Software and Hardware Design of Software GPS

From the system and macro perspectives, after the application layer is stripped off, the work completed by the GPS receiver can be divided into three parts: signal measurement, data receiving, and geometric calculus.

 

Receiving data refers to receiving data transmitted in the form of bitstream or packets (excluding the data that can be obtained only by measuring the phase, frequency, and intensity of the signal ). Each satellite continuously sends its own orbital location data. The data contains its location and time. The orbital position of a satellite is transmitted in the form of an Almanac and an Ephemeris parameter associated with the predicted position. Complex coordinate parameters can be transmitted repeatedly by using calendars and orders. In addition to the location data transmitted by the calendars and orders, there are also several groups of data used to modify the Track location and propagation characteristics.

 

In order to be different from data receiving, the process of obtaining data parameters through measurement of the phase, frequency, and intensity of signals is called signal measurement. Each GPS satellite uses different pseudo-random codes to distinguish it from other satellite signals, including a 1.023M bit rate Gold Code (a group of well-known pseudo-random codes) that occupies a large power) the part of the phase adjustment (C/A code, only on L1 carrier, 1,575.42 M) and the portion of A pseudo-random phase adjustment (P code, in L1 and L2 carriers, L2 is 1,227.60 M ). Signal measurement is to measure the phase relationship and frequency between these pseudo-random code blocks (or with the carrier) to obtain precise timing, then, the complete time difference is obtained by overlays into the inner order of the QR code, the order of the QR code, the packet order, and the rough interval of the packet order.

 

Figure 1: GPS ry calculation is simple.

 

References and Inheritance of time in GPS

 

The GPS receiver takes 12.5 minutes to receive all the data. GPS receivers work in cold start, hot start, tracking, and seek; tracking is a continuous process that uses previous parameters to quickly locate a new point. A Fast positioning technique is used to estimate the parameters of the next measurement point before entering the pile-seeking state. after entering the pile-seeking state, the parameters of the pre-defined pile points are corrected to locate the problem at a high speed.

 

The time/distance that can be determined by gps c/A code-piece inner order, code-piece order, and Data Order correspond to 0.98us/293 m, 1 ms/300km, and 20 ms/6,000 km respectively. The sub-frame sequence and the frame sequence (PAGE) correspond to 6 s and 30 s. The complete page contains time information and does not require a longer time decision. When locating, you usually first check whether there is any time that can be referenced. If the accuracy of the time that can be referenced is sufficient to locate the current time within a certain time range, you only need to measure the time in this time slice. The accuracy of the referenced clock is determined by its drift and the accuracy of the last time it was inherited; the fixed speed deviation can be eliminated by the proportional coefficient.

 

GPS is an accurate timing system. After the system is put into operation, the receiver can adjust the clock. The receiver system may have multiple clock sources that can be referenced, such as the real-time clock of the host processor and the scheduled clock for running the processor commands. Generally, the Calibration Time, calibration accuracy, clock frequency correction and clock drift are required. The deviation is calculated and the reference is determined based on the current clock time. use different numerical expressions to adapt to the changing speed and accuracy ). In most cases, other clock sources can be used for effective timing to within 6 s. For example, when the reference drift is +/-2, 000ppm (equivalent to +/-3 minutes per day, if the inherited accuracy is 1 s, you can determine which 6 s the current sub-frame belongs to within 40 minutes after calibration. If the 40ppm clock is referenced within 25 s, you can determine which 1 ms the current code is.

 

In a larger time range, references and Inheritance of dates, times, and minutes are used to preliminarily determine which satellites are currently receiving signals. In a smaller range, references and inheritance are used to narrow the range of displacement-multiplication when a sample set is calculated. These clock data within different precision ranges can be expressed in the same data structure, and reference, inheritance, and calibration algorithms can also be used in the same structure design.

 

Time Measurement and sample set

 

Figure 2 illustrates the time relationship between GPS data transmission. The duration greater than the GPS data bit, that is, the timing measurement of more than 20 ms is different from that of less than 20 ms; a long period of time is determined by the time when the data bit and data bit change. In this case, you need to check the exact time when the data bit conversion occurs-that is, from which part of the code to start sending the next bit of data.

 

 

Figure 2: time relationship between GPS data and Signals.

 

As described in the previous section, only when the accuracy of the current bit timing cannot be maintained by the reference and Inheritance of time requires the time when the bit change occurs (and other non-maintainable slower timing ;). Since there is no transmission interval between the data bit and the bit, this time can be measured only when the data changes. To identify the changes in the data bit, it is necessary to continuously monitor the PRN block or the collected signal sample set to include at least one bit change. Except that the bits of the 8-byte leading sequence in the TLM packet field are known (10001011b), it is unknown how other time data changes. This makes a large sample set. If the potential bitwise changes of n are included, the correlation product must be calculated in the N2 composite state. Generally, n> 1 sample set is not needed. On the one hand, the simulation conclusion after this section is that it can be effectively calculated when the depth of the sample set is close to one PRN sample set, in addition, each data bit repeat up to 20 identical PRN segments. On the other hand, the leading sequence of the TLM field appears every 6 s and is estimated with a 40ppm clock, the timing accuracy of one inheritance can be located in four sub-frames, namely within 24 s, using the clock to locate one of the 20 PRN segments. Even if a PRN block cannot be located, if only data is collected within 20 ms within one data bit, only one time of possible data changes can be ensured.

 

The data bit change time measurement determines a PRN piece, that is, 1 ms. More precise timing needs to measure the phase relationship of the PRN code. This measurement is the most frequent processing during GPS reception.

 

Considering that there may be a data bit change in the sample set, the related Calculation of a sample set may result in two-digit data, one Data Change Time, And one phase offset time. In addition to the change time of the measurement data, including n = 1 can also be used to deal with the reverse phase caused by frequency offset in low quantization accuracy.

 

Next we estimate the depth of the sample set. Figure 3 shows the correlation product variation curve of gps c/A code sliding correlation with different sample depths. 11 other pseudo-random sequences in the signal sample are used to simulate interference and noise (take the single-star signal power as the base noise-16 bb, in addition, the signal of the other seven stars is used as the receiver noise for interference and reserved 8 dB. The cascade noise coefficient of MAX2741/2741A is <4.7dB .). We can see that after the sample depth exceeds 80%, we can use the mean value of 1.05 to identify the relevant peak position. The impact of sampling frequency and amplitude quantization on the digital sample set generation will be discussed later.

 

 

Figure 3: simulation of gps c/A sliding correlation coefficient for different sample depths.

 

The above simulation uses a complete PRN chip. In actual application, the sample set is generally composed of several parts, each of which is collected in a continuous small period of time, and the entire sample set is collected in a large time span. According to the characteristics of the PRN, the sample sets composed of fragments maintain the statistical characteristics of the original PRN code as a whole.

 

In addition to the minimum depth and maximum time span of the sample set, the actual time span limitation is system time variability. GPS satellites rotate around the earth around 20,200 km above the ground at a speed of 12 hours (the ground observer seems to have only one landing within 24 hours ;). When a satellite is flying at a 45 ° angle above the receiver, its speed is about 5000 km/h or 1.7 m/MS (for comparison: 1000 km/h jet aircraft speed in combination with 0.27 m/MS ). When the Sample Set spans a large amount of time, the signal phase and frequency change. The actual system may not change the data collection rate for each star, but may only change the local coherent code sample (some documents refer to as the copy code ). The Calculation of moving correlation using different micro-bias frequencies before and after a sample set requires multiple local samples and repeated calculations. In comparison, the system uses a fixed micro-frequency offset in a shorter sample set, the obtained location information and moving condition can be corrected and averaged to quickly obtain rough positions and moving data with low computational complexity and real-time requirements; then, the data can be used to correct the micro-frequency offset and movement, and the data with improved precision can be obtained after several iterations. Relative to the satellite speed, the motion changes of the receiver do not cause a significant frequency shift, but only represent a phase shift (the time point of the micro-frequency offset ). The maximum sample set time allowed in this algorithm is determined by the difference between the local frequency and the frequency of the received data, that is, during this time, the frequency difference is not enough to reverse the PRN code multiple times (related to the demodulation method, or it may not be enough to reverse the Carrier Multiple times ). Considering this restriction, the performance of many crystal oscillator models can tolerate 20 ms of sample set time. In addition to some special applications, such as the frontend sequence measurement, this restriction is generally not required.

 

The relative movement of a satellite at a general speed is mainly determined by the movement of the satellite, and the movement of the satellite is stable for a period of time. Therefore, the compensation for the carrier's Doppler shift can remain unchanged for a period of time. Doppler phase and frequency movement cannot be directly reflected in the baseband signal. This is because the baseband signal does not have a single frequency and is also the result of filtering in the channel. When moving compensation is used to calculate the sample set, the average effect makes the satellite equal to the point in the moving path corresponding to the sample time. This simplified processing is available for low-Position Precision and receiver movement speed, and is especially applicable for High-Position Precision and fast movement, then, the related computation is performed based on the collection time of the sample set. For higher location accuracy, we do not need to simplify the compensation because we need to use carrier phase measurement and other means to directly handle this deviation.

 

 

As the second part of this article, this article focuses on the physical layer. Some parts are universal, but they are still closely related to the analog front-end and the processor and software used together.

 

Front-end architecture of GPS receiver Simulation

 

In the GPS receiver architecture represented by MAX2741/MAX2741A, MAX2741 is a simulation front-end designed specifically for applications that use the processing capabilities of the host machine to complete the GPS function. It is expected that GPS receivers of similar architectures will gradually become mainstream in the market due to their low overall cost. The architecture is a two-step sub-frequency super-external receiver, and the output is a digital Second Intermediate Frequency Signal Stream. In addition to the RF input filter, an intermediate frequency output filter, and a phase-locked loop filter, the filter must be set up on the chip. The MAX2741 chip integrates all the components required to form a complete receiver, including the local resonant channel.

 

MAX2471 supports flexible configuration only in the aspect of binary medium frequency filtering quantization and reference frequency configuration. The second-intermediate frequency and the Local Vibration are relatively fixed in the channel. For such a receiver, the frequency division and the design of the above three filters can be determined in the system design planning phase based on the C/A-code-oriented modulation bandwidth, which generally does not need to be adjusted.

 

The secondary If bandwidth, output DC elimination, and gain can be automatically optimized during the receiving process.

DC cancellation is mainly for the receiver's second-intermediate frequency converter offset drift and phase drift to form a Low-Frequency Impedance band. It can be adjusted through the point balance between the zero and the two sides in the statistical sample set.

 

Gain affects the receiving effect by quantizing the position of the step. After the reference inheritance settings or the initial settings are quickly established based on the statistical distribution of the output data, the gain must be self-adaptive in the work. The subsequent sections also discuss the preliminary settings.

 

As shown in figure 4, the dependency of the software GPS system design on the host hardware can be improved by providing a virtual underlying time for MAX2741. Virtual time meters can be implemented by embedded hardware of the host machine processor (such as common capture time counters), or by separate hardware. The output serial data itself is sequential with time information. The time when the VM time is recorded in the absence of serial data.

 

The virtual time meter standardizes the receiver interface and clarifies the real-time requirements of the receiver and processing interface. The hardware interface and Software Porting are simplified to the implementation of the interface based on virtual time and serial stream data streams.

　　

Sample Set and partial slide Correlation Algorithm Based on segment generation

 

According to the discussion in the first part, to ensure effective related computing, a sample set that contains at least a total amount of continuous data exceeding 1 ms must be collected within the time span <20 ms. Not a host system designed for GPS applications may not guarantee continuous data collection and buffering. Therefore, starting from the universality, use the timestamp data segment in Figure 4 to create a set for related computing.

 

Figure 4: Add a virtual hour br> figure 6: Distribution of frequency offset scans and error phase scans and frequency and phase planes.

Part 1 of pseudo-random sequence has been mentioned. If the number of samples is sufficient and the original sequence is still maintained, see Figure 5, when a sequence composed of fragments is used for correlation calculation, if the interval between them is short, it can be connected to a longer sequence using a zero value (or an alternating sequence of 0 and 1; however, a longer sequence requires greater computing overhead. Whether it is filling or separate processing is related to the adopted algorithm; When Using FFT, it is suitable for filling, and when sliding is related, it is suitable for separating.

 

For a specific PRN code, whether the same code exists in the received sequence and the position of the Code in the sequence are reflected by the correlation product. 5, when different offsets are used to slide the PRN blocks generated locally, if the PRN code exists in the receiving sequence and the local slice slides to the position consistent with the Code in the receiving sequence, the related product will peak (or valley value ).

Improve hardware independence of GPS design.

 

 

Figure 5: coherent computing for multiple fragments.

 

The process of generating a local coherent Code chip samples a locally generated PRN code sequence by the clock sequence of the receiving sequence. This clock is determined by the sampling clock of the receiver, there is no direct relationship with the GPS system clock in the receiving sequence; the clock used to generate the local PRN sequence (including the clock used to generate the local carrier) the clock must be consistent with the GPS system, that is, the clock to be measured.

 

The signal-to-noise ratio required by GPS reception cannot ensure effective carrier recovery and synchronization. The time-domain correlation of PRN must be used to suppress the non-coherent part in order to effectively identify the carrier.

 

Low-frequency demodulation and Related Algorithms and Carrier Tracking

 

Similar to the low-frequency output design of MAX2741, we hope to use the capabilities of the host processor to implement BPSK demodulation, rather than adding hardware circuit demodulation; the local sampling of the PRN block in Figure 5 is converted to the sampling of the local BPSK tuned carrier generated by the PRN code modulation. Then, the related Multiplication operation performs the demodulation of the carrier at the same time. See Figure 6. At this time, the correlation Product peak (Valley) shown in the one-dimensional distribution along the offset axis of the PRN code in the lower right of Figure 5) it is manifested in the convex Ridge (concave trench) on the local synthetic Carrier Frequency-phase plane, which is related to the degree of closeness of the peak and valley ).

 

 

Figure 6: frequency offset scan and error phase scan area and frequency phase plane distribution.

 

When the same frequency of the local carrier and the carrier in the receiving sequence is ensured, the correlation Product peak (Valley) values of different local carrier phases are cosine distributed for a sample set.

 

When the carrier is in different steps, different phase shifting values are calculated, either without obvious peaks (troughs) or peaks (troughs) there are multiple changes related to the frequency modulation of the PRN code within the sampling time span.

The complete processing of a sample set includes scanning and calculating the correlation product for different possible PRN codes, PRN codes with or without a data inversion, different local vibration frequencies, and different local vibration phase shifting ranges. The scanning range is determined by the certainty of the parameters that can be referenced by the receiver.

 

For sample sets collected at different times, the correlation product varies with the time with the current vibration frequency. If the Local Vibration deviation remains within a certain range, the samples are not completely processed, but the samples with obvious peaks and troughs are used.

 

Each bit of the PRN code in the BPSK signal of the GPS satellite is transmitted by the complete periodic waveform of the 1540 BPSK Carrier. For a receiver similar to MAX2741, the bit of the PRN code in the intermediate frequency output does not have a synchronization relationship with the phase of the carrier because the lower-frequency Local Vibration Synchronization is not taken into account. Therefore, the host machine does not have to consider the stable phase relationship between the carrier and the PRN when synthesizing the local modulation carrier. When synthesizing a local modulation carrier, you can directly use the PRN code to segment and splice the local carrier to generate a local modulation carrier. The balance of the cumulative filtering effect for compensating satellite signal transmission and receiving can be considered during local modulation wave sampling.

　　

Clock, sampling frequency, and Amplitude Quantization

 

The phase-locked loop and Local Vibration of max2741 suppress external clock jitter or phase noise, which are amplified during frequency conversion and transmitted to the intermediate frequency output. The jitter of the clock used for second-intermediate frequency sampling has a linear effect on carrier detection. For low jitter, the product of speed of light and jitter can be directly used to estimate the influence of the clock jitter on location measurement. A common crystal oscillator with 50 ps jitter, The Impact of sampling time jitter is estimated to be less than 0.15 m. Starting from this point, most of the clock of the host system can be used as the sampling clock. The requirements for this clock mainly assess the delivery of Jitter to the local vibration.

 

Although lower diintermediate frequency output is allowed theoretically and practically, the lower diintermediate frequency output is equivalent to introducing greater noise and accumulating more time measurement data; generally, the output frequency of the Second-intermediate frequency should not be less than 2 m limited by bit rate-bandwidth, and the sampling frequency of the Second-intermediate frequency should be at least a multiplier of the Second-intermediate frequency. The higher diintermediate frequency and sampling frequency reflect more cyclic waveforms and points in the sample set time. The sum of these two numbers affects the product and truncation error in the reciprocal relationship.

 

Figure 6 shows the simulation results corresponding to 100 periodic waveforms () and 25 periodic waveforms () respectively, using a 10th percentile sampling. No matter which group in the graph, it is close enough to the result of using continuous functions. In the center area, along the wrong phase shows a cosine change, along the bias frequency shows a Sinc Function Change. The black plane in the figure is a plane with a product and a value of 0. A set of cross lines that represent the products and values and the zero-plane intersection are grid-like. The interval of this set of straight lines in the biased direction is the reciprocal of the number of periodic waveforms included in the sample, and the slope of the skewed phase pairs is the product of the number of periodic waveforms and π. When the noise is acceptable, using a small number of periodic waveforms is conducive to capturing the carrier in a larger range.

 

Signals from satellite groups can be considered to be of the same source, only statistical fading fluctuations, and can be considered to be basically stable within a short period of time (the Doppler effect between some signals produces relative L1, l2 carrier frequency 5-10ppm of the difference beat, for 6 m two medium frequency about 0.1-0.2%), at the same time, this signal is drowned in the noise. This signal is not cost-effective for linear quantization within the entire range. The simplified analysis shows that the optimal quantization range is about 1.5-1.6 times of the noise power root mean square value. If there is no inherited data, it can be referenced, and its preliminary settings can be used to pre-process the Statistical Features of the data as a test.

 

The limiting phenomenon leads to a large number of interference elements in the band determined by the occurrence time of the limiting amplitude. To remove this interference, data must be preprocessed.

 

When combined with carrier-related demodulation and pseudo-random sequence correlation tests, the data in the time when the addition noise causes overflow is invalid. This is related to algorithms. If overflow lasts for a long time, you need to compromise whether data needs to be separated into different slices of the sample set for processing.

 

Parameter valuation and approximation optimization

 

In the previous article, we analyzed and provided the initial setup valuation and initial verification basis for all parameters of the MAX2741 GPS receiver. Some of these parameters need to be optimized at work, including the Statistical Error Parameters for several layers, the bandwidth of the two intermediate frequency output filter, the two intermediate frequency gain, and the configuration of the DC cancellation of the quantizer.

 

DC cancellation has a certain degree of time variability. The criterion and control relationship of DC cancellation optimization settings are clear, and simple sliding average feedback control can be used.

 

The second-IF Gain requires the use of amplitude-adaptive white noise and disturbance, and the signal strength of the preferred star as the criterion for optimization. The white noise range can be used as a parameter for low-time variability to inherit and slide average over a long period of time.

 

For most measurements, the moving parameters of satellites are considered stable. If the mobile data of the receiver cannot be provided, at least the angle and line rate parameter range must be provided. Generally, the movement of the receiver affects the measurement data processing. Therefore, it is necessary to include the mobile processing of the receiver in the measurement data processing software.

 

Capture (import) and trace policies

 

The offline Parallel Processing Method receiver discussed in this article can flexibly select different capture and tracking methods, which are mainly limited by the data-program storage capability of the host processor.

 

When processing a sample set, the collection time of the sample set is determined, and the appropriate parameters and required measurement processing are determined based on the inherited timing accuracy. Generally, you do not need to start from the beginning, search for all the stars, and re-determine the time of all different precision.

 

In general, the worst case is that no suitable carrier data can be referenced. At this time, FFT detection carrier can be performed on several samples with shorter collection time. In this case, the bandwidth of the Intermediate-frequency signal can be adjusted appropriately.

 

If more accurate carrier frequency data can be referenced, Carrier Frequency-phase search and precise Carrier Frequency-phase data can be performed near zero-plane intersection;

 

If precise Carrier Frequency-phase data can be referenced, a large sample set can be used for correlation testing to identify valid code groups and measurement code group phase timing.

 

After you can inherit the phase timing of the code group and the code group, it depends on the function and performance that the receiver wants to achieve.

 

If it is located within 50 meters, it can be transferred to receive packets. When receiving packets, You can simultaneously measure the packet bit conversion time, measure the phase timing of the code group, and maintain the Carrier Phase Lock Based on the frequency fluctuation of the related product.

 

If necessary, Carrier Frequency-phase tracking can be performed to provide more accurate measurement data. After being imported to the carrier frequency-phase tracking phase, it is necessary to regularly measure the packet bit conversion time and code group phase during the same period. This is mainly because carrier frequency-phase tracking is mainly suitable for short-term tracing, it is highly likely that sliding dislocation occurs when the carrier frequency-phase tracing is continuously dependent, and it needs to be re-calibrated by the pseudo-random phase.

 

During the tracking, if frequency-phase scanning is performed near the frequency of the received carrier, and the related product amplitude changes are not significant, therefore, the frequency-phase offset data cannot be obtained by scanning the data of a sample set in this range. If the carrier frequency has been locked within the frequency offset that can be reflected by the sample collection time, for example, within Hz, you can observe the difference pattern and use the difference pattern tracking in a series of sequential measurements. Otherwise, the carrier frequency-phase search should be performed near the zero-plane intersection. In this search computation, the related product data cannot be obtained simultaneously.

 

Author: Tan lei

Application Engineer

MAXIM Beijing Office

 

 

Note:

 

[A]: Unlike the abrupt inversion produced by modulation, a small frequency offset causes a differential modulation. The reverse phase caused by the differential beat oscillator at different times may be identified as the carrier reverse phase. In the case of higher quantization accuracy, we can observe that the reverse phase of the difference beat is slow, but the reverse phase may also appear suddenly at a lower quantization accuracy.

 

[B]: The simulation conditions are intentionally excessively deteriorated. In fact, the difference between 3-5 dB can be expected [8].

 

[C]: A 5 MHz crystal oscillator is used to calculate that more than one inversion condition exists within 20 ms, that is, a half-cycle waveform error occurs in the 10 k complete cycle waveform. We can calculate the 20Hz jitter equivalent to the peak value of 50 ps.

 

[D]: The carrier bandwidth of GPS is determined by its bit width, which is about 2.048 M. The bandwidth and center frequency of the input filter are determined by the GPS signal. After the division ratio is determined, the center frequency of the intermediate frequency is determined. The secondary if output low-pass filter is only used for anti-aliasing filtering.

 

[E]: MAX2741 uses a 4-bit DAC to form a digital feedback amplifier. However, the bandwidth is limited by the read/write speed of MAX2741, which cannot help suppress low-frequency stray signals. Its actual use only ensures the center position of the quantizer. The simple moving average of any iconic parameter, such as the sum of the data collected after preprocessing [s], can meet the needs of feedback adjustment.

 

[F]: The amplitude of the quantization step of MAX2741 is fixed, and the equivalent quantization step and range need to be changed by changing the gain. When adjusting the gain settings, you cannot obtain the exact increase value or quantify the Step Amplitude value. Instead, you must use the Statistical Features of the output signal to reflect the adjustment effect.

 

[G]: If only the sign bit is retained, the 0 value of the data corresponds to the 0-1 sequence that appears alternately. When both the sign bit and the amplitude bit are used, the value + 0 and-0 actually represent a non-zero signal. How to fill in the 0 value is related to the scheme of converting + 0,-0 to non-zero value. The simple method is to convert + 0 and-0 to + 1 and-1, and move the amplitude value to a high amplitude. At this time, the zero value of the data corresponds to 0. This solution is equivalent to improving near zero small signal.

 

For the FFT calculation process, because the GPS data has a large number of zero-value strings after preprocessing, the FFT Algorithm for multiple zero-strings is used. Therefore, using FFT computing can be directly filled with zero processing, split into different small pieces will not provide any benefit.

 

For the calculation process of simultaneous mixed carrier demodulation and correlation detection, if you consider only the calculation results that can be obtained from the orthogonal search process for suitable data and discard those unsuitable results, the linear relationship between the calculated amount and the string growth is because the length of the pseudo-random code is determined. If the vacancy between the two sample sets is m-bit, and the same unit of time is used for filling in the zero, multiplication, and addition, when calculated as a continuous sample set, the calculation time related to this M bit is 3 m units. When calculated separately as two sets, the additional overhead is mainly to create the starting point offset, pointer group, and loop control for the multi-increment set. If it is estimated that these operations are performed within several hundred time units, the number of vacant digits to be calculated separately or filled must be no more than dozens. In any actual system, the number of two collection operations must exceed 100 bits. At the same time, for systems with lower frequency doubling sampling, after the gain and zero point are properly set, dozens of long zeros are rarely displayed. Therefore, this computation process can only be calculated by fragment.

 

[H]: For Carrier Tracking, high sensitivity does not occur when the same frequency and phase are used. Therefore, different local modulation wave sample sets are required for calculating PRN correlation and carrier correlation.

 

[I]: This change can be observed only when the difference frequency is less than the bandwidth limit of the sample set collection time. This bandwidth is allowed to be slightly higher than the reciprocal of the collection time.

 

[J]: In the joint scan, orthogonal approach can reduce the relationship between the number of computations and the sample size and form a linear relationship with the size. Because the correlation Product peak value is not single in the carrier frequency phase, reliable orthogonal search requires strict and small search range. In fact, FFT and other search methods and repeated searches are also required. In this sense, any attempt to reduce the scan range is meaningful.

 

[K]: if there are several sample sets that can be referenced with the same precision, the first choice is to process these samples within the same scanning range and select the desired data. The cost of expanding the scanning scope is higher than that of checking multiple sample sets.

 

[M]: the process of generating a local modulation carrier is to sample the product of the locally synthesized carrier and the modulation signal using the sampling frequency collected by the signal. It is not feasible to calculate the carrier and modulation speed and efficiency in a timely manner. Therefore, we need to prepare a model of the sine wave and modulation signal for search. The phase change is reflected in the offset in the template table. As a high-frequency component of the modulated square wave, noise is generated in the calculation. Therefore, only the fundamental frequency of the modulated Square Wave needs to be reserved. If only the fundamental wave of the shortest duration T-square wave is applied to all symbol combinations during the change, it is equivalent to the increase of 2 T, 3 T, 4 T, and the 2nd, 3, 4, and multiplier. Further simplification can use the slope of the fundamental wave near zero crossing to trim the square wave into a ladder wave. This slope is 2 π/2.048Mhz ≈ 6/2. 048 Mhz. After normalization, it is shown that it reaches the trapezoid of the platform at the moment of 1/2 π. The time and amplitude differentiation rate when these templates are generated must be set according to the time and amplitude accuracy of sampling the received signal, that is, the deviation caused by inaccurate time pair and inaccurate amplitude expression is better than the sampling deviation of the received signal. Consider the slope of 2π times at zero point, the template must be created at 8 to 16 times the resolution rate of the received signal amplitude on the timeline. The sampling capability is consistent with or doubled on the amplitude axis.

 

[N]: The Slow variation of sampling time is the same as the signal phase shift. Only the slow components are not collected by the sample set for time homogenization.

 

[O]: The bandwidth of the max2741 PLL filter is 10-20 K. This filter and the frequency response of the DC canceling DAC jointly determine the low-frequency phase noise sensitivity of the Receiving System to the external reference frequency. The bandwidth of this noise is extended after the frequency conversion, and then restricted by Two-stage intermediate frequency filters, so that the residual affected range is approximately the same as the relative bandwidth of the satellite signal, which is about 0.13-0.14%. The noise in this range of external reference sources needs to be carefully investigated.

 

[P]: For Sine Signal sr = sin (ω T), use Ss = sin (α ω T + p) the product integral in the C-cycle waveform is equivalent to the ratio z of the product integral to the duration of 2 π C/ω. The expression is:

 

For a periodic function whose α is close to 1 and whose first part is C and whose value is not greater than 0.5, the linear function whose denominator is C decreases with 1/C. This option is ignored when the value of C is large.

 

The second part of the above formula is further integrated with the product transformation:

 

=

 

In this formula, the left part is the Sinc Function centered on α = 1, and the right part is the shifted cosine function. When α approaches 1, there is an extreme value of COS (P ).

 

[Q]: using the following expression in [p], we can see that the Sinc and Cosine Functions cause zero values of Z respectively. The zero value caused by sinc occurs in all places where C (1-α) is an integer, And the Trace Line is a straight line that is flat on the P axis. The zero trace line caused by cosine is a set of diagonal lines, and the slope of P to α is π C. The spine of Z is between the peak values of sinc and Cosine functions. It is not suitable for measurement because it does not change significantly near the peak value.

 

[R]: when the signal A = Sin (PSI) is used to detect the correlation between sine wave B = Sin (PSI + PHI), the product Integral Mean is Sin (PHI ). This formula is most sensitive to phase changes when Phi = π/2. If the amplitude limiting clamp is advantageous to the phase change detection, because A and B can be mutually easy, the favorable clamping amplitude is consistent for A and B. Considering that all harmonic elements will be eliminated and filtered out during the integral process, the phase change is most sensitive to the phase change when the detection is still at Phi = π/2. Calculating the clamp occurs when it is higher than Sin (π/4) and lower than Sin (π/4) respectively. We can see that any clamp is unfavorable for phase detection. Therefore, if the signal amplitude is within the quantitative range, the best effect is achieved.

 

After introducing a large addition noise, If we allocate a finite quantitative series (a linear and continuous component area) to a large range related to the noise amplitude, it is related to the noise power spectrum, and the probability that the signal appears at a larger quantization level is low. The possibility of recognizing signal changes at each quantization level decreases as the quantization level increases. The detailed estimation of the reasonable quantitative range at the specific quantitative level is related to the signal valuation method adopted and the signal collection time, which is very complicated. As an optimization of initial settings, we can simply identify that the noise amplitude in each quantization level is evenly distributed and that the quantization level is greater than the signal amplitude. We can simply think that the ratio of the signal amplitude to the noise amplitude corresponding to the quantization level is equal to the possibility of recognizing the signal variation. However, when the sine signal is added with narrow band noise, the signal-to-noise ratio of GPS signals and the amplitude envelope spectrum are represented by the Ruili distribution. Corresponding to the in-band noise power En and signal power Sn, when Quantizing to n level, according to the above simplified quantization amplitude optimization corresponding to solving the following probability P for A extreme value:

 

P =, X = 1.12 at the extreme value

 

The extreme value of this formula is unrelated to Sn because the relationship between Sn and A is simplified to linear, reflecting how to effectively use each quantization step in noise quantization. At the extreme value, the whole quantization range nA is about 1.58 times the noise power gain value. Considering that all the noise amplitude with a higher amplitude falls into the time range of the low Amplitude Quantization level, the signal will be detected at the low quantization level according to the time ratio, the quantitative range set for initial optimization needs to be adjusted in a small direction. The probability consistency between the signal amplitude of the Fourier distribution on both sides of π/2 ≈ 1.57 can be used as a preliminary test. At this time, about half of the time signal exceeds the quantization range, and can be used as a limit suppression.

 

If only the symbol bit is used, the signal may be detected only when the noise amplitude is less than twice the signal amplitude, and other times are equivalent to the limited suppression.

 

[S]: preprocessing includes entering 0 values for all data during the clamp period and removing low frequencies. The filling process is equivalent to using a square wave in the same band to modulated the original signal. The original signal spectrum is modulated by the square wave and its harmonic to the out-of-band and low frequency. After such preprocessing, a large number of zero-value and zero-value sub-sequences appear in the signal sequence. This sequence is easier to process than the original output. For example, the ups and downs of the starting data are small, and the feature quantity used for DC cancellation is easy to provide Optimized Feedback and stability. It is unsigned and can be used to reflect the ratio of clamp. For data that conforms to the Ruili distribution, if the clamp occurs in a period of less than half, its unsigned and mean values are about half of the clamp value.

 

[T]: two channels are used to narrow down the second-intermediate-frequency bandwidth: lowering the second-intermediate-frequency output low-pass filter passthrough and changing the high-pass filter in digital processing. After the bandwidth is reduced, all background components, including more suppression of the signal spectrum, are conducive to identifying the fundamental frequency. At this time, the fundamental phase information has been affected, and it is not suitable for other checks.