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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 3, March 2015. www.ijiset.com ISSN 2348 – 7968 Problem Solutions of Phase Ambiguity and Initial Phase Shifts of the Phase Radio Navigation System for Aircraft Blind Landing 1 2 Saed SasiP ,P Nasar Aldian ShashoaP P 1 P DepartmentP of Electrical and Computer Engineering , Libyan Academy, Jansour, Tripoli, Libya 2 P P Electrical Engineering Departme, Azzaytuna University, Tarhuna, Tripoli, Libya Abstract fast processing capabilities to resolve timing differences This work is a continuation of a design of a phase radio for fine-grained measurements, this problem is amplified navigation system for aircraft blind landing in case of non- over short distances. The other problem with these systems equipped runways proposed in [1], where, the proposed system is is the need to have and maintain high synchronization based on measuring the phase shifts of signals received from four between the transmitter and receiver, which adds an extra ground transmitters (antennas), placed on corners of the runway strip, which provide distance measurements accuracy in burden on the system cost and design. Unfortunately, the millimeters. However, there are two important points that need time of flight measurement is not accurate enough for the serious consideration. First, the phase measurement is going to high demands of landing systems. As third approach, by sending one or two signals of different carrier frequencies, give the total phase (ρ0 − ϕ) , while the actual phase shift of and then measuring the difference of phase shifts of the interest is ‘ϕ ’, ρ is the transmitter initial phase. The second 0 received waveforms the distances estimated. This scheme problem is that, the measured phase angle (ρ0 −ϕ) between the is more suitable for low power applications since the transmitted and the received signal can only be measured in the processing can be performed at reasonably low speeds. interval from 0 to 2π radians, this problem is called phase The distance estimation using signal phase measurements ambiguity. The answer of these problems lies in the use of more occasionally has been used in the past. One of the most than one frequency (signal). Two sinusoidal signals with famous is the worldwide international radio navigation different frequencies ( f1 and f2 ) but the same initial phase can system Omega. In [1], a new radio navigation system for be used. Taking the difference of the measured phases, the initial aircraft blind landing for non-equipped runways and phase ρ0 can vanish. To get around phase ambiguity would be squares was proposed.Fig.1, shows the system coordinates to make sure that the actual phase difference ∆ϕ12 does not of the airport runway, and coordinates of the four ground exceed 2π , this technique called equivalent or synthetic transmitters. The onboard navigation algorithm used to wavelength. determine the location of the airplane with respect to the touch point on the runway using the received signals phase Keywords: Phase Ambiguity; Aircraft blind landing; phase shifts. The onboard antenna ( ac ) coordinates with respect shift; Radio Navigation. to the runway coordinate system given as; (L2 − 4N ) 1. Introduction x = (1) 1 4L There are three main methods used to perform the distance M z = measurement using radio signals. These are received 1 2W signal strength, time of flight, and phase difference of 2 2 2 arrival. Received signal strength is a strong function of the 1 2 (L − 4N) M W y1 = 16(Rac A1) − −16 − environment. It is the simplest range estimation method 4 L2 2W 2 but also requires strong calibration. It is a simple but not very reliable method of distance estimation. As an Where; alternative and more accurate way of distance estimation, N = (Ra A )2 − (Ra A )2 ; M = (Ra A )2 − (Ra A )2 time of flight measurements. This method is how GPS c 3 c 1 c 2 c 1 receivers measure the ranges to the transmitting satellites. Ra1A1 – measured distance between onboard antenna( a1 ), The main problems of this scheme, it requires relatively and ground antenna ( A1 ). 183 IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 3, March 2015. www.ijiset.com ISSN 2348 – 7968 Ra1A2 – measured distance between onboard antenna ( a1 ), the phase shift ϕ can be measured, the distance can be and ground antenna ( A2 ). obtained. Ra1A3 – measured distance between onboard antenna ( a1 ), and ground antenna ( A3 ) [1]. Fig. 2 Phase difference between transmitted and received signals However, there are two important points that need serious Fig. 1 Runway system coordinates and onboard antenna system consideration. First, the phase measurement is going to coordinates give the total phase (ρ0 −ϕ) , while the actual phase shift of interest is ϕ . The second problem is that, the measured 2. Distance Measurement Using Signal Phase phase angle (ρ0 −ϕ) between the transmitted and the Shifts received signal can only be measured in the interval from 0 to 2π radians. Therefore, equation (3) reduces to: In the case of a single frequency sinusoidal signal, the d transmitted signal has a phase shift at the receiving end. ϕ = 2π ⋅ mod λ The amount of the phase shift due to the distance travelled can be determined using the fact that the received signal is ϕ or d = λ ⋅n + (4) a delayed version of the transmitted as shown in fig.2. 2π Hence, the received signal r(t) is written as: Where n is an integer. It is clear that the distance cannot be measured r(t) = sin[2πf (t − td )+ ρ0 ]= sin[2πft − 2πftd + ρ0 ]= (2) unambiguously, because n cannot be determined with a π −ϕ + ρ sin[2 ft 0 ] simple phase measurement. Where d = td – is the time delay ( td ). 3. Resolving phase ambiguity and initial v p phase mismatch d – Distance between the transmitter and the receiver; 8 v p – Propagation speed of the radio signal ( ≈ 3*10 m/s). Fortunately, there are ways to overcome the problems of f – is the received signal frequency; phase ambiguity, and initial phase mismatch. The answer lies in the use of more than one frequency. Two sinusoidal ρ0 – is the initial phase of the sinusoid; signals with different frequencies ( f1 and f2 ) but the same π Then, the phase shift 2 ftd can be expressed as a function initial phase can be used. Taking the difference of the of distance and speed of radio signal; measured phases, the initial phase ρ can vanish from the 2πf ∗ d 0 ϕ = ; rest of the equations. v p ∆ϕ12 = (ρ0 −ϕ1 )− (ρ0 −ϕ2 ) = (ϕ2 −ϕ1 ) = d d d 2πf ∗ d 2πf ∗ d 2π ( f − f )∗ d (5) ϕ = 2π ⋅ = 2π ⋅ int + mod (3) 1 − 2 = 1 2 λ λ λ v p v p v p v p λ – Wavelength of the used radio signal ( λ = ) Where, ∆ϕ12 is defined to be the difference of the f measured phases. Where ϕ is defined as the phase shift from the initial One way to get around ambiguity would be to make sure phase. It is clearly seen from the phase shift relation that if that the actual phase difference ∆ϕ12 does not exceed 2π . Satisfying the following relation can ensure this: 184 IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 3, March 2015. www.ijiset.com ISSN 2348 – 7968 2π∆f ∗ d v p < 2π ,∆f ∗ d v p < 1 ,∆f < v p d 4. Frequency allocations This technique called equivalent or synthetic wavelength According to the Table of Frequency Allocations in [2]. Using this concept one can obtain an estimated ′ Article 5 of the Radio Regulations issued by the distance, d from International Telecommunication Union (ITU) [3], 5.328 ∆ϕ The use of the band 960-1 215 MHz by the aeronautical d′ = λeq ⋅ N + (6) 2π radio navigation service is reserved on a worldwide basis Where; for the operation and development of airborne electronic N – is the integer synthetic fringe order aids to air navigation and any directly associated ground- λ λ based facilities. (WRC-2000). For unambiguous range 40 λ λ = 1 2 eq – is the synthetic wavelength ( eq ) Km, the synthetic wavelength λd = 80000 m. λ2 − λ1 If f =960000000 Hz, then for λ = 80000 m, f d′ – is the estimated distance. 1 d 2 =960003749.941 Hz, and the frequency difference f2 − f1 If N =0, then one can make an estimate n1′ of the wavelength fringe order by substituting Eq. (6) into Eq. (4) = 3749.941 Hz. f3 = 961000000 Hz, f4 = 961003749.941 and rearranging: Hz, f5 = 962000000 Hz, f6 = 962003749.941 Hz, f7 = ∆ϕ ⋅ λ 963000000 Hz, f = 963003749.941 Hz ′ 1 eq 8 n1 = −ϕ1 2π λ1 However, the sinusoids of very close frequencies are used Then the final measured distance is and they must be filtered and separated from each other using long filters. This problem will be discussed and ϕ ′ 1 d = int(n1) + ⋅ λ1 solved in the coming article. 2π Where; d – is the final distance measurement. 5. Conclusion The function int( ) returns the nearest integer to its argument. The unambiguous range has now been extended The method of measurement of a phase of complex radio to the synthetic wavelength λ , which may be much signals is proposed, which allows determining the location eq of the plane with respect to the runway with sufficient larger than λ . The unambiguous range now determined by accuracy. However, there are two important points that the wavelength (synthetic wavelength) λeq of the need serious consideration. First, the received phase ϕ frequency difference of f1 and f2 : includes not only phase shift , which occurs due to the distance between the transmitter and the receiver, but also v p λeq = includes the initial phases of the oscillator of the f1 − f2 transmitter ρ0 .

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