Moreover, the estimate of ���� may be erroneous due to the existence of noise and clutter. Several effective methods have been proposed to resolve the range-Doppler coupling [4-6]; however, the robust phase unwrapping is not considered in these methods. In next section we propose a new algorithm to resolve both of the range-Doppler coupling and the phase wrapping.3.?Multiple Stepped-Frequency Pulse Trains ProcessingIn this section, we present a new waveform named multiple stepped-frequency pulse trains and describe how to resolve both range-Doppler coupling and phase wrapping using this waveform.We replace the single stepped-frequency pulse train by multiple stepped-frequency pulse trains. This new waveform is shown in Figure 1, where three (or multiple) stepped-frequency pulse trains with different base carrier frequencies are simultaneously used. This can be realized by the following way: three antennas are fixed in the radar platform, and the same stepped-frequency pulse train is modulated on different carrier frequencies fc1, fc2 and fc3 and transmitted by three antennas, respectively, and then the different echoes onfc1, fc2 and fc3 are collected and demodulated by three antennas, respectively. Without loss of generality, we assume fc1 < fc2 < fc3 and (fc2 ? fc1) and (fc3 ? fc1) are two distinct positive real numbers and not integer multiple of each other.Figure 1.Multiple stepped-frequency pulse trains with different base carrier frequencies.Now we perform the processing described in the previous section on three stepped-frequency pulse trains. By performing P-point IDFT in terms of n in (3), we haver��R?2fcivTc=Ki+piP+��i,(5)where integers pi are the peak position estimates in the P-point IDFT results on fci, 0 �� pi< P, ��i are estimation errors, and Ki are unknown integers, i =1, 2, 3. When P is larger than the pulse number N, the sequence x(n) in (3) should be zero-padded before the IDFT. Assume that the errors ��i are bounded by|��i|��12P+��P,(6)where 0 �� �� < M is the maximal error level in estimation of the remainderspi. At the right hand side of (6), the first term is the quantization error and the second term is caused by possible interference, e.g., noise or clutter. Herein we are interested in the estimation of r and v from (5).We first estimate v. Subtracting the first equation from the other two equations in (5), respectively, we have2vTc(fc2?fc1)=L1+��1P+��12vTc(fc3?fc1)=L2+��2P+��2,(7)where��1=p1?p2��2=p1?p3L1=K1?K2L2=K1?K3��1=��1?��2��2=��1?��3,(8)and |��i|<1P+2��P. The problem is to estimate v using the reminders ��1 and ��2. In (7), while ��i cause small errors and they are difficult to be eliminated, the wrong Li may cause large folding errors. Thus, to estimate v, it is necessary
Due to environmental pollution, specific and sensitive detection methods are in need for environmental contaminants. To investigate the impact of toxic agents on organisms, biological test systems have been developed and applied to in various means.