Ambiguity resolving method based on baseline length and included angle constraint

Abstract

The invention discloses a baseline length and included angle constraint ambiguity resolving method, which is characterized in that attitude resolving of baseline length and included angle constraint is carried out by adopting a step-by-step ambiguity fixing and self-adaptive constraint weight dynamic adjustment method, and the method specifically comprises the following steps of: calculating floating point solutions of two baselines; a corresponding floating point solution covariance matrix is obtained; fixing the ambiguity by using a base line length constrained LAMBDA method, and estimating a fixed solution of one base line; establishing double constraints based on the baseline length and the included angle for the other baseline; determining the weights of the two constraints by adopting a self-adaptive constraint weight adjustment method; and carrying out ambiguity fixation on the other baseline by using a baseline length and included angle constrained LAMBDA method. Compared with the prior art, the method can more comprehensively utilize geometric information between antennas, improves the accuracy and reliability of ambiguity calculation, is especially suitable for high-precision positioning requirements of unmanned driving, precision agriculture, geographic information systems and the like, and has a wide application prospect.

Description

Technical Field

[0001] The present invention relates to the technical field of Global Navigation Satellite System (GNSS), and particularly to a method for resolving ambiguity with baseline length and angle constraints applied to a three-antenna GNSS receiver system. Background Art

[0002] Attitude measurement is an important application of GNSS. Traditional GNSS receivers mainly adopt a two-antenna system, which can usually only provide measurements of two angles, namely heading and pitch. In contrast, a GNSS receiver equipped with three antennas can achieve complete measurements of three angles, namely heading, pitch, and roll, which makes it show broad application prospects in the field of high-precision attitude measurement.

[0003] Ambiguity fixing is a key technology to ensure attitude measurement accuracy. The widely used Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) has good performance in open space, but in scenarios such as dynamic attitude measurement in urban environments, limitations such as the observation environment, equipment conditions, and the number of available satellites pose great challenges to ambiguity fixing. In order to maintain the usability of the attitude measurement system in complex environments, research on ambiguity fixing algorithms with additional prior information constraints has been carried out in depth. Existing ambiguity fixing methods with additional prior information constraints mainly consider baseline length constraints, and it has been verified that compared with the traditional LAMBDA method, this method can fix the integer ambiguity in a shorter time and has higher reliability. Although the existing baseline length-aided ambiguity fixing method provides a new idea for ambiguity fixing, in the field of short-baseline attitude measurement, its effect on improving the angle measurement accuracy is limited. And currently, the three-antenna solution usually resolves two baselines separately, failing to fully utilize the geometric relationship between the baselines, resulting in insufficient exploration of data redundancy and limiting the accuracy and reliability of the overall solution.

[0004] In summary, existing three-antenna attitude measurement technologies have problems such as insufficient utilization of geometric constraints and weak anti-environment interference ability, lack effective association and constraint on the resolution results of two baselines, and lack overall optimality, making it difficult to fully exert the high-precision advantages of the three-antenna attitude measurement system in complex environments. Summary of the Invention

[0005] The object of the present invention is to provide a method for ambiguity resolution based on baseline length and included angle constraints in view of the deficiencies of the prior art. By adopting the methods of step-by-step constrained ambiguity fixing and adaptive constrained weight dynamic adjustment, one of the baselines, AB, is fixed first, and the LAMBDA method (such as Baseline Constrained-Least Square Ambiguity Decorrelation Adjustment, BC-LAMBDA) with baseline length constraint is used to improve the efficiency of ambiguity fixing. After the baseline AB is fixed, a double constraint of baseline length and included angle is imposed on the other baseline AC, and combined with the dynamic adjustment of adaptive constrained weights, an improved least square ambiguity decorrelation algorithm with additional baseline length and included angle constraints (Baseline and Included Angle Constrained-Least Square Ambiguity Decorrelation Adjustment, BIC-LAMBDA) is used for ambiguity search to improve the efficiency and accuracy of ambiguity fixing. This method can make more comprehensive use of the geometric information between antennas. By combining the double constraints of baseline length and included angle and establishing an adaptive constrained weight mechanism, it improves the accuracy and reliability of ambiguity resolution, and is especially suitable for high-precision positioning requirements such as unmanned driving, precision agriculture, and geographic information systems, having broad application prospects and commercial development value.

[0006] The specific technical solution for achieving the object of the present invention is: a method for ambiguity resolution with baseline length and included angle constraints, which is characterized by adopting a step-by-step ambiguity fixing strategy and adaptive constrained weight dynamic adjustment. In the step-by-step ambiguity fixing strategy, the baseline AB is fixed first, and the ambiguity fixing efficiency is improved by using the baseline length constraint. Then, based on the fixed solution of the baseline AB, the attitude angle (such as the heading angle) is obtained, and multi-dimensional constraints (such as baseline length, included angle) are imposed on the baseline AC. In the adaptive constrained weight dynamic adjustment, according to the carrier motion state (such as the covariance dynamic factor), the constraint weights are adjusted in real time to dynamically adapt to the carrier motion (such as sharp turns), avoiding misconstraints caused by fixed weights. The specific steps of the ambiguity resolution include:

[0007] Step 1: Calculate the two baselines formed by three antennas, one along the main axis direction and the other perpendicular to the main axis direction, calculate the float solutions of the two baselines, and obtain the corresponding float solution covariance matrices.

[0008] Step 2: Select one of the two baselines, fix the ambiguity by using the LAMBDA method with baseline length constraint, and estimate the fixed solution of one of the baselines (referred to as baseline AB). If neither of the two baselines can be fixed, directly output the float solution.

[0009] Step 3: If the baseline AB is successfully fixed, a double constraint based on the baseline length and the included angle is established for the second baseline (referred to as baseline AC).

[0010] Step 4: Use an adaptive constraint weight adjustment method to determine the weights of the two constraints in Step 3;

[0011] Step 5: Use the LAMBDA method with baseline length and included angle constraints again to fix the ambiguity of baseline AC, and obtain the attitude solution results with baseline length and included angle constraints.

[0012] In Step 1, the floating solutions of the two baselines formed by three antennas are synchronously solved through an extended Kalman filter.

[0013] In Step 2, the ambiguity parameters of baseline AB are extracted from the floating solutions, a target function with baseline length constraints is constructed, and the baseline fixed solution is obtained. When it fails, the floating solution is output.

[0014] In Step 3, the double constraint of baseline length and included angle shown in the following formula (a) is used, that is, the double constraint of baseline length and included angle is added in the least squares solution:

[0015]

[0016] In the formula, R is the real number field; Z is the integer field; y is the observation vector (including carrier phase and pseudorange observations); A and B are the design matrices respectively; a is the ambiguity parameter; b is the site coordinate parameter to be estimated; the floating residual vector where is the floating solution of the ambiguity, is the real value of the site coordinate parameter; represents the baseline solution based on the ambiguity vector a; Q aa is the covariance matrix of the ambiguity parameter; Q bb is the covariance matrix of the position and velocity; Q yy is the weight matrix of the observations; is the weighted norm; L AB 、L AC 、θ are the lengths of the two baselines and the dot product between the baselines used to characterize the included angle between the baselines; is the corresponding variance; ΔL AB 、ΔL AC 、Δθ are the differences between the measured values and the actual values of the lengths of the two baselines and the dot product between the baselines, as shown in the following formula (b):

[0017]

[0018] In the formula, b AB 、b AC are the baseline vectors respectively; ||b AB ||、||bAC || is the baseline length obtained from the baseline vector.

[0019] The weights of the two constraints of the baseline length and the included angle in step 4 are determined as follows:

[0020] 4-1: In the process of solving the floating-point solution, the covariance matrix related to position and velocity can be obtained. The dynamic factor η(t) is used to describe the severity of the motion. The dynamic factor η(t) is expressed by the following (c):

[0021]

[0022] 4-2: The constraint weight ω L (t) of the baseline length and the constraint weight ω θ (t) of the baseline included angle are dynamically adjusted by the following formula (d):

[0023]

[0024] In the formula, is the initial weight, which is generally given in advance. There is a variance calculation for the prior constraint ( ). α, β, γ, and δ are all adjustable gain coefficients to control the sensitivity of the weight to the motion state and the constraint deviation. is the exponential decay term used to suppress the mismatch of the constraint caused by noise, where is the value calculated first among the baseline AB and the baseline AC, L is the prior length value of this baseline, and σ L is the standard deviation of L; is used to reduce the non-linear influence of the angle deviation on the weight; is the calculated value of the baseline AB, is the calculated value of the baseline AC. This process can weaken the geometric constraint in the high-dynamic scenario and avoid the distortion of the search space; in addition, when the constraint deviation is small, the prior information is strengthened, and when the deviation is large, it depends on the statistical residual.

[0025] Step 5 adopts the BIC-LAMBDA algorithm to improve the fixing efficiency.

[0026] Compared with the prior art, the present invention has the following beneficial technical effects and remarkable technical progress:

[0027] 1) In the ambiguity resolution link, the BIC-LAMBDA algorithm of the present invention combines the step-by-step fixing strategy, embeds multi-dimensional geometric constraints (such as baseline length, included angle) into the integer search process, improves the success rate of ambiguity fixing, and also improves the heading angle accuracy in the dynamic vehicle test.

[0028] 2) For complex motion scenarios, the adaptive weight adjustment mechanism dynamically balances geometric constraints and noise interference by tracking the carrier motion state in real time (such as the covariance dynamic factor), successfully suppressing the risk of false fixation under sudden change conditions such as sharp turns, and reducing the roll angle error.

[0029] 3) It is especially suitable for high-precision positioning requirements such as unmanned driving, precision agriculture, and geographic information systems, and has broad application prospects and commercial development value. Brief Description of the Drawings

[0030] Figure 1 is the flow chart of the present invention;

[0031] Figure 2 is the attitude solution result diagram of baseline length constraint (BC-LAMBDA);

[0032] Figure 3 is the attitude solution result diagram of Embodiment 1. Detailed Embodiments

[0033] Refer to Figure 1 and perform attitude solution for baseline length and angle constraints according to the following steps:

[0034] Step 1: For the two baselines formed by three antennas, one along the main axis direction and the other perpendicular to the main axis direction, calculate the floating-point solutions of the two baselines and obtain the corresponding floating-point solution covariance matrices.

[0035] Step 2: Select one of the two baselines (referred to as baseline AB) and fix the ambiguity using the LAMBDA method with baseline length constraint; if neither of the two baselines can be fixed, directly output the floating-point solution.

[0036] Step 3: If baseline AB is successfully fixed, establish double constraints based on baseline length and angle for the second baseline (baseline AC). The double constraint method for baseline length and angle is shown in the following formula (a):

[0037]

[0038] In the formula, R is the real number field; Z is the integer field; y is the observation vector (including carrier phase and pseudorange observations); A and B are the design matrices respectively; a is the ambiguity parameter; b is the site coordinate parameter to be estimated; the floating-point residual vector where is the floating-point solution of the ambiguity, is the real value of the site coordinate parameter; represents the baseline solution based on the ambiguity vector a; Q aa is the covariance matrix of the ambiguity parameter; Q bb is the covariance matrix of position and velocity; Q yyis the weight matrix of observations; is the weighted norm; L AB , L AC , θ is the length of the two baselines and the dot product between the baselines used to characterize the angle between the baselines; is the corresponding variance; ΔL AB , ΔL AC , Δθ is the length of the two baselines and the difference between the measured and actual values of the dot product between the baselines, as shown in the following formula (b):

[0039]

[0040] Where b AB 、b AC are the baseline vector, ||b AB ||、||b AC || is the baseline length obtained from the baseline vector.

[0041] Step 4: Use the adaptive constraint weight adjustment method to determine the weights of the two constraints in step 3. The weights of the two constraints of baseline length and angle are determined as follows:

[0042] 4-1: In the process of solving the floating-point solution, the covariance matrix related to position and velocity can be obtained. The dynamic factor η(t) is used to describe the intensity of the movement. The dynamic factor η(t) is expressed as follows (c):

[0043]

[0044] 4-2: Constraint weight ω on baseline length L (t) and the constraint weight ω of the baseline angle θ (t) is dynamically adjusted by the following formula (d):

[0045]

[0046] Where, is the initial weight, which is usually given in advance, and the variance calculation with prior constraints ( ), α, β, γ, and δ are all adjustable gain coefficients to control the sensitivity of the weight to the motion state and constraint deviation. is an exponential decay term used to suppress the mismatch of noise to constraints, where is the value first calculated from baseline AB and baseline AC, L is the prior length value of the baseline, σ L is the standard deviation of L; Used to reduce the nonlinear effect of angle deviation on weight; is the calculated value of baseline AB, It is the solution value of the baseline AC. This process can weaken geometric constraints in high-dynamic scenarios and avoid distortion of the search space; in addition, when the constraint deviation is small, prior information is strengthened, and when the deviation is large, it relies on statistical residuals.

[0047] Step 5: Use the LAMBDA method again to fix the ambiguity of the baseline AC, and obtain the attitude solution results constrained by the baseline length and included angle.

[0048] The following further illustrates the present invention (BIC-LAMBDA) through specific embodiments of attitude solution based on a three-antenna GNSS receiver system.

[0049] Embodiment 1

[0050] Step 1: Install three antennas on the carrier. Two baselines formed by the three antennas, one along the main axis direction and the other perpendicular to the main axis direction. First, calculate the floating-point solutions of the two baselines formed by the three antennas, and obtain the corresponding floating-point solution covariance matrix.

[0051] Step 2: Select one of the two baselines, and use the LAMBDA method constrained by the baseline length to estimate the fixed solution of one baseline (baseline AB). If neither of the two baselines can be fixed, directly output the floating-point solution.

[0052] Step 3: If baseline AB is successfully fixed, establish double constraints based on the baseline length and included angle for the second baseline (baseline AC).

[0053] Step 4: Use the adaptive constraint weight adjustment method to determine the weights of the two constraints in Step 3.

[0054] Step 5: Use the LAMBDA method with baseline length and included angle constraints again to fix the ambiguity of baseline AC, and obtain the attitude solution results constrained by the baseline length and included angle.

[0055] Refer to Figure 2 , through the attitude solution results and true value results (i.e., the values of high-precision inertial navigation and GNSS tight integration) of the three-antenna baseline length constraint (BC-LAMBDA), the RMSEs of the heading angle, pitch angle, and roll angle are 0.55°, 0.45°, and 2.26° respectively.

[0056] Refer to Figure 3, the attitude solution results and true value results of the present invention (BIC-LAMBDA) through the three-antenna baseline length constraint and included angle constraint show that the heading angle result obtained after adding the angle constraint in the present invention is more stable, the accuracy in the pitch angle direction is improved, and the solution result of the transverse baseline vector of the roll angle is also improved; the RMSEs of the heading angle, pitch angle, and roll angle are 0.46°, 0.40°, and 1.73° respectively, and the accuracy is improved by 16%, 11%, and 22% respectively compared with the attitude solution result using only the baseline length constraint.

[0057] The above specific implementation is only to further illustrate the present invention, and is not used to limit the patent of the present invention. All equivalent implementations of the present invention should be included within the scope of the claims of the present invention. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention, and any reference signs in the claims should not be regarded as limiting the claims involved. In addition, it should be understood that although this specification is described according to the embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for ambiguity resolution with baseline length and angle constraints, characterized in that The attitude solution with baseline length and angle constraints is carried out by using the method of step-by-step ambiguity fixing and adaptive constraint weight dynamic adjustment, which specifically includes: Step 1: For the two baselines formed by three antennas, one baseline is along the main axis direction and the other baseline is perpendicular to the main axis direction. Calculate the floating-point solutions of the two baselines and obtain the corresponding floating-point solution covariance matrices; Step 2: Arbitrarily select one baseline, use the LAMBDA method with baseline length constraint to fix the ambiguity and estimate the fixed solution of one baseline. If neither of the two baselines can be fixed, directly output the floating-point solution; Step 3: After one baseline is fixed, establish double constraints based on baseline length and angle for the other baseline; Step 4: Use the adaptive constraint weight adjustment method to determine the weights of the two constraints in Step 3; Step 5: Use the LAMBDA method with baseline length and angle constraints to fix the ambiguity of the other baseline and obtain the attitude solution result with baseline length and angle constraints.

2. The baseline length and included angle constraint ambiguity resolution method according to claim 1, characterized in that In Step 3, the double constraints of additional baseline length and angle are adopted in the least squares solution of the following formula (a): Wherein, R is the real number field; Z is the integer field; y is an observation vector including carrier phase and pseudorange observations; A and B are design matrices respectively; a is an ambiguity parameter; b is an unknown parameter such as station coordinates to be estimated; the float residual vector where is the float solution of the ambiguity, is the real value of the station coordinate parameter; is the baseline solution based on the ambiguity vector a; Q aa is the covariance matrix of the ambiguity parameter; Q bb is the covariance matrix of the position and velocity; Q yy is the weight matrix of the observations; is the weighted norm; L AB 、L AC 、θ are the lengths of two baselines and the dot product between the baselines used to characterize the included angle between the baselines; is the corresponding variance; ΔL AB 、ΔL AC 、Δθ are the differences between the measured values and the actual values of the lengths of two baselines and the dot product between the baselines, and are expressed by the following formula (b) as: where b AB and b AC are respectively baseline vectors; ||b AB || and ||b AC || are baseline lengths obtained from the baseline vectors.

3. The baseline length and included angle constraint ambiguity resolution method according to claim 1, characterized in that The weights of the two constraints of baseline length and angle in Step 4 are determined as follows: 4-1: In the process of solving the floating-point solution, the covariance matrices related to position and velocity can be obtained. The dynamic factor η(t) shown in the following formula (c) is used to describe the severity of the motion: 4-2: Constraint weight ω for baseline length L (t) and constraint weight ω for baseline angle θ (t) is dynamically adjusted by the following equation (d): In the formula, is the initial weight; α, β, γ, and δ are all gain coefficients; is the exponential decay term, where is the value solved first among the baseline AB and the baseline AC, L is the prior length value of the baseline, and σ L is the standard deviation of L; is the reduction term for the non-linear influence of the angular deviation on the weight; is the solved value of the baseline AB; is the solved value of the baseline AC.

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