Efficient detection and signal parameter estimation with application to high dynamic GPS receiver

In a system for deriving position, velocity, and acceleration information from a received signal emitted from an object to be tracked wherein the signal comprises a carrier signal phase modulated by unknown binary data and experiencing very high Doppler and Doppler rate, this invention provides combined estimation/detection apparatus for simultaneously detecting data bits and obtaining estimates of signal parameters such as carrier phase and frequency related to receiver dynamics in a sequential manner. There is first stage for obtaining estimates of the signal parameters related to phase and frequency in the vicinity of possible data transitions on the basis of measurements obtained within a current data bit. A second stage uses the estimates from the first stage to decide whether or not a data transition has actually occurred. There is a third stage for removing data modulation from the received signal when a data transition has occurred and a fourth stage for using the received signal with data modulation removed therefrom to update global parameters which are dependent only upon receiver dynamics and independent of data modulation. Finally, there is a fifth stage for using the global parameters to determine the position, velocity, and acceleration of the object.

TECHNICAL FIELD 
The invention relates to tracking systems employing analysis of a known 
frequency being emitted by the tracked object and, more particularly, in a 
system for deriving position, velocity, and acceleration information from 
a single emitted from an object to be tracked wherein the signal comprises 
a carrier signal phase modulated by unknown binary data and experiencing 
very high Doppler and Doppler rate, to the method of providing the 
parameters associated with the signal from which the position, velocity, 
and acceleration information can be derived comprising the steps of, 
sampling the signal during multiple sample times within a first binary bit 
period; using data from samples obtained during the first binary bit 
period to determine the phase of the signal just prior to the end of the 
first binary bit period; sampling the signal during multiple sample times 
within a next binary bit period; using data from samples obtained during 
the next binary bit period to determine the phase of the signal just after 
the end of the first binary bit period; comparing the phase of the signal 
just after the end of the first binary bit period to the phase of the 
signal just prior to the end of the first binary bit period; adjusting the 
signal data associated with the second binary period to reflect a change 
in bit status if the phase of the signal just after the end of the first 
binary bit period is offset from the phase of the signal just prior to the 
end of the first binary bit period by more than a preestablished threshold 
amount; repeating the foregoing steps to create modified signal data 
reflecting the signal in an unmodulated state; and, using the modified 
signal data to estimate the parameters from which the position, velocity, 
and acceleration information are derived. 
In the preferred embodiment, the steps of using data from samples obtained 
during the first binary bit period to determine the phase of the signal 
just prior to the end of the first binary bit period and using data from 
samples obtained during the next binary bit period to determine the phase 
of the signal just after the end of the first binary bit period each 
comprises the steps of, using the data from the samples in a first 
instance to estimate the phase of the signal; using an estimate from the 
first instance to update an estimation algorithm being employed to 
estimate the phase; and, reusing the data from the samples in a second 
instance to re-estimate the phase of the signal whereby errors tend to 
cancel out and an improved estimate of the phase is provided. Preferably, 
an adaptive Hilbert transform in a phase locked loop is employed to 
estimate the parameters. 
BACKGROUND ART 
In the field of tracking systems employed for tracking satellites, 
missiles, and the like, it is the object of the apparatus and methods 
employed therein to provide accurate tracking information about the 
tracked object. While radar is useful for slower moving objects in 
providing ranging information, tracking systems employed with, for 
example, Global Positioning Systems (GPS), space probes under dynamics, 
the Space Shuttle, space stations, satellite communications, and the like, 
must provide more information and more accurate information, all under 
extremely adverse conditions. For example, a rocket (both outgoing and 
incoming) is typically under high dynamic forces imparting rapid 
acceleration and increases in velocity. 
In a great many cases in the area of interest, the tracked object is 
emitting a detectable radio frequency (RF) signal. Most often, the RF 
signal is the carrier for digital information being relayed to a ground 
station. As is well known, any alternating signal will be effected by the 
Doppler effect of its movement. Thus, a siren on a vehicle operating at a 
fixed audio frequency will appear to be at a higher frequency when 
approaching a point at a fixed velocity and will appear to be at a lower 
frequency when moving away from the same point at the same fixed velocity. 
If the vehicle is under acceleration, the frequency (and therefore the 
tone) of the siren will appear to be increasing and vice versa when in a 
state of deceleration. With respect to object tracking, the Doppler effect 
on an emitted detectable frequency can be put to good use in deriving 
speed and acceleration data about the object employing known mathematical 
techniques and a computer's rapid computational power. 
Where the speeds and dynamics involved are not in the excess, well known 
prior art techniques have been employed to perform the data analysis on 
the received signal as sampled to provide the data which is analyzed. 
Thus, phase-locked loops or extended Kalman filters are commonly employed 
in the prior art for carrier phase estimation. Likewise, a Fast Fourier 
Transform (FFT) is a commonly employed mathematical technique. Where the 
parameters involved are in the excess as in the case of a very high 
dynamic GPS receiver, these prior art techniques simply do not operate. 
For example, FFT requires a 30dB-Hz (1000:1) signal power-to-noise 
spectral density ratio (SNR) or better to provide accurate results. Under 
the high dynamics and the sample sizes in the environment of interest, 
such a SNR is not possible so FFT analysis is not possible. 
The problem can possibly best be understood by reference to the simplified 
waveform and timing diagram of FIG. 1. As will be recalled, the typical 
signal 10 comprises an alternating waveform carrier with binary data 
impressed thereon. If the binary data were not present, the analysis of 
the signal 10 would not be a problem as the sample period could be 
sufficiently long to provide a high enough SNR for standard analysis 
techniques and circuitry to be effective. Such is not the case, however. 
For example, the signal 10 of FIG. 1 depicts a portion representing the 
binary sequence 101. Because of the spacing of the binary data on the 
signal 10, the signal 10 must be sampled during sampling periods (T.sub.b) 
12 of limited length. During each period (T.sub.b) typically ten to twenty 
samples are taken. This cannot provide a sufficiently high SNR for FFT, 
for example. As can be seen from FIG. 1, as the signal 10 changes from 
representing the first "1" to the "0", the phase of the signal 10 shifts 
180.degree. . This phase shift occurs close adjacent the end of the first 
sample period (T.sub.b) 12 designated as "T.sub.b ". A similar phase shift 
occurs close adjacent the end of the second sample period (T.sub.b) 12 
designated as "2T.sub.b " where the signal 10 changes from representing 
the "0" to the second "1". It is this change in phase as the signal 10 
changes between "1" and "0" states which prevents the signal 10 from being 
analyzed for more than one sample period 12. Thus, since the sample 
periods 12 are not long enough to produce the required SNR for 
conventional analysis methods and apparatus, they cannot be used in this 
environment to produce reliable and accurate results. 
The problem of estimating the parameters of a received quasi sinusoidal 
signal in the presence of noise has received considerable attention in the 
literature; however, for the case when the received carrier is modulated 
by unknown data and simultaneously experiences considerably high Doppler 
and Doppler rate, the research reported in the published literature is 
somewhat limited. One proposed prior art approach which has been analyzed 
for the GPS application is an estimator structure based on the maximum 
likelihood estimation (MLE) of code delay and Doppler frequency over a 
single data bit period. The "pseudo" estimates over different bit 
intervals are combined by a Kalman filter to provide tracking of Doppler 
frequency. By limiting the primary (ML) estimation period to less than one 
data bit period, the problem of detecting the data bits is bypassed; 
however, perhaps due to such a limitation and also due to high frequency 
rate involved (not explicitly estimated by the MLE), a threshold of about 
30 dB-Hz in terms of the received carrier power-to-noise power spectral 
density ratio (P/N.sub.o) was obtained. Due to the lack of knowledge of 
the data bits, phase estimation is not feasible by this scheme. 
In terms of GPS applications, the problem of data modulation can be 
overcome by establishing a parallel (non-dynamic) link between the GPS 
satellites and a control ground receiver which also simultaneously 
receives the frequency translated version of the GPS signals. The data 
demodulation and estimation is then performed at the ground receiver. Once 
the data modulation is removed from the GPS receiver signal, the problem 
reduces to simply estimating the phase, frequency, etc., of an unmodulated 
RF carrier. This latter problem, of course, has been studied extensively 
in the literature. 
In the literature describing the prior art, there are several techniques of 
data detection. If the signal waveform is known precisely and does not 
change from bit to bit, the data can be detected coherently by using 
matched filters or correlation receivers, irrespective of the actual 
waveform. If the waveform (carrier) has a constant known frequency, either 
a coherent or a differentially coherent detection can be employed, 
depending upon whether or not the phase of the carrier is known. In a 
decision-directed version of these techniques, the carrier phase and/or 
frequency are estimated by a phase-locked loop technique and the data 
detector becomes part of the loop. It is clear that these techniques most 
likely will not be feasible under the low SNR and high dynamics of the 
required environment in that the frequency may not be even nearly constant 
over the detection period and under such low SNR conditions that it may 
not be possible to acquire the lock with data modulation present. 
In an alternate solution as in the Costas loop, the data detection problem 
is bypassed by a multiplicative technique; however, such a loop also 
suffers in terms of loss of SNR due to the multiplicative noise term which 
can be excessive for the high loop filter bandwidths required and the low 
received SNR. 
It is thus apparent that schemes which incorporate data detection in a loop 
which in turn is made dependent upon the acquisition and tracking of the 
loop may not be desirable under such high dynamic conditions since the 
loop may not acquire to start with and may lose lock during tracking. 
Therefore, what is needed is a technique where data can be detected even 
under open loop condition. 
STATEMENT OF THE INVENTION 
Accordingly, it is an object of this invention to provide a method and 
apparatus for providing a sufficient sample period in a signal of interest 
containing binary data impressed on a carrier signal to allow analysis of 
the signal and estimation of the parameters thereof in the presence of 
high Doppler and Doppler rate. 
It is another object of this invention to provide a method and apparatus 
for estimating the parameters of a received quasi sinusoidal signal in the 
presence of noise when the carrier is modulated by unknown data and the 
signal experiences high Doppler and Doppler rate. 
It is still another object of this invention to provide a method and 
apparatus for estimating the parameters of a received quasi sinusoidal 
signal in the presence of noise when the carrier is modulated by unknown 
data and the signal experiences high Doppler and Doppler rate and for 
removing the modulation from the signal to provide unmodulated signal data 
which can be analyzed to provide estimates of the parameters of the 
signal. 
Other objects and benefits of the invention will become apparent from the 
description which follows hereinafter when taken in conjunction with the 
drawing figures which accompany it.

DETAILED DESCRIPTION OF THE INVENTION 
The inventor herein has written a detailed paper on the subject matter of 
this invention which sets forth with particularity the mathematical basis 
and proofs for the novel approach employed by the invention. In the 
interest of simplicity, however, this specification itself will be 
directed to the novel aspects of the invention and their implementation in 
a working environment shown in simplified form so as to enable one skilled 
in the art wishing to do so to implement the invention easily and quickly. 
The invention is primarily a novel technique for simultaneously detecting 
data and estimating the parameters of a received carrier signal phase 
modulated by unknown data and experiencing very high Doppler, Doppler 
rate, etc. Note that the principal goal is the accurate estimation of the 
parameters of the carrier signal and that the detection of the data is an 
added benefit which flows from the approach employed. Typically, detection 
of the data is also desired; so, in this regard, the present invention can 
be employed to eliminate the need for other equipment dedicated to that 
particular task. As mentioned earlier, this particular environment occurs, 
for example, in the case of Global Positioning Systems (GPS), such as 
those under development by the Jet Propulsion Laboratory (JPL) in 
Pasadena, Calif., where the signal parameters are directly related to the 
position, velocity, and acceleration of the GPS receiver. 
This invention addresses the original and more difficult problem of 
estimating the signal parameters from a data modulated sinusoidal carrier 
and offers a novel simultaneous estimation-detection scheme whose 
performances is very close to the estimation schemes proposed by the prior 
art for the case of an unmodulated carrier. In fact, from simulated 
studies performed by the inventor at JPL, for the case of high dynamics 
under consideration there is virtually no loss in terms of the required 
P/N.sub.o due to data modulation. Apart from the fact that in GPS 
applications this does away with the necessity of having a parallel direct 
satellite to ground receiver communication link, the method of this 
invention is very important in many other similar situations including 
(modulated) signal acquisition from NASA deep space probes undergoing high 
dynamics, where such parallel links may not be feasible. 
The approach employed in the present invention is based upon first 
estimating the received signal local (data dependent) parameters over two 
consecutive bit periods (i.e. the periods 12 of FIG. 1), followed by the 
detection of a possible jump in these parameters. The presence of a 
detected jump signifies a data transition which is then removed from the 
received signal. This effectively demodulated signal is then processed to 
provide the estimates of global (data independent) parameters of the 
signal related to the position, velocity, etc. of the receiver. 
One of the key aspects of this invention to be described hereinafter is the 
introduction of two different and equivalent schemes which can provide an 
improvement of up to 3 dB over the conventional implementation of Kalman 
filtering as applied to phase and frequency estimation under low to medium 
signal-to-noise ratio (SNR) conditions. One scheme is based upon 
reprocessing (cycling) the measurements over an optimally selected 
interval. Both of these schemes are based upon the recognition of two 
available error signals with nearly independent noise. In conventional 
implementations, one of these error signals is simply ignored. In the 
present invention, however, by reprocessing the observations over an 
optimally selected period, one can exploit the other error signal as well. 
It should be emphasized at this point that the improvement provided by the 
present invention is not due to better linearization as in iterated Kalman 
filtering (where the improvement increases with the iteration interval); 
but rather, due to the fact that if the reprocessing interval is optimal, 
the two sets of measurements are nearly independent, resulting in nearly 3 
dB improvement of performance under low SNR. The alternative scheme, 
relevant to classical phase-locked loop structures, employs an adaptive 
Hilbert transform technique resulting in similar improvements. For those 
interested in such aspects, it should be pointed out that the overall 
complexity of the approach of the present invention is about three times 
the complexity of a single third order Kalman filter. The estimation 
algorithm for both the local and global parameters is, in fact, an 
improved version of a Kalman filter. For local parameter estimation, it is 
necessary to use an algorithm capable of estimating both the phase and 
frequency since the data is phase modulated on the carrier. For the global 
estimation algorithm, however, it is not necessary to estimate the phase 
and thus the Kalman filter may be substituted by frequency estimation 
resulting in a marginal reduction of the required P/N.sub.o. 
As set forth in Section 2 of the detailed paper an approximate minimization 
of equation (6) can be achieved by a recursive algorithm like a Kalman 
filter. It then goes on to describe that in the present invention what is 
employed is a computationally simpler suboptimal version of the optimal 
estimator of equation (6). What is accomplished is an estimation of a 
modified parameter vector directly and without knowledge of the particular 
data bit. The estimation of the vector, in turn, permits the computation 
of the total phase at the boundaries of that bit, i.e. just before the bit 
boundary and just after the bit boundary. It is obvious from FIG. 1, for 
example, that the total phase does not have any discontinuity at the 
actual bit boundary (i.e. at the boundary line between adjacent sample 
periods 12) and, thus, any difference between the above two estimates can 
be the result of only two things --data transition or noise. If the SNR is 
adequate, therefore, it is then possible to detect such a data transition 
with a "small" probability of error. 
Simply stated, therefore, the approach of the present invention can be 
stated as follows. An suboptimal estimation of the signal phase is made on 
the basis of the samples within adjacent sample periods just before and 
just after the boundary of the sample periods. The phase differences are 
then compared to a threshold level which, if exceeded, indicates a change 
of data bit state between the adjacent sample periods. The signal is then 
adjusted to reflect a change in state and the corrected signal data 
employed in an extended Kalman filter, or the like, to derive the 
parameter information of interest. The extrapolated data stream, as 
mentioned earlier, can be used as desired in other aspects of the signal 
receiving process. 
More specifically, the present invention employs a novel combined 
estimation/detection scheme which simultaneously detects data bits and 
obtains estimates of signal parameters such as carrier phase, frequency, 
etc., (related to receiver dynamics) in a sequential manner. The method 
employed is recursive in both the number of data bits and the observations 
within any one data bit. The procedure effectively involves two mutually 
coupled estimation processes. In one of these estimation processes, we 
obtain the estimates of the signal parameters (phase, frequency, etc.) in 
the vicinity of possible data transitions (i.e. at the symbol boundaries) 
on the basis of measurements obtained within the current data bit. These 
estimates (which are dependent upon both the data and the receiver 
dynamics and termed "local parameter estimates"), are then used to decide 
whether or not a data transition has actually occurred. On the basis of 
this information, data modulation is removed from the received signal and 
the modified observations are reprocessed to update the "global" 
parameters (dependent only upon the receiver dynamics and independent of 
data modulation) by taking into account the additional observations during 
the current "detected" bit. Thus, as depicted in FIG. 2, the knowledge of 
the data content of the signal 10 of FIG. 1 can be employed to create, in 
effect a modified signal 10' which can then be analyzed as an unmodulated 
signal. 
A functional block diagram of a proposed implementation of the present 
invention is depicted in FIG. 3. It will be noted that, in this preferred 
implementation, a closed-loop configuration involving the feedback 
correction signal to the reference numerically controlled oscillator (NCO) 
14 is required to keep the signal frequency .theta.(t) at the phase 
detector output within the bandwidth of the filter (accumulator) following 
the phase detector. Such a correction at a rate equal to a submultiple of 
bit rate consists of simply transferring the estimate of frequency (and 
possibly that of frequency derivative as well) to the NCO 14. As can be 
seen from the diagram of FIG. 3, the received signal is mixed with the 
feedback signal from the NCO 14 in the mixer 16. A pair of 1 bit delays 18 
clock the signal into the local parameter estimation logic 20 and data 
demodulation logic 22, respectively. The local parameter estimation logic 
20 estimates the phase of the signal just before and just after the bit 
boundary as described in detail elsewhere herein. The two phase values are 
then compared by the transition detection logic 24 as also described in 
detail elsewhere herein. The output of the transition detection logic 24 
is input to the data demodulation logic 22 as a control input. That is, 
the decision by the transition detection logic 24 determines what that 
data demodulation logic 22 does to the signal (i.e. whether to compensate 
for a change in bit state of the incoming signal steam or not). The output 
from the data demodulation logic 22 is then input to the global parameter 
estimation logic 26 which is then able to estimate the parameters of the 
signal on a global basis without the interference of the phase modulated 
data. Note that information from the global parameter estimation logic 26 
is fed into the parameter prediction logic 28 which provides feedback 
information to both the local parameter estimation logic 20 and correction 
logic 30. The correction logic 30, in turn, provides the input to the NCO 
14 and a feedback signal to the global parameter estimation logic 26. 
Thus, it can be seen that the entire process of the present invention as 
shown in FIG. 3 is a closed loop, self-optimizing process that employs 
estimation to make a best guess of the data so that the signal stream can 
be modified to remove the effects of the data thereon and the results of 
the estimation fed back to improve the further estimation that takes place 
as the signal input is analyzed on a continuing basis. 
We will now describe in some detail the overall estimation/detection scheme 
without specific details of the estimation algorithm itself. The inventor 
has applied a modified Kalman filter; but, those skilled in the art will 
readily recognize and appreciate that other appropriate recursive 
parameter estimation algorithms may be adapted to the proposed framework. 
The estimation/detection scheme of this invention involves the following 
recursive (in number of data bits) steps. (For specific details, reference 
should be made to the detailed paper.) 
Recursion in Data Bits 
Step 1-Let N be the total number of samples (assumed to be an integer) in 
any one bit period (e.g. period 12 of FIG. 1) with the first sample 
appearing at time t=0.sup.+ and the Nth sample occurring at time T.sub.b 
-T.sub.s, where T.sub.b denotes the bit period. With a recursive algorithm 
to be described shortly, we obtain the estimates of the parameter vector 
.PHI..sub.0 at time t=0.sup.+ on the basis of the first N measurements. 
Step 2-In order to detect bit transitions we need to obtain estimates of 
"local" parameters at the bit boundaries. Thus, to detect the possible 
transition at the end of the first data bit period, it is required to 
obtain estimates of the parameters t=T.sub.b - and t=T.sub.b +. Noting 
that the parameters at t=T.sub.b - are related to the corresponding 
parameters at t=0.sup.+ by the linear transformation (9) of the paper, one 
could predict the estimate of the parameter vector via the same linear 
transformation. Since we are interested in an optimum modulo 2.pi. 
estimator of the phase, however, this will not produce the desired results 
as explained in the paper. Instead, the desired optimum modulo 2.pi. 
estimator of the phase is obtained by reprocessing the first N 
measurements; but, with their time and phase reference measured with 
respect to t=T.sub.b - as also described in detail in the paper. In this 
manner, as mentioned earlier herein, the knowledge gained by the first 
processing is employed to assure that the subsequent reprocessing of the 
same data achieves an optimum result. Thus, as also mentioned previously, 
the second error signal, which is ignored in prior art techniques, is 
employed to optimize the results in the method of the present invention in 
this implementation. 
Step 3-Assuming that all the parameters except .theta. cannot change 
instantaneously, the predicted estimates of parameters at t=T.sub.b + 
(i.e. just after the possible data transition) are then determined by the 
same processing and reprocessing approach as described in detail in the 
paper. 
Step 4-Having noted that irrespective of the dynamics involved (excluding 
the physically impossible case of instantaneous position change), 
.theta.(T.sub.b +) can differ from .theta.(T.sub.b -) only if a data 
transition occurs at t=T.sub.b, i.e. d.sub.2 .noteq.d.sub.1. In the case 
of no transition, we have d.sub.2 =d.sub.1 and .theta.(T.sub.b 
+)=.theta.(T.sub.b -). Thus, transition detection at the transition 
detection logic 24 of FIG. 3 is according to the simple rule: 
EQU d.sub.2 =d.sub.1 if .vertline..theta.(T.sub.b +).theta.(T.sub.b 
-).vertline.&lt;.pi./2 and d.sub.2 .noteq.d.sub.1 otherwise. 
A detection error thus occurs only if the phase estimation error is greater 
than .pi./2. 
Step 5-In this step, the estimate of the global parameter vector (i.e. 
parameters at t=O.sup.+) is updated on the basis of modified measurements 
as described in the paper. The significance of this step is that this 
yields (near optimum) estimation of the absolute phase as against the 
modulo 2.pi. phase, and from this absolute phase estimate (carrier phase 
in the absence of any data modulation) at any time t can be determined by 
the simple linear transformation of (9) in the appended paper. 
Equivalently, using a dynamic model for phase, one could directly estimate 
total phase .theta.(k) at any time instance k. 
Step 6-Steps 2-4 are repeated for detection of subsequent data transitions 
and step 5 updates the estimate of .psi..sub.0 on the basis of additional 
measurements during consecutive bit intervals. 
Improved Filter: 
We will now describe a novel (and simple) modification to the Kalman filter 
according to the present invention which results in about 3 dB improvement 
in terms of SNR. By the analysis contained in Section 4 of the paper, the 
inventor has shown that an independent observation is available which can 
be exploited to improve the estimate of x(k). Among several possible 
methods, the inventor selected as preferred an iterative method wherein 
the measurements {y(k), z(k)} are divided into groups of M measurements 
with M equal to N or an integer submultiple of N. Each of these groups is 
then processed by the estimation algorithm two or more times. Considering 
the first such group with k between 1 and M, under low SNR conditions the 
estimate of total phase .theta.(k) in the first iteration denoted by 
.theta..sup.1 (k) would be considerably different from its estimate 
.theta..sup.2 (k) in the second iteration, i.e. .vertline..theta..sup.2 
(k)-.theta.(k).vertline.&lt;&lt;.vertline..theta..sup.1 
(k)-.theta.(k).vertline.. Thus, if the difference .theta..sup.2 
(k)-.theta..sup.1 (k) is approximately equal to .pi./2 , the corresponding 
noise samples are nearly independent and a signal processing gain of about 
3 dB is realized. For a given SNR, the value of M can be optimized to 
achieve maximum possible improvement. Note, however, that no such gain can 
be realized under high SNR as under such conditions .theta..sup.1 
(k).congruent..theta.(k).congruent..theta..sup.2 (k). The foregoing 
observations have been verified by the inventor herein by computer 
simulation. It may be stated that the improvement as described is not due 
to iterative linerization of the nonlinearity as is usually the case; but 
rather, due to the very specific properties of the noise. 
Modified Phase Locked Loop With Up to 3 dB Improvement 
An implementation of the present invention in terms of a phase-locked loop 
(PLL) is shown in FIG. 4, where to keep consistency with the notion of 
previous materials herein, both the received bandpass signal s(k+1) and 
the NCO (numerically controlled oscillator) signal are represented in 
terms of the same frequency .omega..sub.e. This too is described in 
greater detail in the paper. Note that the loop filter 32 may be designed 
either on the basis of a steady-state solution of the Riccati equation 
(Kalman gain) or via any other design procedure applicable to PLL filter 
design. For those interested in the basis therefor, the possible 3 dB 
improvement due to the Hilbert transform at 34 is described in detail in 
the paper. 
Thus, it can be seen from the foregoing and the detailed paper appended 
hereto, that the present invention has truly met its stated objectives by 
providing a novel simultaneous estimation/detection scheme which detects 
data and estimates the parameters of a received carrier signal phase 
modulated by unknown data and experiencing very high Doppler, Doppler 
rate, etc., whereby the signal parameters directly related to the 
position, velocity, and acceleration of the receiver can be estimated with 
high precision.