Error Analysis of Sound Source Localization System for Small Microphone Based on Time Delay Estimation Shang-Yue ZHANG

Transcription

1 017 3rd International onferene on omputer Siene and Mehanial utomation (SM 017) ISN: Error nalysis of Sound Soure Loalization System for Small Mirophone ased on Time elay Estimation Shang-Yue ZHNG ept. of Navigation, alian Naval ademy alian of hina Key words: Error analysis, Time delay, Small mirophone, Estimation. bstrat. ased on time delay,sound soure loalization method has a smaller amount of alulation ompared with the sound soure loalization method of ontrollable beam synthesizer and high resolution spetral estimation, and an ahieve a higher positioning auray after improved, so it is the most suitable method for real-time positioning, widely used in the field of passive aousti loalization. This paper tries to spread the fators that affet the positioning auray of time delay method, and provides the diretion for improving the effet of time delay sound soure loalization. Introdution Sound soure loalization method has a long history. From the military to the people's livelihood, a onsiderable part of the field has an urgent need for sound soure loalization. Espeially in military field, in the bakground of information warfare development, threats from the searh radar eletroni jamming, low altitude mutation, stealth tehnology and anti-radiation missile have beome a national onern, the tehnology on passive sensor is therefore drawing attention. Nowadays, passive aousti soure loalization is mainly used in the researh of intelligent mine bombs, airraft detetion and battlefield environment investigation. It is worth mentioning that the Iraq war, merian soldiers equipped with sound progenitor aousti measurement system an definite the position by measuring the muzzle shok wave reeived and projetile shok waves generated by flight, the positioning auray is 1. degree on bearing, horizontal 3 degrees, whih detet 90% shooting. On the battlefield, the auray of the positioning system one inreases by one perentage point, and the asualty rate of soldiers will be greatly dereased. From this point of view, tehnology is life. How to redue the error of the positioning system and improve the positioning auray is the key researh objet of the military sientifi researh personnel. This paper takes the small mirophone positioning system as an example, analyzes the positioning error of passive sound soure positioning, and provides referene for the researhers. Mirophone rray Model of Four Element ross rray Estimation on the reeived signal pikup is the key to time delay loation tehnology. Take the four element ross array as an example. 67

2 Establish a artesian oordinate system as the figure shows, set the orthogonal four pikups,,,,, the distane of the four pikups to the enter is, the soure as S, the artesian oordinates (x, y,z), spherial oordinate ( r,ϕ,θ ). ording to the transformation relationship between the retangular oordinate and the spherial oordinate, there is x rsinθosϕ y rsinθsinϕ z rosθ -90 θ 90, 0 φ 360 The time differene between the arrival time of the sound element,, is,, respetively the distane from,, to is d, d, d,then there is d d d 3400m/s. is the sound speed that sound travels in the air. ording to the priniple that sound is transmitted by spherial wave, the element is on the sphere with S as enter, we have: (1) ( x ) + y + z r x + ( y ) + z ( r + d ) ( x + ) + y + z ( r + d ) x + ( y + ) + z ( r + d ) () r is the distane between the sound soure and the element. From solution of formula () : d + d d r ( d d d ) dr + d x 4 ( d d ) r + ( d d ) y 4 onsidering the formulas, we have y ( d d ) r + d + d tan ϕ x d r + d sin θ ( x + y ) / r ( ) + (3) (4) (5) 68

3 r r + dr + d / d d ( r + ) + ( ) (6) When r d, d, d,there is To simplize the formula above: r + d + d d 1, 0 r + d d d ϕ d tan Therefore the solution is d r r + r ϕ artan (7) r θ arsin( ( ) + ) (8) + The estimation of aousti soure position by time delay estimation is as below: ϕ artan θ arsin( ( ) + ) + r (9) (10) Error nalysis zimuth Error nalysis Statistial error harateristis of time delay,, are the same, the azimuth error aused by time delay is eause that ϕ ϕ ϕ σ σ σ σ ϕ + + (11) 69

4 Let s take the derivatives:: Plug(13)into (11) Pith Error ϕ artan (1) ϕ 1 1 ϕ 1 + tan ϕ 1 (13) 1 + tan ϕ ϕ tan ϕ σ ϕ 1 + os ϕ σ (14) sin θ sin θ ( ) + (15) eause that Take partial respet to (17) Plug (18) into (16),we get: istane Error θ θ θ σ σ σ σ θ + + (16) θ arsin( ( ) + ) (17) θ sin θ θ sin θ ( ) θ sin θ ( ) σ ( θ ) + sin θ 1 + tan ϕ os θ 1 + tan ϕ Without onsidering the influene of effetive sound veloity error and array system error, given the upper bound of root mean square error for the azimuth estimation,we an alulate the upper (18) (19) 70

5 bounds of root mean square error for time delay estimation. The delay estimation error of four element ross array should satisfy the following formula: σ ϕ sin θ 1 + os ϕ (0) rray Mounting Errors The installation error of the array will ause the great ranging error, beause the lift damper an not be stritly arranged in a plane, three side. The four pikups with a little deviation, the positioning result will varies gravely. The researh shows that the influene of [] installation error of the measuring distane inreases with the azimuth angle, distane and the influene on the near distane so large target azimuth angle and distane is unfavorable state of passive loalization. Error aused by Media Sound waves are mehanial waves, and mehanial vibrations propagate in the medium to produe mehanial waves. The vibration of the soure body in the medium is alled sound waves. In the medium, there is interation fore between the partiles, and the sound wave travels in all diretions with the aid of the medium. It is a spherial array wave. The vibration of the partile near the wave soure drives the vibration of the partile far away from the soure, therefore the vibration transmission from the near to the distant. The transmission is vibration form and energy, eah partile vibrates only in their own equilibrium position, and will not move with the wave. The vibration period and frequeny of eah partile are onsistent with the vibration period and frequeny of the soure. Vibration is the ause of the flutuation, and the flutuation is the result of vibration propagation. single partile generates vibration and the vibration of a large number of partiles generates vibration. The higher the temperature is, the faster the speed will be. t 15 degrees, the sound speed is 340m/s in the air and 346m/s at 5 degrees. The relationship between temperature and wave speed an be expressed by the following formula: T (m/s) The propagation distane of aousti wave is first onerned with the absorption of atmosphere, followed by temperature, humidity, air pressure and so on. The near field model takes spherial wave as the objet of study, and the far field model takes plane wave as the objet of study. Noise The proess of pikup piking sound signal is inevitably affeted by environmental noise. Environmental noise inludes sound interferene from otherbody, and irregular osillation interferene air partile itself, but also onsider the reverberation sound field. Even if there is no voal body, the air partiles are always osillating irregularly. The motion is influened by many fators, and the most important fator is temperature. This is also the soure of "white noise". There is no sound field without white noise in the real environment, so the influene of white noise annot be ignored. Noise an be divided into two types, stationary noise and non-stationary noise. Stationary noise an be solved by ombining single mirophone and V based on statistis, and the noise superimposed on human voie will be more troublesome. For noise soures with referene signals, eho anellation algorithms an be used to eliminate them. Referenes [1] Xu Kexi.Some key tehniques of passive aousti detetion:[dissertation].nanjing: Nanjing University of Siene and Tehnology,

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