Multiple discrete frequency ranging with error detection and correction

Claim 1

Range determination apparatus for determining target range within a range depth of D and within a range bin error of e comprising: (a) a carrier frequency transmitter for transmitting a carrier frequency, (b) means for generating at least two modulating signals having frequency f 1 and f 2 respectively, (c) modulation means coupled to said carrier frequency transmitter for modulating said carrier, said modulation means operative for said at least two discrete frequencies f 1 and f 2 for providing one of simultaneous or sequential modulated signals, (d) said at least two modulating frequencies and a common sub-multiple counting frequency f o related such that f.sub.o m.sub.1 'f.sub.1 =m.sub.2 'f.sub.2 where, m.sub.1 '=m.sub.1 m.sub.r m.sub.2 '=m.sub.2 m.sub.r m.sub.r ≧4e+1 m.sub.1 m.sub.2 ≧D/m.sub.r and where m 1 ,m 2 and m r are pairwise relatively prime, (e) a receiver for receiving a reflected signal from said target and for producing a received electrical signal corresponding thereto, (g) phase detection means responsive to said modulating signals of said generating means and said received signals for detecting the phase difference x 1 ' and x 2 ' respectively between the modulating signals of frequencies f 1 and f 2 and each of the corresponding received signals, (h) data processing means coupled to receive said detected phase differences for each of said received signals, said data processing means operative (1) to calculate ##EQU14## where R(x) m is defined as the residue of x modulo m, (2) to compare R(x 1 ') m .sbsb.r with R(x 2 ') m .sbsb.r and if unequal to modify at least one of x 1 ' and x 2 ' by adding or subtracting an integer≦e to produce modified phase differences x 1 " and x 2 " so that residues R(x 1 ") m .sbsb.r and R(x 2 ") m .sbsb.r of the modified phase differences are equal, and (3) to decode one of (1) the residue number triplet [R(x 1 ') m .sbsb.1, R(x 2 ') m .sbsb.2, R(x 1 ') m .sbsb.r ] and the modified residue number triplet [R 1 ") m .sbsb.1, R(x 2 ") m .sbsb.2, R(x 1 ") m .sbsb.r ] relative to the moduli set [m 1 ,m 2 ,m r ] to obtain the target range.

Claim 8

A method for determining the true target range within a range depth of D and within a range bin error of e from multiple pulse repetition frequencies of radar comprising the steps of: a. transmitting signals having at least two distinct frequencies f 1 and f 2 , b. said frequencies related to each other and to a counting frequency f o such that m.sub.1 'f.sub.1 =m.sub.2 'f.sub.2 =f.sub.o where m.sub.1 '=m.sub.1 m.sub.r m.sub.2 '=m.sub.2 m.sub.r m.sub.r ≧4e+1 m.sub.1 m.sub.2 ≧D/m.sub.r and where m 1 , m 2 and m r are pairwise relatively prime, c. receiving reflected echo signals from said target for each frequency f 1 and f 2 , d. detecting the difference in phase difference x 2 ', x 2 ' respectively between the transmitted and received signals for each frequency f 1 and f 2 , e. calculating in response to said phase differences x 1 ', x 2 ' the residues, R(x.sub.1 ').sub.m.sbsb.1 , R(x.sub.2 ').sub.m.sbsb.2 R(x.sub.1 ').sub.m.sbsb.r , R(x.sub.2 ').sub.m.sbsb.r f. comparing R(x 1 ') m .sbsb.r and R(x 2 ') m .sbsb.r, and if unequal, modifying at least one of x 1 ' and x 2 ' by adding or subtracting an integer≧e to produce a modified phase difference x 1 ", x 2 " such that residues R(x 1 ") m .sbsb.r and R(x 2 ") m .sbsb.r of the modified phase differences are equal, and g. decoding one of (1) the residue number triplet [R(x 1 ') m .sbsb.1, R(x 1 ') m .sbsb.2, R(x 1 ') m .sbsb.r ] if R(x 1 ') m .sbsb.r is equal to R(x 2 ') m .sbsb.r in step f and (2) the modified residue number triplet [R(x 1 ") m .sbsb.1, R(x 2 ") m .sbsb.2, R(x 1 ") m .sbsb.r ] if R(x 1 ') m .sbsb.r is not equal to R(x 2 ') m .sbsb.r in step f., each triplet decoded relative to the moduli set [m 1 , m 2 , m r ] to obtain the true target range.

Claim 9

A method for determining the true target range within a range depth of D and within a range bin error of e from multiple pulse repetition frequencies of radar comprising the steps of: a. transmitting signals having at least two distinct frequencies f 1 and f 2 , b. said frequencies related to each other and to a counting frequency f o such that m.sub.1 'f.sub.1 =m.sub.2 'f.sub.2 =f.sub.o where m.sub.1 '=m.sub.1 m.sub.r m.sub.2 '=m.sub.2 m.sub.r m.sub.r ≧4e+1 m.sub.1 m.sub.2 ≧D/m.sub.r and where m 1 , m 2 and m r are pairwise relatively prime, c. receiving reflected echo signals from said target for each frequency f 1 and f 2 , d. detecting the difference in phase difference x 2 ', x 2 ' respectively between the transmitted and received signals for each frequency f 1 and f 2 , e. calculating in response to said phase differences x 1 ', x 2 ' the residues, R(x.sub.1 ').sub.m.sbsb.1 , R(x.sub.2 ').sub.m.sbsb.2 R(x.sub.1 ').sub.m.sbsb.r , R(x.sub.2 ').sub.m.sbsb.r f. comparing R(x 1 ') m .sbsb.r and R(x 2 ') m .sbsb.r, and if unequal, modifying at least one of x 1 ' and x 2 ' by adding or subtracting an integer≧e to produce a modified phase difference x 1 ", x 2 " such that residues R(x 1 ") m .sbsb.r and R(x 2 ") m .sbsb.r of the modified phase differences are equal, and g. decoding one of (1) the residue number triplet [R(x 1 ') m .sbsb.1, R(x 1 ') m .sbsb.2, R(x 1 ') m .sbsb.r ] if R(x 1 ') m .sbsb.r is equal to R(x 2 ') m .sbsb.r in step f and (2) the modified residue number triplet [R(x 1 ") m .sbsb.1, R(x 2 ") m .sbsb.2, R(x 1 ") m .sbsb.r ] if R(x 1 ') m .sbsb.r is not equal to R(x 2 ') m .sbsb.r in step f., each triplet decoded relative to the moduli set [m 1 , m 2 , m r ] to obtain the true target range.

Claim 10

A method for determining the true target range within a range depth D and within a range bin error e from multiple modulated frequencies of radar comprising the steps of: (a) transmitting a plurality of distinct frequencies f 1 , f 2 . . . f i . . . f s , (b) said plurality of frequencies related such that, for i=1, 2, . . . s, m.sub.1 'f.sub.1 =m.sub.2 'f.sub.2 =m.sub.1 'f.sub.i where ##EQU15## where the m i 's are pairwise relatively prime, (c) receiving reflected echo signals from said target for each frequency f i , i=1,2, . . . s, (d) detecting the phase difference x 1 ' respectively between the transmitted and received signals for each frequency f i , i=1,2 . . . s, (e) calculating in response to each x 1 ', the residues ##EQU16## (f) for each distinct pair of indices i,j where i=1,2 . . . s and j=1,2 . . . s, computing, d(i,j)=min(R(x.sub.i.sup.r -x.sub.j.sup.r).sub.m.sbsb.r, m.sub.r -R(x.sub.i.sup.r -x.sub.j.sup.r).sub.m.sbsb.r) and choosing i o , j o at which d (i o ,j o ) is maximal, (g) selecting integer y, o≧y<m r as one of: y=R(x.sub.j.sbsb.0.sup.r +[R(x.sub.i.sbsb.0.sup.r -x.sub.j.sbsb.0.sup.4).sub.m.sbsb.r /2].sub.m.sbsb.r if R(x i .sbsb.0 r -x j .sbsb.0 r ) m .sbsb.r ≧2e, and y=R(x.sub.i.sbsb.0.sup.r +[R(x.sub.j.sbsb.0.sup.4 -x.sub.i.sbsb.0.sup.r).sub.m.sbsb.r /2]) if R(x j .sbsb.0 r -x i .sbsb.0 r ) m .sbsb.r ≦2e when [ ] denotes the greatest integer functions, (h) computing b i , i=1,2, . . . s such that b.sub.i =R(x.sub.i.sup.r -y).sub.m.sbsb.r if R(x.sub.i.sup.r -y).sub.m.sbsb.r ≦e, and b.sub.i =R(x.sub.i.sup.r -y).sub.m.sbsb.r -m.sub.r if R(x.sub.i.sup.r -y).sub.m.sbsb.r >e, (i) subtracting x i -b i to form the differences x.sub.i.sup.* =R(x.sub.i -b.sub.i).sub.m.sbsb.i i=1,2, . . . S, and (j) decoding the set (x 1 * , x 2 * . . . x i * . . . x s * , y) relative to the moduli set (m 1 , m 2 . . . m i . . . m s , m r ) to find the true target range.

Claim 11

A method for determining the true target range within a range depth D and within a range bin error e from multiple modulated frequencies of radar comprising the steps of: (a) transmitting a plurality of distinct frequencies f 1 , f 2 . . . f i . . . f s , (b) said plurality of frequencies related such that, for i=1, 2, . . . s, m.sub.1 'f.sub.1 =m.sub.2 'f.sub.2 =m.sub.1 'f.sub.i where ##EQU15## where the m i 's are pairwise relatively prime, (c) receiving reflected echo signals from said target for each frequency f i , i=1,2, . . . s, (d) detecting the phase difference x 1 ' respectively between the transmitted and received signals for each frequency f i , i=1,2 . . . s, (e) calculating in response to each x 1 ', the residues ##EQU16## (f) for each distinct pair of indices i,j where i=1,2 . . . s and j=1,2 . . . s, computing, d(i,j)=min(R(x.sub.i.sup.r -x.sub.j.sup.r).sub.m.sbsb.r, m.sub.r -R(x.sub.i.sup.r -x.sub.j.sup.r).sub.m.sbsb.r) and choosing i o , j o at which d (i o ,j o ) is maximal, (g) selecting integer y, o≧y<m r as one of: y=R(x.sub.j.sbsb.0.sup.r +[R(x.sub.i.sbsb.0.sup.r -x.sub.j.sbsb.0.sup.4).sub.m.sbsb.r /2].sub.m.sbsb.r if R(x i .sbsb.0 r -x j .sbsb.0 r ) m .sbsb.r ≧2e, and y=R(x.sub.i.sbsb.0.sup.r +[R(x.sub.j.sbsb.0.sup.4 -x.sub.i.sbsb.0.sup.r).sub.m.sbsb.r /2]) if R(x j .sbsb.0 r -x i .sbsb.0 r ) m .sbsb.r ≦2e when [ ] denotes the greatest integer functions, (h) computing b i , i=1,2, . . . s such that b.sub.i =R(x.sub.i.sup.r -y).sub.m.sbsb.r if R(x.sub.i.sup.r -y).sub.m.sbsb.r ≦e, and b.sub.i =R(x.sub.i.sup.r -y).sub.m.sbsb.r -m.sub.r if R(x.sub.i.sup.r -y).sub.m.sbsb.r >e, (i) subtracting x i -b i to form the differences x.sub.i.sup.* =R(x.sub.i -b.sub.i).sub.m.sbsb.i i=1,2, . . . S, and (j) decoding the set (x 1 * , x 2 * . . . x i * . . . x s * , y) relative to the moduli set (m 1 , m 2 . . . m i . . . m s , m r ) to find the true target range.