E:\_NEW \Cv\Pubs\IDC2002_Cepstrum.doc FLIGHT PARAMETER IDENTIFICATION FROM CEPSTRUM TRACKS Y Gao, G Pulford, J Sendt and A Maguer Thomson Marconi Sonar P/L 274 Victoria Road, Rydalmere, NSW, 2116, Australia Gao.yujin@tms.pty.com ABSTRACT By using a single microphone located above the ground, it is possible to determine the flight parameters of an aircraft fly-over. This technique utilises the asymmetry of the Lloyds mirror rings (LMR) that have been converted into a primary rahmonic in the cepstrogram of the acoustic data. Unlike previous techniques, the spectrogram is not needed. The cepstrum data are automatically processed by a hidden Markov model tracker that provides input to the flight parameter estimation stage. The Levenberg Marquardt optimisation procedure is then applied to derive aircraft speed along with the time, horizontal distance and height of the closest point of approach. Reliable cepstrogram estimates are obtainable when at least three LMR's are present in the spectrogram data. 1. INTRODUCTION During an aircraft flyover with sufficient broadband signal being received at an above-ground sensor, the received signal will include signals from the direct path and the reflected path (as shown in Figure 1.1). This generates the so-called Lloyd’s Mirror (LM) phenomenon. In this paper the flight path is assumed to be a straight line with constant height, although the interference pattern occurs with other flight paths, e.g., turning aircraft. The time history of the broadband interference pattern can be exploited to provide estimates of the flight parameters from the data received by a single sensor. It is necessary however that the reflection from the ground be strong enough in amplitude so that the interference fringes can be distinguished by the chosen signal processing technique. This requires that the emitted broadband signal extend as far as is practical in the frequency domain, that the solid grazing angle of the aircraft position as referenced to the sensor is above a minimum value and that the ground has a high reflection coefficient. These criteria limit the maximum range at which useful interference data is received. Increasing the height of the sensor will also increase the maximum range. Fig. 1.1. Source-sensor geometry In the time-frequency domain, the LM forms a defined pattern with peaks and troughs, as shown in the spectrogram in Fig 1.2. These troughs represent the interference frequencies, also called destructive frequencies. Lo and Ferguson showed that the destructive frequencies could be exp ressed as [1]: ( 29 ) ( ) ( ) )( ( ) ( 4 ) 1 2 ( ) , ( 2 2 2 2 2 2 2 2 2 2 2 cpa cpa cpa t r t m t t v t t c v v c d h h h v c c m t f - - - + - + × - - = β (1.1) where h r is the sensor height, c the sound speed and ] , , [ , cpa cpa t t d h v = β (1.2) The components of β are the flight parameters: the constant subsonic aircraft velocity v; the constant height h t ; the ground range at the Closest Point of Approach (CPA) to the sensor d cpa and the time at which the aircraft is at the CPA t cpa , as illustrated in Figure 1.1. The paper is organised as follows. Section 2 briefly discusses the principle of cepstrum analysis and the representation of the multiple path interference in the time-quefrency domain. Section 3 demonstrates how the multiple path interference track (the first rahmonic track in Figure 2.1) is extracted using Hidden Markov Models (HMM). Estimating flight parameters from harmonic tracks is carried out in Section 4. Conclusions are given in Section 5. h t h r d cpa Sensor Aircraft Flight path v