System and method for detection and tracking of targets

Abstract

System and method for detection and tracking of targets, which in a preferred embodiment is based on the use of fractional Fourier transformation of time-domain signals to compute projections of the auto and cross ambiguity functions along arbitrary line segments. The efficient computational algorithms of the preferred embodiment are used to detect the position and estimate the velocity of signals, such as those encountered by active or passive sensor systems. Various applications of the proposed algorithm in the analysis of time-frequency domain signals are also disclosed.

1 . A method for estimating one or more samples of a cross ambiguity function of a first signal and a second signal, the method comprising: 
 computing fractional Fourier transform of the first signal; and    estimating one or more samples of the cross-ambiguity function based on the computed fractional Fourier transforms of the first signal and a fractional Fourier transform of the second signal.    
   
   
       2 . The method of  claim 1 , wherein the step of estimating is further based on using a chirp-z transform.  
   
   
       3 . The method of  claim 2  further comprising computing fractional Fourier transform of the second signal.  
   
   
       4 . The method of  claim 1 , wherein the fractional Fourier transform of the second signal is computed in advance.  
   
   
       5 . A signal processing method comprising: 
 receiving a signal, the received signal being a reflection of a transmitted signal from at least one object;    computing a first slice of the cross-ambiguity function associated with the received signal and the transmitted signal using fractional Fourier transforms of the received and transmitted signals; and    estimating at least one property of the at least one object based on the computed slice.    
   
   
       6 . The method of  claim 5 , wherein the estimated at least one property is the distance to the at least one object.  
   
   
       7 . The method of  claim 5 , wherein the estimated at least one property is the radial speed of the at least one object.  
   
   
       8 . The method of  claim 5  wherein the estimated properties are the distance to the at least one object and the radial speed of the at least one object.  
   
   
       9 . The method of  claim 5 , wherein the first slice has an orientation based on the auto-ambiguity function of the transmitted signal.  
   
   
       10 . The method of  claim 5 , wherein the first slice has a predetermined orientation.  
   
   
       11 . The method of  claim 5  further comprising computing a second slice of the cross-ambiguity function associated with the received signal and the transmitted signal.  
   
   
       12 . The method of  claim 11 , wherein the received signal is reflected from two or more objects.  
   
   
       13 . The method of  claim 12 , wherein at least one object property is estimated for two or more objects.  
   
   
       14 . The method of  claim 13 , wherein the at least one property is not the same for all objects.  
   
   
       15 . The method of  claim 5 , wherein the received signal is a continuous waveform signal.  
   
   
       16 . The method of  claim 5 , wherein the received signal is a discrete time signal.  
   
   
       17 . A signal processing method comprising: 
 receiving a signal, the received signal being a reflection of a transmitted signal from at least one object;    computing a first slice of the cross-ambiguity function associated with the received signal and the transmitted signal using fractional Fourier transforms of the received and transmitted signals; and    estimating at least one parameter of a component of the received signal reflected from the at least one object.    
   
   
       18 . The method of  claim 17 , wherein the estimated parameter is time delay of the signal components.  
   
   
       19 . The method of  claim 17 , wherein the estimated parameter is Doppler shift of the signal component.  
   
   
       20 . The method of  claim 17 , wherein the estimated parameters are Doppler shift and time delay of the signal components.  
   
   
       21 . The method of  claim 17 , wherein the first slice has an orientation based on the auto-ambiguity function of the transmitted signal.  
   
   
       22 . The method of  claim 17 , wherein the first slice has a predetermined orientation.  
   
   
       23 . The method of  claim 17  further comprising computing a second slice of the cross-ambiguity function associated with the received signal and the transmitted signal.  
   
   
       24 . The method of  claim 23 , wherein the received signal has two or more components reflected from two or more objects.  
   
   
       25 . The method of  claim 24  further comprising estimating parameter of the two or more signal components of the received signal associated with the two or more objects.  
   
   
       26 . The method of  claim 25 , wherein the at least one parameter is not the same for all the components.  
   
   
       27 . The method of  claim 17 , wherein the received signal is a continuous waveform signal.  
   
   
       28 . The method of  claim 17 , wherein the received signal is a discrete time signal.  
   
   
       29 . A signal processing method comprising: 
 receiving a signal;    computing a first slice of the cross-ambiguity function associated with the received signal and a reference signal different from the received signal using fractional Fourier transforms of the received and reference signals; and    estimating at least one parameter of a component of the received signal.    
   
   
       30 . The method of  claim 29 , wherein the reference signal is one of: (a) a stored signal, and (b) a signal transmitted by a device.  
   
   
       31 . The method of  claim 29 , wherein the received signal is one of: (a) a signal reflected from one or more objects, and (b) a signal transmitted by a device.  
   
   
       32 . The method of  claim 29 , wherein the estimated parameter is time delay of the signal components.  
   
   
       33 . The method of  claim 29 , wherein the estimated parameter is Doppler shift of the signal component.  
   
   
       34 . The method of  claim 29 , wherein the estimated parameters are Doppler shift and time delay of the signal components.  
   
   
       35 . The method of  claim 29 , wherein the first slice has an orientation based on the auto-ambiguity function of the reference signal.  
   
   
       36 . The method of  claim 29 , wherein the first slice has a predetermined orientation.  
   
   
       37 . The method of  claim 29  further comprising computing a second slice of the cross-ambiguity function associated with the received signal and the reference signal.  
   
   
       38 . The method of  claim 37 , wherein the received signal has components.  
   
   
       39 . The method of  claim 38  further comprising estimating one or more parameter of the two or more signal components of the received signal.  
   
   
       40 . The method of  claim 39 , wherein the at least one parameter is not the same for all the components.  
   
   
       41 . The method of  claim 29 , wherein the received signal is a continuous waveform signal.  
   
   
       42 . The method of  claim 29 , wherein the received signal is a discrete time signal.  
   
   
       43 . A signal processing system comprising: 
 means for computing a slice of the cross ambiguity function associated with a received signal reflected from at least one object and a signal transmitted to the at least one objects using fractional Fourier transforms of the received and transmitted signals; and    means for estimating one or more of (a) delay of a component of the received signal reflected from one of the at least one objects; (b) Doppler shift of a component of the received signal reflected from one of the at least one objects; (c) distance to one of the at least one object; and (d) radial speed of one of the at least one object; all based on the computed slice.    
   
   
       44 . The system of  claim 43 , wherein the means for computing the slice comprises means for determining one or more peaks of the computed slice.  
   
   
       45 . The system of  claim 43 , wherein the means for computing the slice comprises means for selecting an orientation of the slice.  
   
   
       46 . The system of  claim 45 , wherein the selected orientation of the slice is based on one of (a) a priori knowledge; and (b) the auto-ambiguity function of the transmitted signal.  
   
   
       47 . The system of  claim 43 , wherein means for computing the slice is operable to compute two or more slices of the cross ambiguity function.  
   
   
       48 . The system of  claim 47 , wherein means for estimating is operable to estimate one or more of (a) delays of component of the received signal reflected from two or more of the at least one object; (b) Doppler shifts of component of the received signal reflected from two or more of the at least one object; (c) distances to the two or more of the at least one object; and (d) radial speed of the two or more of the at least one object relative to the system; all based on the computed two or more slices.  
   
   
       49 . The system of  claim 43  further comprising means for tracking the at least one object.  
   
   
       50 . The system of  claim 43 , wherein the received signal is a continuous waveform signal.  
   
   
       51 . The system of  claim 43 , wherein the received signal is a discrete time signal.  
   
   
       52 . A computer program product comprising: 
 a medium with instructions stored thereon that cause a computer system to 
 a. receive a signal;  
 b. compute one or more slices of the cross ambiguity function associated with the received signal and a reference signal using fractional Fourier transforms of the received and transmitted signals; and  
 c. estimate one or more of (i) delay of a component of the received signal reflected from one of the at least one objects; (ii) Doppler shift of the component of the received signal reflected from the one of the at least one objects; (iii) distance to the one of the at least one object; and (iv) radial speed of the one of the at least one object; all based on the computed slice.  
   
   
   
       53 . The computer program product of  claim 52 , wherein the instructions stored on the medium further cause the computer system to select an orientation of the computed one or more slices.  
   
   
       54 . The computer program of  claim 53 , wherein the orientation of the first computed slice is based on one of (a) a priori knowledge; and (b) the auto-ambiguity function of the transmitted signal.  
   
   
       55 . The computer program of  claim 54 , wherein the orientations of one or more slices computed after the first slice are based on the orientation of the first computed slice.  
   
   
       56 . The computer program product of  claim 52 , wherein the instructions stored on the medium cause the computer system to estimate one or more of (a) delays of signal components associated with two or more objects; (b) Doppler shifts of the signal component associated with the two or more objects; (c) distances to the two or more objects; and (d) radial speed of the two or more objects; all based on the computed two or more slices.  
   
   
       57 . The computer program product of  claim 52 , wherein the medium has additional instructions that cause the computer system to track the at least one object.  
   
   
       58 . The computer program product of  claim 52 , wherein the instructions stored on the medium that cause the computer system to receive a signal cause the computer system to receive a continuous form signal.  
   
   
       59 . The computer program product of  claim 52 , wherein the instructions stored on the medium that cause the computer system to receive the signal cause the computer system to receive a discrete signal.