A clock synchronization and space registration integrated method for distributed networking radar

Abstract

The application provides a clock synchronization and space registration integrated method for a distributed networking radar, and relates to the technical field of radar signal processing. The application obtains echo and pose data of a sub-radar, determines a common view event, forms time difference, frequency difference and angle difference measurement, establishes cross-node constraints, combines round-trip time measurement, continuity and smoothness priori, and adopts a robust loss to suppress abnormal measurement. A sparse nonlinear least square solution is solved in a sliding window to obtain a unified time scale and a unified space coordinate system, to correct a transmission timing, a sampling clock and a beam pointing in real time, and to serve as a priori of a next window. When a residual error exceeds a threshold, observability enhancement is triggered to improve a geometric condition by increasing bidirectional time measurement and adjusting parameters, to realize high-precision synchronization and registration without external timing, and to guarantee consistency and cooperative performance of the networking radar.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and in particular to an integrated method for clock synchronization and spatial registration for distributed networked radar. Background Technology

[0002] Distributed networked radars work collaboratively through several sub-radar nodes to improve target detection range, angular resolution, and anti-jamming capabilities, while supporting omnidirectional coverage and information redundancy in a multi-static system. In engineering practice, external time bases are typically used for clock synchronization, and spatial registration is performed using target calibration or extrinsic parameter measurement procedures. Each sub-radar operates independently in its local time scale and local coordinate system, and time and space alignment is then performed in the upper-level fusion stage.

[0003] With the increase in multi-platform, mobile, and flexible networking applications, network topology is changing dynamically, target scenarios are becoming more complex, and the availability of available links between nodes and external absolute time references is not stable. This requires handling time drift, frequency deviation, and changes in node extrinsic parameters simultaneously under online operating conditions, and continuously maintaining a unified time scale and a unified spatial coordinate system in the sliding time domain to ensure cross-node coherent accumulation, joint inversion of angle and distance measurement, and stable correlation of target trajectory.

[0004] Existing solutions often implement clock synchronization and spatial registration separately, relying on external benchmarks or offline calibration. The coupling between time errors and extrinsic parameter errors is not modeled and utilized, leading to a decrease in the reliability of cross-node coherent processing and trajectory stitching when external benchmarks fail, calibration frequency is insufficient, or the scene changes rapidly. Existing methods lack an online integrated mechanism for simultaneously estimating clock and extrinsic parameters based on common-view target observations without relying on an external absolute time benchmark, making it difficult to guarantee continuous and robust network-level collaborative sensing quality. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide an integrated clock synchronization and spatial registration method for distributed networked radar. By constructing cross-node constraints through common-view measurements and combining prior and robust optimization, the distributed networked radar can still achieve high-precision clock synchronization and spatial registration under conditions of no external time synchronization and dynamic networking, thereby ensuring the long-term consistency and collaborative detection performance of the network as a whole.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] An integrated clock synchronization and spatial registration method for distributed networked radar includes:

[0008] Acquire local time-stamped echoes and pose data of each sub-radar, perform cross-node correlation within a sliding window based on range, angle, and Doppler consistency, determine common-view events, and calculate common-view measurements, namely time difference of arrival, frequency difference of arrival, and line-of-sight angle difference.

[0009] Set clock skew, frequency drift, extrinsic rotation matrix and extrinsic translation for each node, and fix the extrinsic parameters of the reference node to eliminate global uncertainty;

[0010] The common-view measurement forms a cross-node constraint set, which is superimposed with round-trip timing constraints, drift continuity priors and extrinsic parameter smoothing priors, and robust loss is used to suppress outlier measurements.

[0011] Sparse nonlinear least squares solution is performed on the constraint set within a sliding window to obtain the clock and extrinsic parameters of each node, thereby forming a unified time scale and a unified spatial coordinate system;

[0012] Based on the clock and extrinsic parameters, the transmission timing, sampling clock and beam pointing are corrected online, and the clock and extrinsic parameters are used as the next window prior.

[0013] Observability enhancement is triggered when any of the following conditions occur: the root mean square of the arrival time difference residual exceeds a preset first threshold, or the root mean square of the line-of-sight angle difference residual exceeds a preset second threshold, or the chi-square statistic of the normalized residual exceeds a preset third threshold; the observability enhancement includes adding bidirectional timing and adjusting operating parameters.

[0014] Preferably, the co-observation event is a correlated observation of the same scatterer by at least two nodes within the same window.

[0015] Preferably, the local time-stamped echo and pose data of each sub-radar are acquired, and cross-node correlation is performed within a sliding window based on range, angle, and Doppler consistency to determine common-view events. Common-view measurements are then calculated, including time difference of arrival, frequency difference of arrival, and line-of-sight angle difference, including:

[0016] Set the sliding window length and step size as preset values, and extract target detection entries containing local time stamps, slant range, line-of-sight angle and Doppler frequency shift, as well as corresponding pose data from the nodes of each sub-radar to form a detection set within the window;

[0017] Based on the pose data, propagation and motion compensation are performed on each detection item: the propagation time is calculated using the slant range and electromagnetic wave propagation speed, and the arrival time is compensated; the Doppler frequency shift is compensated using the platform radial velocity; and the line-of-sight angle is transformed according to the reference node coordinate system.

[0018] Thresholds are set for distance, angle, Doppler effect, and arrival time, respectively, and are denoted as distance threshold, angle threshold, Doppler threshold, and time threshold; the thresholds are jointly determined by a preset constant and the estimation result of the previous window.

[0019] Between the detections of nodes of different sub-radars, candidate association pairs are recorded according to the conditions that the distance difference does not exceed the distance threshold, the angle difference does not exceed the angle threshold, the Doppler difference does not exceed the Doppler threshold, and the arrival time difference does not exceed the time threshold. An undirected graph is constructed with the detection as the vertex and the candidate association pairs as the edges.

[0020] For the undirected graph, a connected subgraph is extracted. Within each connected subgraph, by minimizing the joint residual consisting of slant range, transformed line-of-sight angle, compensated Doppler and compensated arrival time, a combination consisting of at most one detection for each sub-radar node is selected. When the number of sub-radar nodes included in the combination is not less than two, it is determined to be a co-view event.

[0021] Within each shared-view event, a reference node is designated, and any participating node calculates the arrival time difference, the arrival frequency difference, and the line-of-sight angle difference relative to the reference node.

[0022] Preferably, clock skew, frequency drift, extrinsic rotation matrix, and extrinsic translation are set for each node, and the extrinsic parameters of the reference node are fixed to eliminate global uncertainty, including:

[0023] The extrinsic rotation matrix of the reference node is set to the identity matrix, and the extrinsic translation vector is set to the zero vector to eliminate global uncertainty in the unified spatial coordinate system; the unified spatial coordinate system is taken as the reference node coordinate system.

[0024] For each non-reference node i, let the unified time scale With local time stamp satisfy ,in This is the frequency drift coefficient. For clock skew; the unified time scale Defined as a common time reference within a sliding window after frequency drift and clock skew compensation;

[0025] For each node i, let the point coordinates in the unified spatial coordinate system be... with local coordinates satisfy ,in For extrinsic rotation matrix, The extrinsic translation vector; It satisfies the conditions of orthogonality and unit determinant;

[0026] The arrival time difference, arrival frequency difference, and line-of-sight angle difference measured by co-view measurement are respectively compared with... Establish explicit correlation equations to form a set of parameters to be estimated. and fixed constraints on the extrinsic parameters of the reference nodes.

[0027] Preferably, a cross-node constraint set is formed using the common-view measurement, superimposed with round-trip timing constraints, drift continuity priors, and extrinsic parameter smoothing priors, and robust loss is used to suppress outlier measurements, including:

[0028] For each shared-view event, between any participating node and the reference node, time residuals, frequency residuals, and angle residuals are constructed using arrival time difference, arrival frequency difference, and line-of-sight angle difference, respectively. Frequency drift coefficients, clock bias, extrinsic rotation matrix, and extrinsic translation vector are substituted into the time residuals, frequency residuals, and angle residuals. The residual weights of the time residuals, frequency residuals, and angle residuals are taken from the confidence level of the shared-view event.

[0029] When there are round-trip time records of transmission and echo at two nodes, the receiving-transmission time difference is calculated under a unified time scale, and the geometric round-trip time determined by the external parameter translation vector and propagation speed is subtracted to obtain the time consistency residual, which is used to enhance the observability of time parameters.

[0030] Between adjacent sliding windows, a differential residual is established for the frequency drift coefficient and clock deviation of the same node, so that the frequency drift coefficient and the clock deviation are continuous and bounded in time, thereby limiting the jump between windows;

[0031] Between adjacent sliding windows, smoothing constraints are established for the extrinsic rotation matrix and extrinsic translation of the same node; the extrinsic rotation matrix is ​​parameterized using a unit quaternion or an equivalent rotation matrix, the logarithmic mapping of the relative rotation is calculated and the three-dimensional vector of the logarithmic mapping is taken as the difference of the extrinsic rotation matrix, and the difference of the extrinsic translation vectors of the two windows is taken as the difference of the extrinsic translation; the difference of the extrinsic rotation matrix and the difference of the extrinsic translation are used as the residuals of the smoothing prior;

[0032] A robust loss function with a bounded influence function is applied to the time residual, the frequency residual, the angle residual, the time consistency residual, the difference residual, the extrinsic parameter rotation matrix difference, and the extrinsic parameter translation difference, and weighted according to the event confidence and preset weights, and summarized into a constraint set across nodes; the robustness threshold of the robust loss function is set according to the root mean square of the residuals of the previous window.

[0033] Preferably, sparse nonlinear least squares solution is performed on the constraint set within a sliding window to obtain the clock and extrinsic parameters of each node, thereby forming a unified time scale and a unified spatial coordinate system, including:

[0034] The set of parameters to be estimated obtained from the above sliding window As an initial value, all residuals in the constraint set are linearized at the initial value to obtain the Jacobian matrix. With residual vector ;in, This is the frequency drift coefficient. Due to clock skew, For extrinsic rotation matrix, The extrinsic translation vector;

[0035] Constructing normal equations ,in , Sparse decomposition is performed according to the elimination order of node blocks, prioritizing the elimination time parameter. Further elimination space extraparameter To reduce filler and retain key coupling terms, the increment is obtained. ;in, The coefficient matrix of the normal equation, The right-hand term;

[0036] The extrinsic parameter rotation matrix is ​​updated using an exponential mapping, and then updated using addition. Convergence is determined based on the preset incremental norm threshold and weighted residual reduction threshold; if convergence fails, the calculation is repeated. Continue iterating; the formula for updating the extrinsic rotation matrix using exponential mapping is: And normalize quaternions or preserve Orthogonality; where, For rotation increment vector, For Li Qun Exponential mapping;

[0037] When the window slides, the parameters and measurements that are about to be moved out of the window are marginalized, and the prior factors are formed by reducing them using Schur complement or equivalent information and incorporated into the constraint set of the new window; the extrinsic parameters of the reference node are kept fixed to maintain the global observability benchmark; where marginalization means transforming the constraint information of the moved-out variables into prior constraints on the retained variables to ensure the continuity of optimization.

[0038] After convergence, using the mapping Define a unified time scale, with Define the set of extrinsic parameters from the local coordinate system of each node to the coordinate system of the reference node, as a unified spatial coordinate system. This provides for subsequent coherent processing and multi-site fusion; among which, For local time stamps, To standardize time scales, Let be the extrinsic rotation matrix and translation set of the node.

[0039] Preferably, the online correction of the transmission timing, sampling clock, and beam pointing is based on the clock and extrinsic parameters, and the clock and extrinsic parameters are used as the next window prior, including:

[0040] Based on a unified time scale, the local transmission trigger time of each node is mapped and adjusted to ensure that the transmission signals of each node remain consistent under the unified time scale.

[0041] Compensation is applied to the local sampling rate and sampling phase to keep the sampling process aligned with a unified time scale; when the hardware does not support continuous compensation, equivalent adjustment is achieved through numerically controlled oscillation or resampling.

[0042] The desired beam direction in the unified spatial coordinate system is converted into the command direction in the local coordinate system, and the phased array weighting or servo control is adjusted according to the command direction to ensure that the beam is correctly aligned in the global coordinate system.

[0043] After correction, the residuals of arrival time and pointing angle are checked using the first batch of observation data. When they exceed the preset threshold, the corresponding module is triggered to make a fine adjustment again.

[0044] The clock and extrinsic parameters and confidence information obtained in the current window are recorded as the initial values ​​for the next window to ensure continuity and stability within the sliding window.

[0045] Preferably, observability enhancement is triggered when any of the following conditions occur: the root mean square of the arrival time difference residual exceeds a preset first threshold, or the root mean square of the line-of-sight angle difference residual exceeds a preset second threshold, or the chi-square statistic of the normalized residual exceeds a preset third threshold; the observability enhancement includes increasing bidirectional timing and adjusting operating parameters, including:

[0046] After the current sliding window solution is completed, the root mean square of arrival time difference residual, root mean square of line-of-sight angle difference residual, and chi-square statistics of normalized residual are calculated and compared with the corresponding preset thresholds; when any indicator exceeds the threshold, it is determined that the current observability is insufficient.

[0047] When observability is deemed insufficient, enhancement commands are sent to each node in the network, specifying the need to perform additional timing tasks and parameter adjustment strategies.

[0048] Under the enhanced command, each node initiates additional round-trip timing operations according to the scheduling protocol and sends back the timing results to increase the number of independent measurements in the constraint equations.

[0049] In cases of poor line-of-sight geometry, the number of co-view targets can be increased or the angular distribution can be more balanced by adjusting the transmission power of some nodes, the coverage of the working beam, or the transmission pulse scheduling.

[0050] The newly added round-trip timing results, along with the new measurements generated due to parameter adjustments, are incorporated into the constraint set of the next sliding window as enhanced observation conditions.

[0051] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0052] First, this invention addresses the problem of unutilized error coupling caused by separate estimation of clock and spatial parameters. By introducing common-view measurements and establishing a joint error model, clock bias, frequency drift, extrinsic parameter rotation matrix, and extrinsic parameter translation are simultaneously solved within the same optimization framework, making temporal and spatial errors mutually constrain and compensate for each other. This mechanism effectively avoids the error superposition caused by step-by-step correction and improves the stability of cross-node coherent accumulation and multi-base information fusion.

[0053] Second, this invention overcomes the dependence of existing technologies on external absolute time bases and offline calibration. In situations where external time synchronization is unavailable or nodes are dynamically networked, this invention utilizes common-view targets and bidirectional time measurement to construct cross-node constraints, achieving self-consistent synchronization and registration without the need for external bases. This design significantly enhances the system's independence and robustness under denied environments and complex operational conditions.

[0054] Third, this invention ensures the temporal continuity and anti-interference capability of the solution. By introducing a drift continuity prior and an extrinsic parameter smoothing prior into the sliding window, it suppresses parameter abrupt changes caused by node maneuvers, target occlusion, and scatterer variations. At the same time, it combines robust loss to weaken the influence of abnormal measurements, so that the solution results can remain stable and reliable even in rapidly changing environments.

[0055] Fourth, this invention achieves closed-loop application and real-time correction of parameters. The calculated clock and extrinsic parameters are not only used for subsequent optimization, but also directly fed back to the front-end control of transmission timing, sampling clock, and beam pointing, ensuring that new observations are naturally placed within a unified time scale and a unified spatial reference frame. This closed-loop mechanism avoids the accumulation of delays and deviations between "calculation and application," guaranteeing the long-term consistency of the network's global calibration.

[0056] Fifth, this invention improves robustness under conditions of insufficient observability. By setting triggering conditions based on residual statistics, once a decrease in observability is detected, the system immediately implements enhancement measures, including increasing bidirectional timing and adjusting operating parameters to improve geometric distribution and measurement redundancy. This mechanism effectively prevents optimization degradation and solution divergence, ensuring stable maintenance of a unified time scale and unified spatial coordinate system even under sparse targets or incomplete links. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 This is a flowchart of a method provided in an embodiment of the present invention. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] The purpose of this invention is to provide an integrated method for clock synchronization and spatial registration for distributed networked radar. By modeling and solving clock synchronization and spatial registration in a unified manner within a sliding window, a unified time scale and a unified spatial coordinate system can be maintained without the need for an external reference, thereby significantly improving the stability and collaborative detection accuracy of distributed networked radar in complex environments.

[0061] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0062] Figure 1 The method flowchart provided in the embodiments of the present invention is as follows: Figure 1 As shown, this invention provides an integrated method for clock synchronization and spatial registration for distributed networked radar, comprising:

[0063] Step 100: Obtain the local time-stamped echo and pose data of each sub-radar, perform cross-node correlation within the sliding window according to range, angle and Doppler consistency, determine common-view events, and calculate common-view measurements, namely time difference of arrival, frequency difference of arrival and line-of-sight angle difference.

[0064] Step 200: Set clock skew, frequency drift, extrinsic rotation matrix and extrinsic translation for each node, and fix the extrinsic parameters of the reference node to eliminate global uncertainty;

[0065] Step 300: Form a cross-node constraint set using common-view measurements, superimpose round-trip timing constraints, drift continuity priors and extrinsic parameter smoothing priors, and use robust loss to suppress outlier measurements;

[0066] Step 400: Perform sparse nonlinear least squares solution on the constraint set within the sliding window to obtain the clock and extrinsic parameters of each node, thereby forming a unified time scale and a unified spatial coordinate system;

[0067] Step 500: Correct the transmission timing, sampling clock and beam pointing online based on clock and extrinsic parameters, and use clock and extrinsic parameters as the prior for the next window;

[0068] Step 600: Observability enhancement is triggered when any of the following conditions occur: the root mean square of the arrival time difference residual exceeds a preset first threshold, or the root mean square of the line-of-sight angle difference residual exceeds a preset second threshold, or the chi-square statistic of the normalized residual exceeds a preset third threshold; Observability enhancement includes adding bidirectional timing and adjusting operating parameters.

[0069] Specifically, in step 100 of this embodiment, the length and step size of the sliding window are first set as preset values ​​to ensure the continuity and controllability of the observation data in time. This embodiment extracts target detection entries from each sub-radar node. These detection entries include local time stamps, slant range, line-of-sight angle, and Doppler frequency shift, and simultaneously extracts the corresponding pose data. Based on the pose data, this embodiment performs propagation and motion compensation on each detection entry: propagation compensation corrects the target arrival time using the propagation time calculated from the slant range and electromagnetic wave propagation speed; motion compensation corrects the Doppler frequency shift using the platform's radial velocity; and line-of-sight angle compensation is achieved by transforming the local observation direction to the reference node coordinate system to ensure that the observation results from different nodes are within the same spatial reference frame.

[0070] After compensation, thresholds are set for distance, angle, Doppler, and time of arrival, determined jointly by a preset constant and the estimation result of the previous sliding window. Subsequently, conditional filtering is performed between detections from different sub-radar nodes. When the distance difference, angle difference, Doppler difference, and time of arrival difference do not exceed their respective thresholds, the detection pair is recorded as a candidate association pair. In this embodiment, an undirected graph is constructed using candidate association pairs as edges and detections as vertices, and connected subgraph extraction is performed on the undirected graph. Within each connected subgraph, the combination result is selected by minimizing the joint residual composed of slant range, compensated line-of-sight angle, corrected Doppler, and compensated time of arrival. When the number of sub-radar nodes included in the combination is not less than two, this embodiment determines that the combination corresponds to the same scatterer, constituting a co-observation event. A co-observation event is defined here as the situation where at least two sub-radar nodes form co-observable observations of the same target scatterer within the same sliding window.

[0071] Within each shared-view event, a reference node is designated as a unified baseline node. Using this reference node as a benchmark, the measurement differences of other participating nodes relative to the reference node are calculated one by one. Specifically, the arrival time difference is obtained by the difference between the locally compensated arrival time and the reference node's compensated arrival time; the arrival frequency difference is obtained by the difference between the locally corrected Doppler frequency shift and the reference node's corrected Doppler frequency shift; and the line-of-sight angle difference is obtained by the angle between the local line-of-sight direction (transformed to the reference coordinate system) and the reference node's line-of-sight direction. These three types of differences together constitute the shared-view measurement results and serve as inputs for subsequent joint modeling and optimization of clock synchronization and spatial registration.

[0072] Specifically, in step 100 of this embodiment, assuming common-view measurements have been obtained, step 200 first selects a reference node, preferably one with stable link quality, high clock quality, and the highest online rate. In this embodiment, the spatial orientation of this reference node in a unified spatial coordinate system is set to unit rotation, and the position offset is set to zero vector. The unified spatial coordinate system is defined as the local coordinate system of this reference node; simultaneously, the unified timescale is defined as the sole time reference for all subsequent time-related quantity calculations and publications. These settings are used to eliminate the uncertainty of the overall "rigid body degrees of freedom" and the overall "time zero point," ensuring that time and spatial quantities between different nodes can be directly compared and fused under the same reference.

[0073] In step 200 of this embodiment, a linear mapping from local time to a unified timescale is established for each non-reference node. The mapping consists of a scaling factor and an additive bias: the local time is first multiplied by the scaling factor, and then the additive bias is added to obtain the unified timescale. The scaling factor reflects the relative drift of the local sampling frequency and is used to compensate for long-term accumulated scaling errors; the additive bias reflects the difference in clock start points at the beginning of the current window and is used to compensate for fixed delays and short-term offsets. The initial value of the scaling factor can be taken from the manufacturer's nominal frequency stability index or the estimation result of the previous window, and the initial value of the bias can be taken as close to zero or derived from power-on synchronization records; both are constrained by common-view measurements and priors during the optimization process and gradually converge. To ensure that the model is realizable and observable, this embodiment applies a "small deviation close to 1" constraint to the scaling factor and a "bounded continuity within the window" constraint to the additive bias, and uses the output of the previous window as the prior for this window.

[0074] In step 200 of this embodiment, a spatial extrinsic parameter mapping from local coordinates to unified coordinates is established for each node. The mapping consists of a three-dimensional rotation and a three-dimensional translation: first, rotation is used to align the local orientation and attitude to the unified spatial coordinate system, and then translation is used to align the local origin to the unified origin. The rotation must satisfy the condition that the rows and columns are pairwise orthogonal and the determinant is positive, and the translation is a three-dimensional real vector; the initial values ​​of both are derived from installation calibration or the previous window estimation. This embodiment establishes an explicit correlation between common-view measurement and extrinsic parameters: the arrival time difference corresponds to the difference in arrival times of the two nodes under the unified time scale; the arrival frequency difference corresponds to the difference in Doppler of the two nodes after scaling factor correction; the line-of-sight angle difference corresponds to the angle between the line-of-sight directions of the two nodes under the unified spatial coordinate system. Through the above relationships, the scaling factor, additive bias, three-dimensional rotation, and three-dimensional translation are all included in the same set of parameters to be estimated, and the fixed extrinsic parameters of the reference node are used as a constraint to ensure the identifiability of the overall solution. To suppress anomalous observations, this embodiment employs a robust weighting of the bounded influence on the measurement residuals, with the weights determined by the event confidence level and historical residual statistics.

[0075] In step 200 of this embodiment, after fixing the reference node and determining the unified reference frame, a quantitative range of values ​​for key parameters is further provided. The reference node is preferably selected with an online rate greater than 99% and a clock stability better than ±1×10⁻⁶. -8 For nodes with a link packet loss rate of less than 0.1%, the sliding window length is set between 1.0 and 3.0 seconds, and the step size is set between 0.2 and 0.5 seconds to balance real-time performance and accuracy requirements. The initial range of the frequency drift coefficient is limited to ±50ppm, and the initial convergence radius is set to ±20ppm; the initial range of the clock offset is limited to ±500 microseconds, and the optimized convergence threshold is no greater than 5 microseconds. The initial value of the extrinsic parameter rotation matrix is ​​derived from the installation calibration or the result of the previous window, and the variation between adjacent windows is allowed to be no greater than 0.2 degrees; the initial value of the extrinsic parameter translation is also derived from the installation calibration or the previous window, and the variation between adjacent windows is allowed to be no greater than 0.10 meters. For common-view events, this embodiment stipulates that at least two nodes must participate simultaneously, and each event must contain at least two types of valid measurements (any two of time difference, frequency difference, and angular difference). To ensure robustness, the residual robustness threshold is set based on the root mean square (RMS) of the residuals from the previous window, specifically 3 times the RMS for the time difference channel, 2.5 times the RMS for the angle difference channel, and 3 times the RMS for the frequency difference channel. When the RMS of the time difference residual exceeds 50 microseconds or the RMS of the angle difference residual exceeds 0.5 degrees, a re-initialization mechanism is triggered, the corresponding prior parameters are reset, and the weight of the measurement in that window is reduced.

[0076] In step 300 of this embodiment, for each common-view event, corresponding time residuals, frequency residuals, and angle residuals are first constructed between the participating nodes and the reference node based on the arrival time difference, arrival frequency difference, and line-of-sight angle difference, respectively. Parameters such as clock offset, frequency drift, extrinsic parameter rotation matrix, and extrinsic parameter translation of each node are introduced into the residuals to reflect the relationship between the measured and estimated parameters. A common-view event is defined here as a situation where at least two sub-radars form correlated observations of the same target scatterer within the same sliding window. The above residuals are all weighted according to the event confidence level to reflect the measurement reliability. Furthermore, when there are round-trip time records of transmission and echo between nodes, this embodiment calculates the reception and transmission time difference under a unified time scale and subtracts the theoretical round-trip time determined by the geometric distance between nodes and the electromagnetic wave propagation speed to form a time consistency residual, which is used to enhance the observability of the time parameters.

[0077] In step 300 of this embodiment, to ensure the continuity and stability of the solution, two types of prior constraints are introduced between adjacent sliding windows. One type is the drift continuity prior, which establishes differential residuals for the frequency drift coefficients and clock deviations of the same node, keeping them continuous and bounded between windows, thereby avoiding unreasonable jumps. The other type is the extrinsic parameter smoothing prior, which applies smoothing constraints to the extrinsic parameter rotation matrix and extrinsic parameter translation of the same node in adjacent windows. The extrinsic parameter rotation matrix is ​​parameterized using a unit quaternion or an equivalent rotation matrix, and then a three-dimensional rotation difference vector is obtained through a Lie group logarithmic mapping; the extrinsic parameter translation is calculated by the difference between the translation vectors of adjacent windows to obtain the translation difference. The rotation difference and translation difference are included as residuals in the prior constraints to limit large non-physical changes in the extrinsic parameters within a short period of time.

[0078] In step 300 of this embodiment, to suppress outlier interference caused by abnormal measurements and occlusion effects, a robust loss function with a bounded influence function is uniformly applied to all the aforementioned residuals, including time residuals, frequency residuals, angle residuals, time consistency residuals, drift continuity residuals, extrinsic parameter rotation matrix differences, and extrinsic parameter translation differences. The robust threshold is set according to the root mean square of the residuals of the previous sliding window to ensure that the threshold adapts to changes in the scene. Finally, all weighted and robust residual factors are summarized to form a cross-node constraint set, which serves as the input for subsequent factor graph optimization to synchronously solve for the clock and extrinsic parameter parameters of each node, thereby maintaining a unified time scale and a unified spatial coordinate system.

[0079] In step 400 of this embodiment, the parameters to be estimated output by the previous sliding window are used as the initial state. At this initial state, the first-order sensitivity is calculated item by item for the cross-node constraint set obtained in step 300, and a linear approximation is performed to obtain the "Jacobi matrix" and the "residual vector". The Jacobian matrix is ​​a matrix composed of the first-order partial derivatives of each residual with respect to the corresponding parameter, used to describe the sensitivity of the residual to small changes in the parameter. The residual vector is the set of errors calculated from constraints such as time difference, frequency difference, angle difference, round-trip timing consistency, drift continuity, and extrinsic parameter smoothing. This embodiment also determines the measurement weights based on event confidence and robust influence functions, forming a weighted linear model that is insensitive to abnormal observations.

[0080] In step 400 of this embodiment, a normal equation is constructed based on the linear model described in the previous section, and sparse decomposition is used to solve it. To reduce "filling" (i.e., the addition of non-zero terms during the decomposition process) in numerical computation and improve the solution speed, this embodiment performs elimination in a block order of "time parameters first, followed by spatial extrinsic parameters," while simultaneously performing fill-suppression arrangement on the node order to maintain the sparse structure of the coefficient matrix of the large-scale factor graph. The parameter increments obtained from the solution are used to correct the initial state, thereby obtaining an intermediate state closer to the optimal solution. The aforementioned "normal equation" refers to writing the first-order optimality condition of the weighted least squares objective into the form of a system of linear equations; "sparse decomposition" refers to block decomposition or multi-level decomposition using matrix sparsity.

[0081] In step 400 of this embodiment, an "exponential mapping" is used to update the extrinsic rotation matrix: the small-angle 3D rotation increment is transformed into a finite rotation through the mapping from rotation vector to rotation matrix, and then multiplied by the current pose to complete the update; the extrinsic rotation matrix is ​​renormalized using quaternions or orthogonal matrices to ensure that the numerical values ​​maintain unit length or orthogonality. Time-related parameters and extrinsic translations are updated additively. Convergence is determined using a "double threshold" rule: first, the overall magnitude of the parameter increment is lower than a preset threshold; second, the reduction in weighted residuals is not less than a preset proportion. If either condition is not met, the system is relinearized and enters the next iteration. To avoid individual outlier measurements pulling the solution, this embodiment adaptively adjusts the robust weights according to the residual magnitude after each linearization, and reduces the weights of outliers.

[0082] In step 400 of this embodiment, as the sliding window moves forward, the variables to be removed from the window and their associated measurements are "marginalized." This means that only prior constraints that still apply to the new window are retained through equivalent information compression, while the removed variables are no longer explicitly retained. This ensures the continuity of optimization and controls the problem size. Marginalization can be calculated using Schur complement or equivalent information reduction. Throughout the process, the extrinsic parameters of the reference node remain fixed to maintain a global observability benchmark. After convergence, a unified time-scaled mapping and a set of extrinsic parameters from local coordinates to reference coordinates are formed based on the latest time and space parameters. This unified reference is then used for subsequent coherent processing and multi-base fusion.

[0083] In this embodiment, the sliding window length is preferably set to 1.0–3.0 seconds, the step size to 0.2–0.5 seconds, the maximum number of iterations per optimization cycle is set to 5–15, and the parameter increment convergence threshold is set to no more than 1 × 10⁻⁶. -3 (Angles are measured in degrees, time in microseconds, and distance in meters, and are each independently normalized); the relative reduction threshold for weighted residuals is set to be no less than 10%; sparse decomposition uses a filling suppression arrangement, and time-related parameters are placed in the priority elimination block to reduce the number of newly added non-zero terms, with a typical filling rate not exceeding 20% ​​of the original number of non-zero elements; the orthogonality error of rotation and renormalization is limited to 1×10⁻⁶. -6 Within this range, the quaternion normalized residual is limited to 1×10⁻⁶. -6 Within; when marginalizing, only the priors that are still relevant to the next window are retained, and the number of prior factors introduced in a single marginalization does not exceed 20, in order to control the problem size; the target latency from reading to convergence in a single optimization is controlled within 50 milliseconds (taking a medium-sized network as an example, with 10 to 20 nodes and 50 to 200 active co-visible events).

[0084] In step 500 of this embodiment, the target transmission time under a unified time scale is first mapped to the local trigger time of each node based on the clock parameters obtained from the previous sliding window, thereby adjusting the transmission timing of each node to ensure that the transmission signals remain time-aligned across the entire network. This embodiment further utilizes clock offset and frequency drift parameters to compensate for the local sampling rate and sampling phase, ensuring that the sampling process remains consistent with the unified time scale. When hardware conditions cannot support continuous frequency compensation, equivalent adjustments can be achieved through dynamic correction using a numerically controlled oscillator and resampling processing, thereby ensuring the coherence of the sampling sequence under a globally unified time scale.

[0085] In step 500 of this embodiment, the desired beam direction set in the unified spatial coordinate system is converted into the command direction in the local coordinate system of each node using the extrinsic rotation matrix and extrinsic translation obtained from the previous sliding window. Each node adjusts the weighting or servo control mechanism of the phased array antenna according to the command direction, thereby ensuring that the beam is aligned with the target direction in the unified spatial coordinate system. After the correction is completed, this embodiment uses the first batch of new observation data to perform a consistency check. By comparing whether the residual between the arrival time and the pointing angle exceeds a preset threshold, it is determined whether fine-tuning needs to be triggered. When the residual exceeds the limit, it is automatically fed back to the timing or pointing module for secondary correction to ensure that the beam direction and time reference of the entire network are consistent globally.

[0086] In step 500 of this embodiment, the clock parameters and extrinsic parameters obtained in this window, along with their confidence information, are recorded together and used as prior inputs for the next sliding window to ensure the continuity and stability of the solution process. The confidence information here includes the variance estimates and residual statistics of the parameters, which are used to weight the confidence level of the prior in the next window. In this way, the sliding window can robustly converge using historical results during continuous updates, while ensuring that new observation data remains continuously available under a unified time scale and a unified spatial coordinate system.

[0087] In step 600 of this embodiment, after the optimization solution of the sliding window is completed, the arrival time difference residual, line-of-sight angle difference residual, and normalized residual are statistically analyzed. The root mean square of the arrival time difference residual is used to characterize the time synchronization accuracy, the root mean square of the line-of-sight angle difference residual is used to characterize the spatial registration accuracy, and the chi-square of the normalized residual is used to evaluate the overall goodness of fit. These three indicators are compared with preset thresholds. When any indicator exceeds the corresponding threshold, it is determined that the current constraints are insufficient, observability is defective, and enhancement measures need to be triggered. Here, "observability" refers to the system's ability to independently and stably solve for clock and extrinsic parameters under the current measurement conditions.

[0088] In step 600 of this embodiment, after determining that observability is insufficient, the reference node or central node broadcasts an enhancement command to the entire network. This command explicitly specifies the additional timing tasks and parameter adjustment strategies to be performed, such as specifying additional two-way timing between certain nodes or adjusting the observation modes of some nodes. Upon receiving the enhancement command, each sub-radar node executes the corresponding operation according to a unified scheduling protocol, ensuring that the enhancement process is synchronized and controllable across the entire network.

[0089] In step 600 of this embodiment, under the enhanced instruction, the designated node pair sequentially initiates and receives round-trip timing signals according to the scheduling protocol, and feeds back the timing results to the optimization module. The newly added bidirectional timing measurement provides an independent time constraint equation, which can significantly improve the observability of clock parameters. The round-trip timing measurement is defined as the total delay of the signal propagation between two nodes. This value is directly related to the node clock deviation and spatial geometric distance, and therefore plays a strong constraint role on time parameters in joint optimization.

[0090] In step 600 of this embodiment, to address the problem of insufficient geometric conditions caused by node distribution, some nodes will adjust their transmit power, beam coverage, or transmit pulse scheduling under enhancement commands. Increasing transmit power increases the participation of edge nodes; expanding or changing the beam coverage direction increases the coverage of common-view targets; and reallocating transmit pulse timing reduces observation conflicts and increases the probability of common-view events. These adjustments increase the number of common-view events and make the target angle distribution more balanced, thereby improving the observability of spatial extrinsic parameters.

[0091] In step 600 of this embodiment, all newly added bidirectional timing results and new measurements generated due to parameter adjustments are recorded and incorporated as constraint factors into the optimization process of the next sliding window. These enhanced measurement conditions provide additional independent information in subsequent solutions, thereby improving the robustness of parameter estimation. Through continuous monitoring and triggering, this embodiment can maintain the stability of a unified time scale and a unified spatial coordinate system under dynamic networking, target sparsity, or link quality fluctuations.

[0092] This embodiment further specifies the quantitative range of key parameters when triggering observability enhancement. The root mean square threshold of the arrival time difference residual is preferably set to 20–50 microseconds; exceeding this range indicates insufficient time synchronization. The root mean square threshold of the line-of-sight angle difference residual is preferably set to 0.2–0.5 degrees; exceeding this range indicates a decrease in spatial registration accuracy. The chi-square statistic of the normalized residual is determined at a 95% confidence level; exceeding this level indicates insufficient overall model fitting, requiring enhanced constraints. After triggering enhancement, the additional number of bidirectional timing operations is preferably 2–3 times, with a timing interval set to 10–20 milliseconds to ensure sufficient new measurements are provided without increasing excessive communication burden. The transmit power adjustment range is preferably between 3–6 dB, the beam coverage angle adjustment range is preferably between 5–10 degrees, and the pulse scheduling redistribution ratio does not exceed 20%.

[0093] The beneficial effects of this invention are as follows:

[0094] (i) This invention models clock synchronization and spatial registration as a unified coupled problem. Within the factor graph framework, it simultaneously constrains clock deviation, frequency drift, extrinsic parameter rotation matrix, and extrinsic parameter translation using common-view measurements (time difference of arrival, frequency difference of arrival, and line-of-sight angle difference). This avoids the error propagation and amplification caused by traditional serial calibration that follows either "time first, then space" or "space first, then time." Since time and space parameters serve as priors and correction sources for each other in the same objective function, the inherent consistency of cross-node coherent accumulation, joint ranging and angle measurement, and multi-base fusion is significantly improved.

[0095] (ii) This invention achieves self-consistent solution within a sliding window through common-view measurement and bidirectional timing constraints, without relying on an external absolute time reference or offline extrinsic parameter calibration. Therefore, it can maintain a unified time scale and a unified spatial coordinate system even under conditions of limited external time synchronization, blocked or interfered satellite signals, temporary node disconnections, and frequent topology changes. This "de-dependence on external references" capability significantly enhances the system's continuous operation capability and operational adaptability in denied environments and rapid field deployment scenarios.

[0096] (III) This invention introduces prior knowledge of drift continuity and extrinsic parameter smoothing, and employs incremental sparse nonlinear least squares solution within a sliding window. By setting physically reasonable smoothing and bounded constraints on parameter changes between windows, it suppresses parameter jumps caused by platform maneuvers, target changes, and environmental disturbances, thereby improving the convergence and temporal continuity of the solution. Compared to schemes that rely solely on independent estimation within a single window, this invention can maintain stable solution quality over long periods of operation and reduce the frequency of re-initialization.

[0097] (iv) This invention immediately performs closed-loop correction of the front end after solving: the estimated clock and extrinsic parameters are directly used for online adjustment of the transmission timing, sampling clock, and beam pointing, so that the new measurements are naturally generated under a unified reference frame. This "solution-correction-re-observation" closed loop significantly reduces the lag accumulation of front-end errors due to back-end compensation, improves trajectory continuity, coherent accumulation efficiency, and beamforming gain, and is particularly advantageous for high-speed targets, rapid formations, and temporary node access.

[0098] (v) To address the risk of insufficient observability, this invention establishes an enhancement mechanism triggered by residual statistics (root mean square thresholds for time difference and angle difference, and chi-square threshold for normalized residuals). Once triggered, it automatically increases bidirectional timing and adjusts transmit power, beam coverage, and pulse scheduling to proactively improve geometric conditions and measurement redundancy. This adaptive enhancement avoids unidentifiable parameter coupling and solution divergence caused by poor measurement or geometric degradation, enabling the system to maintain repeatable and convergent unified calibration even when targets are sparse, links fluctuate, or line-of-sight conditions deteriorate.

[0099] (vi) In its engineering implementation, this invention employs sparse decomposition, block elimination, and edge-based prior preservation techniques to achieve near-linear growth in computational complexity with node size. Simultaneously, it balances real-time performance and robustness by using robust loss and confidence-based weighted suppression to mitigate the impact of outlier measurements and non-line-of-sight scattering on the solution. This not only reduces reliance on high-performance hardware and maintenance costs but also provides a generalizable interface and workflow for multi-platform heterogeneous networking, facilitating rapid integration and expansion into existing radar systems.

[0100] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0101] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for integrated clock synchronization and spatial registration for distributed networked radar, characterized in that, include: Acquire local time-stamped echoes and pose data of each sub-radar, perform cross-node correlation within a sliding window based on range, angle, and Doppler consistency, determine common-view events, and calculate common-view measurements, namely time difference of arrival, frequency difference of arrival, and line-of-sight angle difference. Set clock skew, frequency drift, extrinsic rotation matrix and extrinsic translation for each node, and fix the extrinsic parameters of the reference node to eliminate global uncertainty; The common-view measurement forms a cross-node constraint set, which is superimposed with round-trip timing constraints, drift continuity priors and extrinsic parameter smoothing priors, and robust loss is used to suppress outlier measurements. Sparse nonlinear least squares solution is performed on the constraint set within a sliding window to obtain the clock and extrinsic parameters of each node, thereby forming a unified time scale and a unified spatial coordinate system; Based on the clock and extrinsic parameters, the transmission timing, sampling clock and beam pointing are corrected online, and the clock and extrinsic parameters are used as the next window prior. Observability enhancement is triggered when any of the following conditions occur: the root mean square of the arrival time difference residual exceeds a preset first threshold, or the root mean square of the line-of-sight angle difference residual exceeds a preset second threshold, or the chi-square statistic of the normalized residual exceeds a preset third threshold; the observability enhancement includes adding bidirectional timing and adjusting operating parameters. Within a sliding window, a sparse nonlinear least squares solution is performed on the constraint set to obtain the clock and extrinsic parameters of each node, thereby forming a unified time scale and a unified spatial coordinate system, including: The set of parameters to be estimated obtained from the above sliding window As an initial value, all residuals in the constraint set are linearized at the initial value to obtain the Jacobian matrix. With residual vector ;in, This is the frequency drift coefficient. Due to clock skew, For extrinsic rotation matrix, The extrinsic translation vector; Constructing normal equations ,in , Sparse decomposition is performed according to the elimination order of node blocks, prioritizing the elimination time parameter. Further elimination space extraparameter To reduce filler and retain key coupling terms, the increment is obtained. ;in, The coefficient matrix of the normal equation, The right-hand term; The extrinsic parameter rotation matrix is ​​updated using an exponential mapping, and then updated using addition. Convergence is determined based on the preset incremental norm threshold and weighted residual reduction threshold; if convergence fails, the calculation is repeated. Continue iterating; the formula for updating the extrinsic rotation matrix using exponential mapping is: And normalize quaternions or preserve Orthogonality; where, For rotation increment vector, For Li Qun Exponential mapping; When the window slides, the parameters and measurements that are about to be moved out of the window are marginalized, and the prior factors are formed by reducing them using Schur complement or equivalent information and incorporated into the constraint set of the new window; the extrinsic parameters of the reference node are kept fixed to maintain the global observability benchmark; where marginalization means transforming the constraint information of the moved-out variables into prior constraints on the retained variables to ensure the continuity of optimization. After convergence, using the mapping Define a unified time scale, with Define the set of extrinsic parameters from the local coordinate system of each node to the coordinate system of the reference node, as a unified spatial coordinate system. This provides for subsequent coherent processing and multi-site fusion; among which, For local time stamps, To standardize time scales, Let be the extrinsic rotation matrix and translation set of the node.

2. The integrated clock synchronization and spatial registration method for distributed networked radar according to claim 1, characterized in that, The co-observation event is a co-observable event where at least two nodes observe the same scatterer within the same window.

3. The integrated clock synchronization and spatial registration method for distributed networked radar according to claim 1, characterized in that, Acquire local time-stamped echoes and pose data from each sub-radar. Within a sliding window, perform cross-node correlation based on range, angle, and Doppler consistency to determine common-view events and calculate common-view measurements, namely time difference of arrival, frequency difference of arrival, and line-of-sight angle difference, including: Set the sliding window length and step size as preset values, and extract target detection entries containing local time stamps, slant range, line-of-sight angle and Doppler frequency shift, as well as corresponding pose data from the nodes of each sub-radar to form a detection set within the window; Based on the pose data, propagation and motion compensation are performed on each detection item: the propagation time is calculated using the slant range and electromagnetic wave propagation speed, and the arrival time is compensated; the Doppler frequency shift is compensated using the platform radial velocity; and the line-of-sight angle is transformed according to the reference node coordinate system. Thresholds are set for distance, angle, Doppler effect, and arrival time, respectively, and are denoted as distance threshold, angle threshold, Doppler threshold, and time threshold; the thresholds are jointly determined by a preset constant and the estimation result of the previous window. Between the detections of nodes of different sub-radars, candidate association pairs are recorded according to the conditions that the distance difference does not exceed the distance threshold, the angle difference does not exceed the angle threshold, the Doppler difference does not exceed the Doppler threshold, and the arrival time difference does not exceed the time threshold. An undirected graph is constructed with the detection as the vertex and the candidate association pairs as the edges. For the undirected graph, a connected subgraph is extracted. Within each connected subgraph, by minimizing the joint residual consisting of slant range, transformed line-of-sight angle, compensated Doppler and compensated arrival time, a combination consisting of at most one detection for each sub-radar node is selected. When the number of sub-radar nodes included in the combination is not less than two, it is determined to be a co-view event. Within each shared-view event, a reference node is designated, and any participating node calculates the arrival time difference, the arrival frequency difference, and the line-of-sight angle difference relative to the reference node.

4. The integrated clock synchronization and spatial registration method for distributed networked radar according to claim 1, characterized in that, For each node, clock skew, frequency drift, extrinsic rotation matrix, and extrinsic translation are set, while the extrinsic parameters of the reference node are fixed to eliminate global uncertainty, including: The extrinsic rotation matrix of the reference node is set to the identity matrix, and the extrinsic translation vector is set to the zero vector to eliminate global uncertainty in the unified spatial coordinate system; the unified spatial coordinate system is taken as the reference node coordinate system. For each non-reference node i, let the unified time scale be... With local time stamp satisfy ,in This is the frequency drift coefficient. For clock skew; the unified time scale Defined as a common time reference within a sliding window after frequency drift and clock skew compensation; For each node i, let the point coordinates in the unified spatial coordinate system be... with local coordinates satisfy ,in For extrinsic rotation matrix, The extrinsic translation vector; It satisfies the conditions of orthogonality and unit determinant; The arrival time difference, arrival frequency difference, and line-of-sight angle difference measured by co-view measurement are respectively compared with... Establish explicit correlation equations to form a set of parameters to be estimated. and fixed constraints on the extrinsic parameters of the reference nodes.

5. The integrated clock synchronization and spatial registration method for distributed networked radar according to claim 1, characterized in that, A cross-node constraint set is formed using the aforementioned common-view measurements, superimposed with round-trip timing constraints, drift continuity priors, and extrinsic parameter smoothing priors, and robust loss is used to suppress outlier measurements, including: For each shared-view event, between any participating node and the reference node, time residuals, frequency residuals, and angle residuals are constructed using arrival time difference, arrival frequency difference, and line-of-sight angle difference, respectively. Frequency drift coefficients, clock bias, extrinsic rotation matrix, and extrinsic translation vector are substituted into the time residuals, frequency residuals, and angle residuals. The residual weights of the time residuals, frequency residuals, and angle residuals are taken from the confidence level of the shared-view event. When there are round-trip time records of transmission and echo at two nodes, the receiving-transmission time difference is calculated under a unified time scale, and the geometric round-trip time determined by the external parameter translation vector and propagation speed is subtracted to obtain the time consistency residual, which is used to enhance the observability of time parameters. Between adjacent sliding windows, a differential residual is established for the frequency drift coefficient and clock deviation of the same node, so that the frequency drift coefficient and the clock deviation are continuous and bounded in time, thereby limiting the jump between windows; Between adjacent sliding windows, smoothing constraints are established for the extrinsic rotation matrix and extrinsic translation of the same node; the extrinsic rotation matrix is ​​parameterized using a unit quaternion or an equivalent rotation matrix, the logarithmic mapping of the relative rotation is calculated and the three-dimensional vector of the logarithmic mapping is taken as the difference of the extrinsic rotation matrix, and the difference of the extrinsic translation vectors of the two windows is taken as the difference of the extrinsic translation; the difference of the extrinsic rotation matrix and the difference of the extrinsic translation are used as the residuals of the smoothing prior; A robust loss function with a bounded influence function is applied to the time residual, the frequency residual, the angle residual, the time consistency residual, the difference residual, the extrinsic parameter rotation matrix difference, and the extrinsic parameter translation difference, and weighted according to the event confidence and preset weights, and summarized into a constraint set across nodes; the robustness threshold of the robust loss function is set according to the root mean square of the residuals of the previous window.

6. The integrated clock synchronization and spatial registration method for distributed networked radar according to claim 1, characterized in that, Based on the aforementioned clock and extrinsic parameters, online correction of transmission timing, sampling clock, and beam pointing is performed, and the aforementioned clock and extrinsic parameters are used as the next window prior, including: Based on a unified time scale, the local transmission trigger time of each node is mapped and adjusted to ensure that the transmission signals of each node remain consistent under the unified time scale. Compensation is applied to the local sampling rate and sampling phase to keep the sampling process aligned with a unified time scale; when the hardware does not support continuous compensation, equivalent adjustment is achieved through numerically controlled oscillation or resampling. The desired beam direction in the unified spatial coordinate system is converted into the command direction in the local coordinate system, and the phased array weighting or servo control is adjusted according to the command direction to ensure that the beam is correctly aligned in the global coordinate system. After correction, the residuals of arrival time and pointing angle are checked using the first batch of observation data. When they exceed the preset threshold, the corresponding module is triggered to make a fine adjustment again. The clock and extrinsic parameters and confidence information obtained in the current window are recorded as the initial values ​​for the next window to ensure continuity and stability within the sliding window.

7. The integrated clock synchronization and spatial registration method for distributed networked radar according to claim 1, characterized in that, Observability enhancement is triggered when any of the following conditions occur: the root mean square of the arrival time difference residual exceeds a preset first threshold, or the root mean square of the line-of-sight angle difference residual exceeds a preset second threshold, or the chi-square statistic of the normalized residual exceeds a preset third threshold. The observability enhancements include adding two-way timing and adjusting operating parameters, including: After the current sliding window solution is completed, the root mean square of arrival time difference residual, root mean square of line-of-sight angle difference residual, and chi-square statistics of normalized residual are calculated and compared with the corresponding preset thresholds. When any indicator exceeds the threshold, it is determined that the current observability is insufficient. When observability is deemed insufficient, enhancement commands are sent to each node in the network, specifying the need to perform additional timing tasks and parameter adjustment strategies. Under the enhanced command, each node initiates additional round-trip timing operations according to the scheduling protocol and sends back the timing results to increase the number of independent measurements in the constraint equations. In cases of poor line-of-sight geometry, the number of co-view targets can be increased or the angular distribution can be more balanced by adjusting the transmission power of some nodes, the coverage of the working beam, or the transmission pulse scheduling. The newly added round-trip timing results, along with the new measurements generated due to parameter adjustments, are incorporated into the constraint set of the next sliding window as enhanced observation conditions.

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