Navy University of Engineering, Wuhan, China
46190145@qq.com
Abstract. The current research of the statistical resolution limit (SRL), which is
based on the hypothesis test, usually takes Taylor expansion and approximation
to get a linear model of general likelihood rate test (GLRT) and achieves an
analytical expression of the SRL. In the way, one dimension (range, angle) and
two dimensions (range-Doppler, angle-Doppler) SRLs have been explored. In
this paper we dwell on the three-dimension (3D) SRL in range-angle-Doppler
domain and discuss the factors which make effects on 3D SRL. Our theoretical
and simulation results both demonstrate that the 3D SRL is the weighting square
sum of three respective SRLs, which will throw some insights into the systemic
design to improve the resolution ability.
Keywords: Hypothesis test Á Active array Á 3D SRL Á GLRT Á
Taylor expansion and approximation
1 Introduction
Statistical resolution limit (SRL) indicates the minimum separation from the statistical
standpoint, which describes the ability of the system distinguishing two very close
parameters under some given resolution rate and false-alarm rate, and the ability is
related to the signal-noise-rate (SNR) and signal waveforms, etc. Nowadays, there are a
lot of researches about this, and on the one-dimension aspect, the authors in [1] studied
the range SRL in the optics domain, while authors in [2] and [3] made researches on the
passive array, which adopted the approximation general likelihood rate test (GLRT)
and the information entropy criteria, respectively. The DOA and DOD united SRL was
explored in [4]. On the multi-dimension aspect, the range-Doppler SRL was studied in
[5] for the active array, while the angle-Doppler SRL with space-time snaps was
explored in [6]. The authors in [7] had expended the united angle SRL to the Doppler
dimension. However, there is no research on the range-angle-Doppler domain yet.
In the reality for sensors like radar observing two or more very closely targets, their
parameters along with the range, angle and Doppler may be very close, so the research
of 3D SRL is necessary. From the results of the 2D SRL we can see that, the unit SRL
is a function of single SRLs, while for the transmitted the linear frequency modulation
(LFM) signal, the range-Doppler SRL in [5] is the weighting sum of range SRL and
Doppler SRL. In [6] the angle-Doppler SRL is also the function of the angle SRL and
© Springer Nature Singapore Pte Ltd. 2020
Q. Liang et al. (Eds.): Artificial Intelligence in China, LNEE 572, pp. 369–377, 2020.
https://doi.org/10.1007/978-981-15-0187-6_43