a detailed description of the present invention is provided below with reference to the figures . while illustrative circuits are given , other embodiments can be constructed with other circuit configurations . all u . s . patents and copending u . s . applications cited herein are herein incorporated by reference . fig1 a depicts a pulse radar system 10 employing a pulse center detector ( pcd ) 20 of the present invention . pulse radar 12 is generally a pulse - echo radar employing equivalent time sampling techniques . rf transmit pulses are radiated from transmit antenna 14 to target 16 and returning echoes are received by antenna 14 and detected by radar 12 to produce , in combination with the transmit pulses , baseband transmit and echo pulses on line 18 . in the preferred embodiment , the baseband output is a sampled , equivalent time replica of the transmit and echo pulses passing through antenna 14 . also in the preferred embodiment , the baseband pulses are envelope detected unipolar pulses . details of a pulse radar 12 are described in u . s . pat . no . 6 , 137 , 438 , precision short - range pulse - echo systems with automatic pulse detectors , to mcewan . line 18 is input to pcd 20 . pulse center detector 20 detects the baseband transmit and echo pulses at their centers and produces a range output on line 22 that is proportional to range , as defined by the time difference between the center of the baseband transmit pulse on line 18 and the center of the echo pulse on line 18 . it should be understood that , in a less preferred mode , the transmit pulse on line 18 may be substituted with a reset pulse or a digital start pulse rather than the detected transmitted main - bang rf pulse . also , the transmit pulse may be in the form of a close - in reflection from antenna 14 or other nearby reference reflector , ( i . e ., a fiducial pulse ). a readout or processor 24 responsive to range output on line 22 may process and / or display range data , or provide an output on line 26 to control a parameter of another system such as a toilet valve or a vehicle braking system . fig1 b depicts a tdr system 30 employing the pulse center detector ( pcd ) 20 of the present invention . tdr 32 is generally a pulse - echo time domain reflectometer employing equivalent time sampling techniques . details of a sampling tdr 32 are described in u . s . pat . no . 5 , 610 , 611 , high accuracy material level sensor , to mcewan . transmit pulses are propagated on transmission line 34 to a transmission line probe 36 which is at least partially immersed in a liquid 38 in a tank 39 . liquid 38 reflects the transmitted tdr pulses back as echo pulses to tdr 32 , which produces baseband transmit and echo pulses on line 18 . the function of references blocks 20 and 24 , and line 26 are the same as for fig1 a . it should be understood that , in a less preferred mode , the transmit pulse on line 18 may be substituted with a reset pulse or a digital start pulse rather than the detected transmitted main - bang rf pulse . also , the transmit pulse may be in the form of a tank - top reflection from probe 36 or other reference reflector , ( i . e ., a fiducial pulse ). fig2 a plots the waveforms associated with pulse center detector 20 . baseband pulses 40 are input to the pulse center detector on line 18 and comprise a transmit pulse t and an echo pulse e . baseband pulses 40 preferably occur on a millisecond equivalent - time scale . detection pulses 42 result from threshold detecting the baseband pulses with a fixed threshold v th , having an exemplary amplitude illustrated by dashed line 41 . leading - pwm pulse 44 and trailing - pwm pulse 46 result from triggering a first flip - flop ( or logical equivalent ) on the leading edges ( shown as edge circles 1 and 2 ) of the detection pulses 42 to produce leading - pwm pulse 44 , and from triggering a second flip - flop ( or logical equivalent ) on the trailing edges ( shown as edge circles 3 and 4 ) of detection pulses 42 to produce trailing - pwm pulse 46 . pwm pulses 44 and 46 are then added and scaled to produce , in effect , a center triggered response , as will be discussed with respect to fig3 a and 3 b . an effective center - detected pwm pulse is plotted with dashed lines to illustrate its centering on the t and e pulse centers . it should be understood that the effective center - detected pwm is a computed result of adding the leading - pwm and trailing - pwm digital counts , or of adding the corresponding analog voltages , as will be discussed with reference to fig3 a and 3 b ; it does not exist as a real pulse . fig2 b illustrates the amplitude independent nature of the pcd . echo pulse e ′ is shown with reduced amplitude compared to e of fig2 a . detection pulses exhibit shifted edges 2 ′ and 4 ′ due to pulse e ′ barely exceeding threshold 41 . however , edges 2 ′ and 4 ′ have shifted in equal and opposite directions as can be seen with reference to edges 2 and 4 ( dashed lines of fig2 b ). after addition of pwm pulses 44 and 46 , the effect of edge shifts from 2 to 2 ′ and 4 to 4 ′ cancel each other , thereby illustrating the amplitude independence of the apparatus and method . fig3 a is a block diagram of a digital implementation of pulse center detector 20 . baseband pulses are input on line 18 to a fixed threshold comparator 60 , which compares the pulses with a threshold v th and outputs detection pulses on line 62 to leading flip - flop 64 and to inverter 66 , whose output coupled to trailing flip - flop 68 . leading flip - flop 64 and trailing flip - flop 68 produce leading - pwm and trailing - pwm pulses on lines 72 and 74 , respectively . flip - flops 64 , 68 may be other logic elements . the width of the leading - pwm and trailing - pwm pulses correspond to the transmit - to - echo time delays of the leading and trailing edges of the corresponding t to e detection pulses of fig2 a . a reset is provided on line 70 to the flip - flops after each operation cycle ( i . e ., range sweep ). it should be understood that flip - flops 64 and 68 may incorporate additional logic , such as a lock - out function , to prevent re - toggling if additional pulses beyond the two detection pulses are input within one operation cycle . the leading - pwm and trailing - pwm pulses gate counters 76 and 78 , respectively , which produce range counts on lines 80 and 82 . adder 84 adds the counts from lines 80 and 82 to produce an average count on line 86 which effectively corresponds to a count from a single pwm pulse centered on the t and e pulses , i . e ., extending from center to center of the two pulses ( neglecting a scale factor of 2 ). an optional divide - by - two circuit 88 scales the digital count from line 86 to compensate for the addition operation of element 84 . however , the output on line 22 is usually in an unscaled binary format that requires processing by readout / processor 24 to present meaningful data scaled to some measurement quantity , for example , a fluid volume in a tank . thus the scaling provided by divide - by - two element 88 can be incorporated in display / processor 24 . fig3 b is a block diagram of an analog implementation of pulse center detector 20 . elements 60 , 64 , 66 and 68 , and lines 18 , 62 , 70 , 72 , and 74 have the same function as described with reference to fig3 a . the leading - pwm and trailing - pwm pulses on lines 72 and 74 , respectively , are input to an analog summer 90 via resistors r l and r t , respectively , which are both connected to one input of op amp a . a feedback connection comprising r f and c f across op amp a provides voltage scaling and pulse integration or smoothing to the pwm pulses input to r l and r t . the time constant set by r f c f is much longer than the pwm duration to smooth the pwm pulses . a lowpass filter may be connected to line 22 for further smoothing . operational amplifier a outputs a voltage on line 22 that is the sum of the voltages on lines 72 and 74 , integrated over time to a smooth dc value . thus , summer 90 adds and smoothes the leading - pwm and trailing - pwm pulses to produce a proportional analog voltage that corresponds to a single smoothed pwm pulse centered on the t and e pulses , thereby implementing an amplitude - independent pulse center detection function . if the leading or trailing edges of the baseband t or e pulses have different transition times , which would result in reduced amplitude independence for the pcd , either r l or r t can be scaled , i . e ., weighted , to compensate the asymmetry and regain amplitude independence . for example if the trailing edges of the baseband t and e pulses are 2 × slower than the leading edges , resistor r t would need to be doubled to regain amplitude independence . weighting can also be accomplished digitally by simple means known in the art with respect to fig3 a . although the invention has been described with reference to an equivalent time radar or tdr , the principles of the pcd apply to other pulse - echo embodiments as well , such as a realtime radar or tdr . changes and modifications in the specifically described embodiments can be carried out without departing from the scope of the invention , which is intended to be limited only by the scope of the appended claims .